http://2012.igem.org/wiki/index.php?title=Special:Contributions/Vparasco&feed=atom&limit=50&target=Vparasco&year=&month=2012.igem.org - User contributions [en]2021-03-03T21:35:21ZFrom 2012.igem.orgMediaWiki 1.16.0http://2012.igem.org/File:BsAs2012TrpvHisvv.jpgFile:BsAs2012TrpvHisvv.jpg2012-10-27T03:56:04Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:55:14Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretion rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the secretation rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 350px]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 350px]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 350px]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHisvv.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 600px]]<br />
<br />
[[File:BsAs2012coculture2.jpg| 600px]]</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:54:53Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretion rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the secretation rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 350px]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 350px]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 350px]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 600px]]<br />
<br />
[[File:BsAs2012coculture2.jpg| 600px]]</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/StrainsTeam:Buenos Aires/Results/Strains2012-10-27T03:44:47Z<p>Vparasco: /* Result */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
<br />
<br />
== Description of strains ==<br />
<br />
Through our experiments we worked with the following strains kindly provided by [http://www.ifibyne.fcen.uba.ar/new/temas-de-investigacion/laboratorio-de-fisiologia-y-biologia-molecular-lfbm/biologia-de-sistemas/dr-alejandro-colman-lerner/ Alejandro Colman-Lerner's] Lab: <br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" | Strain ID<br />
! scope="row" style="background: #7ac5e8" |Relevant Auxotrophies<br />
! scope="row" style="background: #7ac5e8" |Fluorescence<br />
! scope="row" style="background: #7ac5e8" |Used as<br />
|-<br />
|TCY 3043<br />
| style="text-align: center;" |(-H-T)<br />
|No fluorescence<br />
|Negative control<br />
|-<br />
|TCY 3190<br />
| style="text-align: center;" |(+H-T)<br />
|YFP + (Induced CFP)<br />
|For coculture<br />
|-<br />
|TCY 3265<br />
| style="text-align: center;" |(-H+T)<br />
|CFP<br />
|For coculture<br />
|-<br />
|TCY 3154<br />
| style="text-align: center;" |(+H+T)<br />
|CFP +(induced YFP)<br />
|Positive Control<br />
|}<br />
| rowspan="2" style="text-align: center;" |<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-figura1.jpg|300px]]<br />
|}<br />
|- valign="top"<br />
|<br />
<br />
In the table we can see Hystidine (H) and Tryptophane (T) auxotrophies per strain, type of fluorescence and description of most common utilization during the experiments.<br />
<br />
Nearly 15 other similar strains were evaluated and discarded due to several reasons (low screening potentiality; requirement of hormones for fluorescence induction; high reverting rate of auxotrophies, among others)<br />
|}<br />
<br />
== Measurement of strains fluorescence ==<br />
<br />
We measured Strains 3281 (YFP) and 3265 (CFP) and got a spectrum of each one prooving that these strains can be distinguished by their fluorescence in culture. <br />
<br />
'''Reference graph'''<br />
Image: YFP and CFP Emission and Absorption Spectra. Obtained from http://flowcyt.salk.edu/fluo.html<br />
<br />
{| style="width: 100%"<br />
| align="center" | [[File:Bsas2012-strains-Refefluro.png|300px]]<br />
|}<br />
<br />
<br />
'''Results'''<br />
<br />
{| style="width: 100%"<br />
| align="center" | [[File:Fluoro- igembsas2012. strains.png|650px]]<br />
|-<br />
|'''CFP Fluorescence Screening and YFP Fluorescence Screening'''<br />
|}<br />
<br />
When measuring YFP Strain 3281, we can see a clear peak around 530 while when measuring CFP Strain 3265, we can see a clear peak around 500, as expected.<br />
<br />
<br />
<br />
'''Discussion'''<br />
<br />
We were able to measure fluorescence in strains 3281 and 3265 using the spectrofluorometer. However, we considered it would not be precise enough for the purposes of measuring cocultures at different proportions. We also noticed a high background noise produced by dead yeast cells at high concentrations, which would make it possible to measure in this way only at a short range of OD while the culture is at exponential phase.<br />
<br />
== Screening of strain proportion ==<br />
<br />
A more precise way of measuring the proportion of the strains, is with a epifluorescence microscope.<br />
<br />
We mixed strains 3281 (expresses YFP) and 3265 (expresses CFP) in different proportions and analized the images obtained in the microscope, where we counted cells with different fluorescences. We also did a negative control with a non fluorescent strain (TCY 379). <br />
<br />
'''Description of Mixtures'''<br />
<br />
Mix 1: Negative Control Mix 2: 80% CFP; 20%YFP Mix 3: 60% CFP; 40%YFP<br />
<br />
Mix 4: 50% CFP; 50%YFP Mix 5: 40% CFP; 60%YFP Mix 6: 20% CFP; 80%YFP<br />
<br />
<br />
'''Results'''<br />
<br />
<br />
<br />
{| style="width: 100%"<br />
| align="center" | [[File:Montage-annotated.jpg|900px]]<br />
|-<br />
| style="text-align: center;" | Mixtures showing YFP and CFP fluorescence. <br />
|}<br />
<br />
<br />
<br />
As shown by images 1-6, cells showing different fluorescences can be count and distinguished from each other in a mixture of strains, and this could be used to measure strains proportion in a coculture. <br />
<br />
<br />
'''Counting of cells'''<br />
<br />
{| class="wikitable"<br />
|-<br />
|Fluorescence<br />
|Mix 1<br />
|Mix 2<br />
|Mix 3<br />
|Mix 4<br />
|Mix 5<br />
|Mix 6<br />
|-<br />
|YFP<br />
|0 <br />
|23 <br />
|67 <br />
|115 <br />
|135 <br />
|110<br />
|-<br />
|CFP<br />
|0* <br />
|235 <br />
|82 <br />
|107 <br />
|99 <br />
|78<br />
|}<br />
<br />
The table shows the number of cells counted by expression of fluorescence YFP and CFP in the different mixtures 1-6. I can be observed that the amount of cells is near the proportion stablished by OD measures when preparing the mixtures. This results confirms that epifluorescence measures are reliable and suitable for our research.<br />
<br />
== Auxotrophy confirmation ==<br />
<br />
<br />
Several times during the experiments we control and checked if the auxotrophies in the selected strain were functional by plating all of them in medium deficient in aminoacids (-H; -T; -H-T and control +H+T). <br />
We observed differential growth according to expected due to the description of each strain in point a)<br />
<br />
{| class="wikitable" <br />
|+ Auxotrophy check<br />
|-<br />
|[[File:Bsas2012-strains-figura3.jpg|100px]]<br />
|[[File:Bsas2012-strains-figura2.png|100px]]<br />
|[[File:Bsas2012-strains-figura4.png|100px]]<br />
|[[File:Bsas2012-strains-figura5.png|100px]]<br />
|-<br />
| style="text-align: center;" | Medium complete<br />
| style="text-align: center;" | Medium without H<br />
| style="text-align: center;" | Medium without T<br />
| style="text-align: center;" | Medium without H and T<br />
|}<br />
<br />
<br />
We observed all the strains grew in the SC plate (top left) and only 3154 (+H+T) grew in the -H-T plate (bottom right). In the -T plate (bottom left), only those strains able to synthesize T grew (3265 and 3154) and in the -H plate (top right) only those able to produce H grew (3190 and 3154), as expected. This means our strains work according to their description. We did this several times during the months to check for reversions or contaminations.<br />
<br />
== Coculture in liquid medium ==<br />
<br />
We used for these experiment TCY3190(H+T-) and TCY3265(H-T+)<br />
Positive control: TCY3154 (H+T+) and negative control TCY3043(H-T-)<br />
<br />
==== At different initial OD and proportions ====<br />
<br />
Cultures were set at different initial concentrations (0.25, 0.1 and 0.01) and proportions (1:1; 1:9; 9:1). After 24 hs, we measured OD with the use of a spectrophotometer (two replicas) and we calculated the mean OD and a Growth factor (as Mean OD en time 1 over Initial OD time 0). <br />
<br />
<br />
{| class="wikitable"<br />
|+ Coculture at different initial OD and proportions (Days 0 and 1)<br />
! scope="row" style="background: #7ac5e8" | Coculture Proportion (H+T-):(H-T+) <br />
! scope="row" style="background: #7ac5e8" |Initial OD(t=0) <br />
! scope="row" style="background: #7ac5e8"|OD1 (t=1) <br />
! scope="row" style="background: #7ac5e8"|OD2 (t=1) <br />
! scope="row" style="background: #7ac5e8"|dilution used for measure t=1 <br />
! scope="row" style="background: #7ac5e8"|Mean OD <br />
! scope="row" style="background: #7ac5e8"|Growth Factor<br />
|-<br />
|01:01 <br />
|0,25 <br />
|0,32 <br />
|0,314 <br />
|10 <br />
|3,17 <br />
|12,68<br />
|-<br />
|09:01 <br />
|0,25 <br />
|0,148 <br />
|0,144 <br />
|10 <br />
|1,46 <br />
|5,84<br />
|-<br />
|01:09 <br />
|0,25 <br />
|0,138 <br />
|0,189 <br />
|10 <br />
|1,635 <br />
|6,54<br />
|-<br />
|01:01 <br />
|0,1 <br />
|0,109 <br />
|0,169 <br />
|10 <br />
|1,39 <br />
|13,9<br />
|-<br />
|09:01 <br />
|0,1 <br />
|0,04 <br />
|0,045 <br />
|10 <br />
|0,425 <br />
|4,25<br />
|-<br />
|01:09 <br />
|0,1 <br />
|0,067 <br />
|0,053 <br />
|10 <br />
|0,6 <br />
|6<br />
|-<br />
|01:01 <br />
|0,01 <br />
|0,067 <br />
|0,061 <br />
|1 <br />
|0,064 <br />
|6,4<br />
|-<br />
|09:01 <br />
|0,01 <br />
|0,056 <br />
|0,05 <br />
|1 <br />
|0,053 <br />
|5,3<br />
|-<br />
|01:09 <br />
|0,01 <br />
|0,074 <br />
|0,073 <br />
|1 <br />
|0,0735 <br />
|7,35<br />
|-<br />
|} <br />
<br />
<br />
{|<br />
|-<br />
|<!--column1-->[[File:HIS-BSAS2012.png|400px]]<br />
|}<br />
<br />
<br />
As shown in graph and table there is a basal growth that does not depend on the initial OD or strain proportion, of a growth factor of 6 approximately.<br />
However we observed a much higher growth at the proportion 1:1 when the initial OD 0.25 and 0.1. Therefore we can assume that at these proportions there is a natural cooperation between the strains and that should be the level of growth that we would like to assess through our bioengineering. Besides we would like to be able in the future to tune the strains in order to be able to obtain in the proportions 9:1 and 1:9 similar results to those obtained in the 1:1, at our own will.<br />
<br />
==== At the same initial OD: 0.2, followed over time ====<br />
<br />
We set the same cultures and cocultures as in point i), but starting all of them at the same OD: 0.2 and we followed them over 2 days. At day 1 we took pictures of them and at day 2 we measured the final OD. <br />
<br />
{| align="center" <br />
|- valign="top"<br />
|<br />
{| class="wikitable"<br />
|+ Cultures set at initial OD: 0.2 and measured over time (Days 0 and 2)<br />
! scope="row" style="background: #7ac5e8"|Strain<br />
! scope="row" style="background: #7ac5e8"|Day 0 <br />
! scope="row" style="background: #7ac5e8"|Day 2<br />
|-<br />
|TCY 3190 (-H+T) <br />
|0,2<br />
|2,92<br />
|-<br />
|TCY 3265 (+H-T) <br />
|0,2<br />
|0,19<br />
|-<br />
|Coculture of strains (TCY 3190- TCY 3265) <br />
|0,2<br />
|2,76<br />
|-<br />
|Negative control (TCY 3043 / -H-T) <br />
|0,2<br />
|0,6<br />
|-<br />
|Positive Control (TCY 3154/ +H+T) <br />
|0,2<br />
|2,54<br />
|}<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-wednesday.png|500px]]<br />
|-<br />
|Picture: Day 1 after starting cultures, shows different OD reached by strains. <br />
|}<br />
<br />
We repeated this experiment 4 times with different modifications: increasing the amount of days for up to a week, measuring every 12 hs instead of every 24 hs and using different strains. However, bacterial contaminations and the high rate of revertants prevented us from getting to a valid results in those cases, whereas the experiment up to day 2 always worked correctly. This denotes that we should assess the problem of contamination (for example including ampicilin in the cultures) and revertant rate (revising the design of the experiment or looking for more stable strains) as the impossibility to go further than day 2 may put limitations to some applications of the Synthetic Community.<br />
|}<br />
<br />
== Coculture in Agar and Revertant mutation control ==<br />
<br />
<br />
Through this experiment we aim to quantify the rate of revertants of each strain, and to asses if cross-feeding between a lawn of cells of one strain and colonies from and other strain is posible. <br />
<br />
We used petri dishes with agar medium with (+) and without (-) Trp and His as shown in the following table.<br />
<br />
We started a culture of each strain in synthetic complete medium, measured its OD 24 hs after the culture initiated, replaced the synthetic complete medium for one lacking both H and T (to avoid residual growth) and plated ~10^6 cells (lawn) or ~10^2 cells (seed) as shown by the following table (we considered OD600=1 represents 3*10^7 cells). <br />
At the same time, 3 controls (one for each strain) were carried in YPD complete medium to check the viability of each strain separately, and to estimate the seed CFU (colony formin units) more precisely. <br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8"|Medium H<br />
! scope="row" style="background: #7ac5e8"|Medium T<br />
! scope="row" style="background: #7ac5e8"|Lawn (10^6 cells) <br />
! scope="row" style="background: #7ac5e8"|Seed (10^2 cells) <br />
! scope="row" style="background: #7ac5e8"|Description of experiment <br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 1<br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 2<br />
|-<br />
|(-) <br />
|(+) <br />
|(-) <br />
|Strain –H+T <br />
|Control of His revertants <br />
|7 <br />
|7<br />
|-<br />
|-<br />
|(+)<br />
|(-)<br />
|(-)<br />
|Strain +H-T <br />
|Control of Trp revertants <br />
|2 <br />
|7<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain +H-T<br />
|Strain –H+T<br />
|Coculture; we expect to see natural cooperation<br />
|960<br />
|800<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain –H+T<br />
|Strain +H-T<br />
|Coculture; we expect to see natural cooperation<br />
|500<br />
|712<br />
|-<br />
|(-)<br />
|(-)<br />
|(-)<br />
|Strain +H+T<br />
|Viability of yeasts in medium<br />
|171<br />
|(-)<br />
|}<br />
<br />
'''Table: Shows description of each plate content and results in number of colonies counted by plate at day 3. YPD control results plates are not shown in the table'''. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-placas2.jpg|300px]]<br />
|<!--column1-->[[File:Bsas2012-strains-placas1.jpg|300px]]<br />
|-<br />
|Petri Dishes<br />
| With marks of the counting of colonies<br />
|}<br />
<br />
<br />
==== Results ====<br />
The viability of the strains was high as expected, as well as the viability of a control positive strain in the –H-T medium. <br />
As shown in the table, we have a low, but existent, number of revertants from both his and trp auxotrophy strains. This number should be taken into account when interpreting the results from coculture growth after several days, given that the rate of revertants in liquid medium is probably the same. <br />
<br />
Growth in coculture was puzzling, as it resulted in more colonies than the expected. If cooperation was effective, we expected to see as many colonies as "seed" cells, not more. Revertion of cells from the "lawn" doesn't explain the number of colonies either. Probably a combination of both these effects are taking place.<br />
<br />
== Measurement of Trp in medium ==<br />
<br />
To check the efectiveness of our biobricks, we must first determine the ammount of tryptophan secreted by natural strains to the medium, so we can compare. With that end in mind, we designed a protocol for measurement of tryptophan in medium, based in its fluorescense at 350nm, when excited with 295nm light.<br />
As a previous step, we checked that none of the other aminoacids used in the medium interferes, by graphically comparing the spectres for uncomplemented medium and medium complemented with leucine, uracile and histidine, at an appropiate range.<br />
<br />
To determine Trp concentration, we must first have a way to transform our readings (intensity) to a more useful output, so we made a calibration curve, through serialized 1:2 dilutions of our medium, which Trp's concentration is 20μg/ml, until approximately constant intensity.<br />
<br />
The procedure to measure secretion rates will be growing the strain from a known OD in exponential growth phase in -T medium and plotting it's OD over time, spin-drying at time=t, retrieving the supernatant's Trp concentration and dividing it by the integral of OD vs. time between time=0 and time=t, so we get to a rate which will be proportional to the number of cells in the culture, which means we can actually compare between different strains. Since our medium is free from Trp, all of it should come from within the cells, and if the culture is growing at exponential rates, lysis should be negligible, so the only explanation would be cells exporting and diffusing their own Trp.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Curva.png | 250px]]<br />
|-<br />
|Graph:Tryptophan calibration curve<br />
|}<br />
<br />
<br />
<br />
==== Results ====<br />
<br />
Through this experiment we can be sure that we would be able to measure increase of Trp in medium as it is exported from the cells, within the biological range of export.<br />
The sensitivity of this method seems to be enough to detect concentrations as low as ~0.01μg/ml, and as high as 20μg/ml, maybe more. Since our medium is 20μg/ml, we assume that's the saturation point of the curve. If we get bigger intensities than the one corresponding to it, we will dilute the sample.<br />
<br />
== Growth dependence on the Trp and His concentrations ==<br />
<br />
A important thing to characterize of the system is the dependence of the growth rate of the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His). To do this we measured the final OD after an overnight growth in medium with different concentrations of Trp and His. <br />
<br />
We used strain ACL-379, that is auxotroph for both Trp and His. <br />
We prepared serial dilutions of SC medium in –T and –H medium, therefore creating two curves: one with decreasing concentrations of Trp and the other with decreasing concentrations of His. <br />
We then inoculated equal amounts of ACL-379 in each tube and incubated them overnight at 30°C with agitation. We took a picture of each tube and measured the OD600 reached by each culture.<br />
<br />
{| class="wikitable"<br />
|+Growth of ACL-379 as a function of Trp and His concentration<br />
! scope="row" style="background: #7ac5e8"|Medium<br />
! scope="row" style="background: #7ac5e8"|OD Replica 1<br />
! scope="row" style="background: #7ac5e8"|OD Replica 2<br />
|-<br />
|SC (no cells)<br />
|0,001<br />
|(-0,0036)<br />
|-<br />
| -T<br />
|(-0,003)<br />
|(-0,019)<br />
|-<br />
| Trp/2<br />
|2.56 <br />
|2.17<br />
|-<br />
| Trp/4<br />
|3.01 <br />
|3.11<br />
|-<br />
|Trp/8<br />
|1.54 <br />
|1.55<br />
|-<br />
|Trp/16<br />
|0.393 <br />
|0.409<br />
|-<br />
|Trp/32<br />
|0.013 <br />
|0.003<br />
|-<br />
| -H<br />
|(-0,008) <br />
|(-0,012)<br />
|-<br />
| His/2 <br />
|3.68 <br />
|3.84<br />
|-<br />
| His/4<br />
|2.07 <br />
|2.00<br />
|-<br />
|His/8<br />
|1.17 <br />
|0.97<br />
|-<br />
|His/16 <br />
|0.47 <br />
|0.432<br />
|-<br />
|His/32 <br />
|0.238 <br />
|0.257<br />
|-<br />
|SC (w/cells) <br />
|4.88 <br />
|4.91<br />
|} <br />
<br />
==== Results ====<br />
As expected the growth has a sigmoidal relationship with the concentration of Trp and His, when plotted in semilogarithmic scale. We call EC50 the effective concentration of each aminoacid at which the culture reaches 50% of the maximal growth. We considered these values as proxies of the Khis and Ktrp parameters of the [[Team:Buenos_Aires/Project/Model#Parameter_selection|mathematical model]], which can be used to estimate the secretion rate of each aminoacid needed to get effective crossfeeding. <br />
<br />
These results can also be observed by comparison of images that show the tubes at different OD. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-alan1.png|250px]]<br />
|<!--column2-->[[File:Bsas2012-strains-ultima.jpg|250px]] <br />
|-<br />
|Images from HLU series<br />
|Images from TLU series<br />
|}<br />
<br />
Notes: <br />
SC: Synthetic complete medium with all the aminoacids. It was used as a blank for the spectrofluorometer.<br />
<br />
HTLU is the culture in the medium with all the required aminoacids.<br />
<br />
<br />
== Experimental determination of strains death rate==<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expected to see a decrease in the number of colonies because of cell death. We found that this was not the case in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a persistant state. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
These results are consistent with the chosen parameters. Moreover, the slower the death rate the bigger the area in the Parameter Space where regulation is feasable.</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTestingTeam:Buenos Aires/Results/SynEcoTesting2012-10-27T03:40:15Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
=SynEco Testing =<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first assay to test whether our system works and how two transformed strains grow together. <br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 700px]]<br />
<br />
=== Coculture in liquid medium ===<br />
<br />
We used for these experiment TCY3190(H+T-) and TCY3265(H-T+)<br />
Positive control: TCY3154 (H+T+) and negative control TCY3043(H-T-)<br />
<br />
==== At different initial OD and proportions ====<br />
<br />
Cultures were set at different initial concentrations (0.25, 0.1 and 0.01) and proportions (1:1; 1:9; 9:1). After 24 hs, we measured OD with the use of a spectrophotometer (two replicas) and we calculated the mean OD and a Growth factor (as Mean OD en time 1 over Initial OD time 0). <br />
<br />
<br />
{| class="wikitable"<br />
|+ Coculture at different initial OD and proportions (Days 0 and 1)<br />
! scope="row" style="background: #7ac5e8" | Coculture Proportion (H+T-):(H-T+) <br />
! scope="row" style="background: #7ac5e8" |Initial OD(t=0) <br />
! scope="row" style="background: #7ac5e8"|OD1 (t=1) <br />
! scope="row" style="background: #7ac5e8"|OD2 (t=1) <br />
! scope="row" style="background: #7ac5e8"|dilution used for measure t=1 <br />
! scope="row" style="background: #7ac5e8"|Mean OD <br />
! scope="row" style="background: #7ac5e8"|Growth Factor<br />
|-<br />
|01:01 <br />
|0,25 <br />
|0,32 <br />
|0,314 <br />
|10 <br />
|3,17 <br />
|12,68<br />
|-<br />
|09:01 <br />
|0,25 <br />
|0,148 <br />
|0,144 <br />
|10 <br />
|1,46 <br />
|5,84<br />
|-<br />
|01:09 <br />
|0,25 <br />
|0,138 <br />
|0,189 <br />
|10 <br />
|1,635 <br />
|6,54<br />
|-<br />
|01:01 <br />
|0,1 <br />
|0,109 <br />
|0,169 <br />
|10 <br />
|1,39 <br />
|13,9<br />
|-<br />
|09:01 <br />
|0,1 <br />
|0,04 <br />
|0,045 <br />
|10 <br />
|0,425 <br />
|4,25<br />
|-<br />
|01:09 <br />
|0,1 <br />
|0,067 <br />
|0,053 <br />
|10 <br />
|0,6 <br />
|6<br />
|-<br />
|01:01 <br />
|0,01 <br />
|0,067 <br />
|0,061 <br />
|1 <br />
|0,064 <br />
|6,4<br />
|-<br />
|09:01 <br />
|0,01 <br />
|0,056 <br />
|0,05 <br />
|1 <br />
|0,053 <br />
|5,3<br />
|-<br />
|01:09 <br />
|0,01 <br />
|0,074 <br />
|0,073 <br />
|1 <br />
|0,0735 <br />
|7,35<br />
|-<br />
|} <br />
<br />
<br />
{|<br />
|-<br />
|<!--column1-->[[File:HIS-BSAS2012.png|400px]]<br />
|}<br />
<br />
<br />
As shown in graph and table there is a basal growth that does not depend on the initial OD or strain proportion, of a growth factor of 6 approximately.<br />
However we observed a much higher growth at the proportion 1:1 when the initial OD 0.25 and 0.1. Therefore we can assume that at these proportions there is a natural cooperation between the strains and that should be the level of growth that we would like to assess through our bioengineering. Besides we would like to be able in the future to tune the strains in order to be able to obtain in the proportions 9:1 and 1:9 similar results to those obtained in the 1:1, at our own will.<br />
<br />
==== At the same initial OD: 0.2, followed over time ====<br />
<br />
We set the same cultures and cocultures as in point i), but starting all of them at the same OD: 0.2 and we followed them over 2 days. At day 1 we took pictures of them and at day 2 we measured the final OD. <br />
<br />
{| align="center" <br />
|- valign="top"<br />
|<br />
{| class="wikitable"<br />
|+ Cultures set at initial OD: 0.2 and measured over time (Days 0 and 2)<br />
! scope="row" style="background: #7ac5e8"|Strain<br />
! scope="row" style="background: #7ac5e8"|Day 0 <br />
! scope="row" style="background: #7ac5e8"|Day 2<br />
|-<br />
|TCY 3190 (-H+T) <br />
|0,2<br />
|2,92<br />
|-<br />
|TCY 3265 (+H-T) <br />
|0,2<br />
|0,19<br />
|-<br />
|Coculture of strains (TCY 3190- TCY 3265) <br />
|0,2<br />
|2,76<br />
|-<br />
|Negative control (TCY 3043 / -H-T) <br />
|0,2<br />
|0,6<br />
|-<br />
|Positive Control (TCY 3154/ +H+T) <br />
|0,2<br />
|2,54<br />
|}<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-wednesday.png|500px]]<br />
|-<br />
|Picture: Day 1 after starting cultures, shows different OD reached by strains. <br />
|}<br />
<br />
We repeated this experiment 4 times with different modifications: increasing the amount of days for up to a week, measuring every 12 hs instead of every 24 hs and using different strains. However, bacterial contaminations and the high rate of revertants prevented us from getting to a valid results in those cases, whereas the experiment up to day 2 always worked correctly. This denotes that we should assess the problem of contamination (for example including ampicilin in the cultures) and revertant rate (revising the design of the experiment or looking for more stable strains) as the impossibility to go further than day 2 may put limitations to some applications of the Synthetic Community.<br />
|}<br />
<br />
<br />
=== Coculture in Agar and Revertant mutation control ===<br />
<br />
<br />
Through this experiment we aim to quantify the rate of revertants of each strain, and to asses if cross-feeding between a lawn of cells of one strain and colonies from and other strain is posible. <br />
<br />
We used petri dishes with agar medium with (+) and without (-) Trp and His as shown in the following table.<br />
<br />
We started a culture of each strain in synthetic complete medium, measured its OD 24 hs after the culture initiated, replaced the synthetic complete medium for one lacking both H and T (to avoid residual growth) and plated ~10^6 cells (lawn) or ~10^2 cells (seed) as shown by the following table (we considered OD600=1 represents 3*10^7 cells). <br />
At the same time, 3 controls (one for each strain) were carried in YPD complete medium to check the viability of each strain separately, and to estimate the seed CFU (colony formin units) more precisely. <br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8"|Medium H<br />
! scope="row" style="background: #7ac5e8"|Medium T<br />
! scope="row" style="background: #7ac5e8"|Lawn (10^6 cells) <br />
! scope="row" style="background: #7ac5e8"|Seed (10^2 cells) <br />
! scope="row" style="background: #7ac5e8"|Description of experiment <br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 1<br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 2<br />
|-<br />
|(-) <br />
|(+) <br />
|(-) <br />
|Strain –H+T <br />
|Control of His revertants <br />
|7 <br />
|7<br />
|-<br />
|-<br />
|(+)<br />
|(-)<br />
|(-)<br />
|Strain +H-T <br />
|Control of Trp revertants <br />
|2 <br />
|7<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain +H-T<br />
|Strain –H+T<br />
|Coculture; we expect to see natural cooperation<br />
|960<br />
|800<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain –H+T<br />
|Strain +H-T<br />
|Coculture; we expect to see natural cooperation<br />
|500<br />
|712<br />
|-<br />
|(-)<br />
|(-)<br />
|(-)<br />
|Strain +H+T<br />
|Viability of yeasts in medium<br />
|171<br />
|(-)<br />
|}<br />
<br />
'''Table: Shows description of each plate content and results in number of colonies counted by plate at day 3. YPD control results plates are not shown in the table'''. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-placas2.jpg|300px]]<br />
|<!--column1-->[[File:Bsas2012-strains-placas1.jpg|300px]]<br />
|-<br />
|Petri Dishes<br />
| With marks of the counting of colonies<br />
|}<br />
<br />
<br />
==== Results ====<br />
The viability of the strains was high as expected, as well as the viability of a control positive strain in the –H-T medium. <br />
As shown in the table, we have a low, but existent, number of revertants from both his and trp auxotrophy strains. This number should be taken into account when interpreting the results from coculture growth after several days, given that the rate of revertants in liquid medium is probably the same. <br />
<br />
Growth in coculture was puzzling, as it resulted in more colonies than the expected. If cooperation was effective, we expected to see as many colonies as "seed" cells, not more. Revertion of cells from the "lawn" doesn't explain the number of colonies either. Probably a combination of both these effects are taking place.</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTestingTeam:Buenos Aires/Results/SynEcoTesting2012-10-27T03:38:14Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
=SynEco Testing =<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 600px]]<br />
<br />
[[File:BsAs2012coculture2.jpg| 600px]]<br />
<br />
=== Coculture in liquid medium ===<br />
<br />
We used for these experiment TCY3190(H+T-) and TCY3265(H-T+)<br />
Positive control: TCY3154 (H+T+) and negative control TCY3043(H-T-)<br />
<br />
==== At different initial OD and proportions ====<br />
<br />
Cultures were set at different initial concentrations (0.25, 0.1 and 0.01) and proportions (1:1; 1:9; 9:1). After 24 hs, we measured OD with the use of a spectrophotometer (two replicas) and we calculated the mean OD and a Growth factor (as Mean OD en time 1 over Initial OD time 0). <br />
<br />
<br />
{| class="wikitable"<br />
|+ Coculture at different initial OD and proportions (Days 0 and 1)<br />
! scope="row" style="background: #7ac5e8" | Coculture Proportion (H+T-):(H-T+) <br />
! scope="row" style="background: #7ac5e8" |Initial OD(t=0) <br />
! scope="row" style="background: #7ac5e8"|OD1 (t=1) <br />
! scope="row" style="background: #7ac5e8"|OD2 (t=1) <br />
! scope="row" style="background: #7ac5e8"|dilution used for measure t=1 <br />
! scope="row" style="background: #7ac5e8"|Mean OD <br />
! scope="row" style="background: #7ac5e8"|Growth Factor<br />
|-<br />
|01:01 <br />
|0,25 <br />
|0,32 <br />
|0,314 <br />
|10 <br />
|3,17 <br />
|12,68<br />
|-<br />
|09:01 <br />
|0,25 <br />
|0,148 <br />
|0,144 <br />
|10 <br />
|1,46 <br />
|5,84<br />
|-<br />
|01:09 <br />
|0,25 <br />
|0,138 <br />
|0,189 <br />
|10 <br />
|1,635 <br />
|6,54<br />
|-<br />
|01:01 <br />
|0,1 <br />
|0,109 <br />
|0,169 <br />
|10 <br />
|1,39 <br />
|13,9<br />
|-<br />
|09:01 <br />
|0,1 <br />
|0,04 <br />
|0,045 <br />
|10 <br />
|0,425 <br />
|4,25<br />
|-<br />
|01:09 <br />
|0,1 <br />
|0,067 <br />
|0,053 <br />
|10 <br />
|0,6 <br />
|6<br />
|-<br />
|01:01 <br />
|0,01 <br />
|0,067 <br />
|0,061 <br />
|1 <br />
|0,064 <br />
|6,4<br />
|-<br />
|09:01 <br />
|0,01 <br />
|0,056 <br />
|0,05 <br />
|1 <br />
|0,053 <br />
|5,3<br />
|-<br />
|01:09 <br />
|0,01 <br />
|0,074 <br />
|0,073 <br />
|1 <br />
|0,0735 <br />
|7,35<br />
|-<br />
|} <br />
<br />
<br />
{|<br />
|-<br />
|<!--column1-->[[File:HIS-BSAS2012.png|400px]]<br />
|}<br />
<br />
<br />
As shown in graph and table there is a basal growth that does not depend on the initial OD or strain proportion, of a growth factor of 6 approximately.<br />
However we observed a much higher growth at the proportion 1:1 when the initial OD 0.25 and 0.1. Therefore we can assume that at these proportions there is a natural cooperation between the strains and that should be the level of growth that we would like to assess through our bioengineering. Besides we would like to be able in the future to tune the strains in order to be able to obtain in the proportions 9:1 and 1:9 similar results to those obtained in the 1:1, at our own will.<br />
<br />
==== At the same initial OD: 0.2, followed over time ====<br />
<br />
We set the same cultures and cocultures as in point i), but starting all of them at the same OD: 0.2 and we followed them over 2 days. At day 1 we took pictures of them and at day 2 we measured the final OD. <br />
<br />
{| align="center" <br />
|- valign="top"<br />
|<br />
{| class="wikitable"<br />
|+ Cultures set at initial OD: 0.2 and measured over time (Days 0 and 2)<br />
! scope="row" style="background: #7ac5e8"|Strain<br />
! scope="row" style="background: #7ac5e8"|Day 0 <br />
! scope="row" style="background: #7ac5e8"|Day 2<br />
|-<br />
|TCY 3190 (-H+T) <br />
|0,2<br />
|2,92<br />
|-<br />
|TCY 3265 (+H-T) <br />
|0,2<br />
|0,19<br />
|-<br />
|Coculture of strains (TCY 3190- TCY 3265) <br />
|0,2<br />
|2,76<br />
|-<br />
|Negative control (TCY 3043 / -H-T) <br />
|0,2<br />
|0,6<br />
|-<br />
|Positive Control (TCY 3154/ +H+T) <br />
|0,2<br />
|2,54<br />
|}<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-wednesday.png|500px]]<br />
|-<br />
|Picture: Day 1 after starting cultures, shows different OD reached by strains. <br />
|}<br />
<br />
We repeated this experiment 4 times with different modifications: increasing the amount of days for up to a week, measuring every 12 hs instead of every 24 hs and using different strains. However, bacterial contaminations and the high rate of revertants prevented us from getting to a valid results in those cases, whereas the experiment up to day 2 always worked correctly. This denotes that we should assess the problem of contamination (for example including ampicilin in the cultures) and revertant rate (revising the design of the experiment or looking for more stable strains) as the impossibility to go further than day 2 may put limitations to some applications of the Synthetic Community.<br />
|}<br />
<br />
<br />
=== Coculture in Agar and Revertant mutation control ===<br />
<br />
<br />
Through this experiment we aim to quantify the rate of revertants of each strain, and to asses if cross-feeding between a lawn of cells of one strain and colonies from and other strain is posible. <br />
<br />
We used petri dishes with agar medium with (+) and without (-) Trp and His as shown in the following table.<br />
<br />
We started a culture of each strain in synthetic complete medium, measured its OD 24 hs after the culture initiated, replaced the synthetic complete medium for one lacking both H and T (to avoid residual growth) and plated ~10^6 cells (lawn) or ~10^2 cells (seed) as shown by the following table (we considered OD600=1 represents 3*10^7 cells). <br />
At the same time, 3 controls (one for each strain) were carried in YPD complete medium to check the viability of each strain separately, and to estimate the seed CFU (colony formin units) more precisely. <br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8"|Medium H<br />
! scope="row" style="background: #7ac5e8"|Medium T<br />
! scope="row" style="background: #7ac5e8"|Lawn (10^6 cells) <br />
! scope="row" style="background: #7ac5e8"|Seed (10^2 cells) <br />
! scope="row" style="background: #7ac5e8"|Description of experiment <br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 1<br />
! scope="row" style="background: #7ac5e8"|Results after 3 days - Replica 2<br />
|-<br />
|(-) <br />
|(+) <br />
|(-) <br />
|Strain –H+T <br />
|Control of His revertants <br />
|7 <br />
|7<br />
|-<br />
|-<br />
|(+)<br />
|(-)<br />
|(-)<br />
|Strain +H-T <br />
|Control of Trp revertants <br />
|2 <br />
|7<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain +H-T<br />
|Strain –H+T<br />
|Coculture; we expect to see natural cooperation<br />
|960<br />
|800<br />
|-<br />
|(-)<br />
|(-)<br />
|Strain –H+T<br />
|Strain +H-T<br />
|Coculture; we expect to see natural cooperation<br />
|500<br />
|712<br />
|-<br />
|(-)<br />
|(-)<br />
|(-)<br />
|Strain +H+T<br />
|Viability of yeasts in medium<br />
|171<br />
|(-)<br />
|}<br />
<br />
'''Table: Shows description of each plate content and results in number of colonies counted by plate at day 3. YPD control results plates are not shown in the table'''. <br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Bsas2012-strains-placas2.jpg|300px]]<br />
|<!--column1-->[[File:Bsas2012-strains-placas1.jpg|300px]]<br />
|-<br />
|Petri Dishes<br />
| With marks of the counting of colonies<br />
|}<br />
<br />
<br />
==== Results ====<br />
The viability of the strains was high as expected, as well as the viability of a control positive strain in the –H-T medium. <br />
As shown in the table, we have a low, but existent, number of revertants from both his and trp auxotrophy strains. This number should be taken into account when interpreting the results from coculture growth after several days, given that the rate of revertants in liquid medium is probably the same. <br />
<br />
Growth in coculture was puzzling, as it resulted in more colonies than the expected. If cooperation was effective, we expected to see as many colonies as "seed" cells, not more. Revertion of cells from the "lawn" doesn't explain the number of colonies either. Probably a combination of both these effects are taking place.</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:36:58Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the secretation rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 350px]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 350px]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 350px]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
[[File: BsAs2012Trpratio.jpg|350px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 600px]]<br />
<br />
[[File:BsAs2012coculture2.jpg| 600px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012coculture2.jpgFile:BsAs2012coculture2.jpg2012-10-27T03:36:10Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:35:48Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
[[File: BsAs2012Trpratio.jpg|350px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg | 600px]]<br />
<br />
[[File:BsAs2012coculture2.jpg| 600px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012coculture1.jpgFile:BsAs2012coculture1.jpg2012-10-27T03:34:25Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:33:00Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
[[File: BsAs2012Trpratio.jpg|350px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====<br />
<br />
[[File:BsAs2012coculture1.jpg]]<br />
<br />
[[File:BsAs2012coculture2.jpg]]</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T03:31:51Z<p>Vparasco: /* Protocol */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
<br />
DEVICE TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/DevicesTesting<br />
<br />
<br />
SYNECO TESTING<br />
<br />
http://2012.igem.org/Team:Buenos_Aires/Results/SynEcoTesting<br />
<br />
<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
[[File: BsAs2012Trpratio.jpg|350px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-YFP.jpg|200px]]<br />
|[[File:BsAs2012-icono-CFP.jpg|200px]]<br />
|- align="center"<br />
|YFP Strain<br />
|CFP Strain<br />
|}<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
[[File:Bsas2012kdeathcells.png| 500px]]<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably this would require more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-CFP-202.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|CFP_His<br />
|YFP_TRPb<br />
|}<br />
<br />
<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/DevicesTestingTeam:Buenos Aires/Results/DevicesTesting2012-10-27T03:28:37Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
<br />
= Devices testing =<br />
<br />
== Experimental Setup ==<br />
<br />
=== Plasmids and BBs ===<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Cloning protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
=== Yeast strains ===<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
=== Final transformed strains ===<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
<br />
<br />
== Secretion Rate of Trp as a function of culture growth ==<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 250px]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 250px]]<br />
|}<br />
Figure1. check<br />
<br />
[[File:BsAs2012rate2.jpg| 450px]]<br />
<br />
Figure2. check<br />
<br />
== Tryptophan secretion at increasing histidine concentrations ==<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis1.jpg|350px]]<br />
<br />
FigureX.<br />
<br />
== Measurement of Trp in medium and Basal Production ==<br />
<br />
To check the efectiveness of our biobricks, we must first determine the ammount of tryptophan secreted by natural strains to the medium, so we can compare. With that end in mind, we designed a protocol for measurement of tryptophan in medium, based in its fluorescense at 350nm, when excited with 295nm light.<br />
As a previous step, we checked that none of the other aminoacids used in the medium interferes, by graphically comparing the spectres for uncomplemented medium and medium complemented with leucine, uracile and histidine, at an appropiate range.<br />
<br />
To determine Trp concentration, we must first have a way to transform our readings (intensity) to a more useful output, so we made a calibration curve, through serialized 1:2 dilutions of our medium, which Trp's concentration is 50mg/mL, until approximately constant intensity.<br />
<br />
The procedure to measure secretion rates will be growing the strain from a known OD in exponential growth phase in -T medium and plotting it's OD over time, spin-drying at time=t, retrieving the supernatant's Trp concentration and dividing it by the integral of OD vs. time between time=0 and time=t, so we get to a rate which will be proportional to the number of cells in the culture, which means we can actually compare between different strains. Since our medium is free from Trp, all of it should come from within the cells, and if the culture is growing at exponential rates, lysis should be negligible, so the only explanation would be cells exporting their own Trp.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Trp-bsas2012.png | 250px]]<br />
|-<br />
|Graph:Tryptophan calibration curve<br />
|}<br />
<br />
<br />
<br />
==== Results ====<br />
<br />
As can be seen from the graph the screening of the concentration of the Trp in medium describes an almost lineal function. Through this experiment we can be sure that we would be able to measure increase of Trp in medium as it is exported from the cells, within the biological range of export.<br />
The sensitivity of this method seems to be enough to detect concentrations as low as ~0.02mg/mL, and as high as 50mg/mL, maybe more. Since our medium is 50mg/mL, we assume that's the saturation point of the curve. If we get bigger intensities than the one corresponding to it, we will dilute the sample.<br />
<br />
Because of time constraints, we haven't been able to check the method with either our designed strains nor the non-exporting ones.</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/DevicesTestingTeam:Buenos Aires/Results/DevicesTesting2012-10-27T03:27:51Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
<br />
= Devices testing =<br />
<br />
== Experimental Setup ==<br />
<br />
=== Plasmids and BBs ===<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Cloning protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
=== Yeast strains ===<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
=== Final transformed strains ===<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
<br />
<br />
== Secretion Rate of Trp as a function of culture growth ==<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 250px]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 250px]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 250px]]<br />
<br />
Figure X. check<br />
<br />
== Tryptophan secretion at increasing histidine concentrations ==<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis1.jpg|350px]]<br />
<br />
FigureX.<br />
<br />
== Measurement of Trp in medium and Basal Production ==<br />
<br />
To check the efectiveness of our biobricks, we must first determine the ammount of tryptophan secreted by natural strains to the medium, so we can compare. With that end in mind, we designed a protocol for measurement of tryptophan in medium, based in its fluorescense at 350nm, when excited with 295nm light.<br />
As a previous step, we checked that none of the other aminoacids used in the medium interferes, by graphically comparing the spectres for uncomplemented medium and medium complemented with leucine, uracile and histidine, at an appropiate range.<br />
<br />
To determine Trp concentration, we must first have a way to transform our readings (intensity) to a more useful output, so we made a calibration curve, through serialized 1:2 dilutions of our medium, which Trp's concentration is 50mg/mL, until approximately constant intensity.<br />
<br />
The procedure to measure secretion rates will be growing the strain from a known OD in exponential growth phase in -T medium and plotting it's OD over time, spin-drying at time=t, retrieving the supernatant's Trp concentration and dividing it by the integral of OD vs. time between time=0 and time=t, so we get to a rate which will be proportional to the number of cells in the culture, which means we can actually compare between different strains. Since our medium is free from Trp, all of it should come from within the cells, and if the culture is growing at exponential rates, lysis should be negligible, so the only explanation would be cells exporting their own Trp.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Trp-bsas2012.png | 250px]]<br />
|-<br />
|Graph:Tryptophan calibration curve<br />
|}<br />
<br />
<br />
<br />
==== Results ====<br />
<br />
As can be seen from the graph the screening of the concentration of the Trp in medium describes an almost lineal function. Through this experiment we can be sure that we would be able to measure increase of Trp in medium as it is exported from the cells, within the biological range of export.<br />
The sensitivity of this method seems to be enough to detect concentrations as low as ~0.02mg/mL, and as high as 50mg/mL, maybe more. Since our medium is 50mg/mL, we assume that's the saturation point of the curve. If we get bigger intensities than the one corresponding to it, we will dilute the sample.<br />
<br />
Because of time constraints, we haven't been able to check the method with either our designed strains nor the non-exporting ones.</div>Vparascohttp://2012.igem.org/File:BsAs2012TrpvHis1.jpgFile:BsAs2012TrpvHis1.jpg2012-10-27T03:26:26Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/DevicesTestingTeam:Buenos Aires/Results/DevicesTesting2012-10-27T03:26:06Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
<br />
= Devices testing =<br />
<br />
== Experimental Setup ==<br />
<br />
=== Plasmids and BBs ===<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Cloning protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
=== Yeast strains ===<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
=== Final transformed strains ===<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
<br />
<br />
== Secretion Rate of Trp as a function of culture growth ==<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
== Tryptophan secretion at increasing histidine concentrations ==<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis1.jpg|350px]]<br />
<br />
FigureX.<br />
<br />
== Measurement of Trp in medium and Basal Production ==<br />
<br />
To check the efectiveness of our biobricks, we must first determine the ammount of tryptophan secreted by natural strains to the medium, so we can compare. With that end in mind, we designed a protocol for measurement of tryptophan in medium, based in its fluorescense at 350nm, when excited with 295nm light.<br />
As a previous step, we checked that none of the other aminoacids used in the medium interferes, by graphically comparing the spectres for uncomplemented medium and medium complemented with leucine, uracile and histidine, at an appropiate range.<br />
<br />
To determine Trp concentration, we must first have a way to transform our readings (intensity) to a more useful output, so we made a calibration curve, through serialized 1:2 dilutions of our medium, which Trp's concentration is 50mg/mL, until approximately constant intensity.<br />
<br />
The procedure to measure secretion rates will be growing the strain from a known OD in exponential growth phase in -T medium and plotting it's OD over time, spin-drying at time=t, retrieving the supernatant's Trp concentration and dividing it by the integral of OD vs. time between time=0 and time=t, so we get to a rate which will be proportional to the number of cells in the culture, which means we can actually compare between different strains. Since our medium is free from Trp, all of it should come from within the cells, and if the culture is growing at exponential rates, lysis should be negligible, so the only explanation would be cells exporting their own Trp.<br />
<br />
<br />
{| class="wikitable" border="1"<br />
|-<br />
|<!--column1-->[[File:Trp-bsas2012.png | 250px]]<br />
|-<br />
|Graph:Tryptophan calibration curve<br />
|}<br />
<br />
<br />
<br />
==== Results ====<br />
<br />
As can be seen from the graph the screening of the concentration of the Trp in medium describes an almost lineal function. Through this experiment we can be sure that we would be able to measure increase of Trp in medium as it is exported from the cells, within the biological range of export.<br />
The sensitivity of this method seems to be enough to detect concentrations as low as ~0.02mg/mL, and as high as 50mg/mL, maybe more. Since our medium is 50mg/mL, we assume that's the saturation point of the curve. If we get bigger intensities than the one corresponding to it, we will dilute the sample.<br />
<br />
Because of time constraints, we haven't been able to check the method with either our designed strains nor the non-exporting ones.</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:43:43Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|550px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|350px]]<br />
|<br />
|-<br />
|<br />
|<br />
[[File:BsAs2012diapv.jpg|350px]]<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the slowest strain's third cell division as a lag time.<br />
<br />
The unit of the color scale is hours, it's clear than for lower initial concentrations and export rates<br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/File:BsAs2012diapv.jpgFile:BsAs2012diapv.jpg2012-10-27T02:27:14Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:26:53Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
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[[File:BsAs2012diapiii.jpg|200px]]<br />
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|-<br />
|<br />
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[[File:BsAs2012diapv.jpg|600px]]<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the slowest strain's third cell division as a lag time.<br />
<br />
The unit of the color scale is hours, it's clear than for lower initial concentrations and export rates<br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:21:31Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|<br />
|-<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the slowest strain's third cell division as a lag time.<br />
<br />
The unit of the color scale is hours, it's clear than for lower initial concentrations and export rates<br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:20:54Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
{|<br />
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[[File:BsAs2012diapi.jpg|450px]]<br />
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[[File:BsAs2012diapii.jpg|350px]]<br />
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[[File:BsAs2012diapiii.jpg|200px]]<br />
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[[File:BsAs2012diap2.jpg|600px]]<br />
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[[File:BsAs2012diap2.jpg|600px]]<br />
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<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the slowest strain's third cell division as a lag time.<br />
<br />
The unit of the color scale is hours, it's clear than for lower initial concentrations and export rates<br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/File:BsAs2012Trpratio.jpgFile:BsAs2012Trpratio.jpg2012-10-27T02:19:07Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T02:18:28Z<p>Vparasco: /* Results */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our project as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-182.jpg | 200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
===== Protocol =====<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the aminoacid secreted by the device and the one diffused. <br />
<br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
===== Results =====<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine whether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa4.jpg|200px]]<br />
|[[File:BsAs2012-icono-YFP-185.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb (control)<br />
|}<br />
<br />
<br />
<br />
<br />
<br />
<br />
<br />
===== Protocol =====<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
===== Results =====<br />
<br />
[[File: BsAs2012TrpvHis.jpg|350px]]<br />
<br />
[[File: BsAs2012Trpratio.jpg|350px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|350px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
===== Protocol =====<br />
<br />
For this experiment we used<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
[[File:BsAs2012-icono-CFP.jpg | 200px]]<br />
<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
===== Result =====<br />
<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done with our strains soon.<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:17:31Z<p>Vparasco: /* Lag Time */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
|-<br />
|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the slowest strain's third cell division as a lag time.<br />
<br />
The unit of the color scale is hours, it's clear than for lower initial concentrations and export rates<br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/File:BsAs2012_11LagK.jpg.jpgFile:BsAs2012 11LagK.jpg.jpg2012-10-27T02:04:35Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T02:03:50Z<p>Vparasco: /* Lag Time */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
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[[File:BsAs2012diapi.jpg|450px]]<br />
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[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
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|explic<br />
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<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the Third cycle as a Standard, <br />
|<br />
[[File:BsAs2012_11LagK.jpg.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/File:BsAs2012_11LagK.jpgFile:BsAs2012 11LagK.jpg2012-10-27T02:03:09Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/File:BsAs2012LagK.jpgFile:BsAs2012LagK.jpg2012-10-27T02:02:22Z<p>Vparasco: uploaded a new version of &quot;File:BsAs2012LagK.jpg&quot;</p>
<hr />
<div></div>Vparascohttp://2012.igem.org/File:BsAs2012LagK.jpgFile:BsAs2012LagK.jpg2012-10-27T01:59:02Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:58:12Z<p>Vparasco: /* Tryptophan secretion at increasing histidine concentrations */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa6.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa5.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
[[File:BsAs2012-icono-Cepa3.jpg| 100px]]<br />
<br />
- YFP_TRPb_PolyWb<br />
[[File:BsAs2012-icono-Cepa4.jpg| 100px]]<br />
<br />
- YFP_TRPb (control)<br />
[[File:BsAs2012-icono-YFP-185.jpg| 100px]]<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg|450px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|450px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
For this experiment we used<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
[[File:BsAs2012-icono-CFP.jpg | 200px]]<br />
<br />
<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:57:48Z<p>Vparasco: /* Tryptophan secretion at increasing histidine concentrations */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa6.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa5.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
[[File:BsAs2012-icono-Cepa3.jpg| 100px]]<br />
<br />
- YFP_TRPb_PolyWb<br />
[[File:BsAs2012-icono-Cepa4.jpg| 100px]]<br />
<br />
- YFP_TRPb (control)<br />
[[File:BsAs2012-icono-YFP-185.jpg| 100px]]<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg|250px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|250px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
For this experiment we used<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
[[File:BsAs2012-icono-CFP.jpg | 200px]]<br />
<br />
<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:57:22Z<p>Vparasco: /* Tryptophan secretion at increasing histidine concentrations */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
<br />
{|<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa3.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPb_TRPZipper2<br />
|YFP_TRPb_PolyWb<br />
|YFP_TRPb<br />
|}<br />
| rowspan="2" |<br />
{|<br />
| [[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
|- align="center"<br />
|YFP<br />
|}<br />
<br />
|-<br />
|<br />
{|<br />
|-<br />
|[[File:BsAs2012-icono-Cepa6.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa5.jpg|200px]]<br />
|[[File:BsAs2012-icono-Cepa2.jpg|200px]]<br />
|- align="center"<br />
|YFP_TRPa_TRPZipper2<br />
|YFP_TRPa_PolyWb<br />
|YFP_TRPa<br />
|}<br />
<br />
|}<br />
<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
[[File:BsAs2012-icono-Cepa3.jpg| 100px]]<br />
<br />
- YFP_TRPb_PolyWb<br />
[[File:BsAs2012-icono-Cepa4.jpg| 100px]]<br />
<br />
- YFP_TRPb (control)<br />
[[File:BsAs2012-icono-YFP-185.jpg| 100px]]<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg|50px]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg|50px]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
For this experiment we used<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
[[File:BsAs2012-icono-CFP.jpg | 200px]]<br />
<br />
<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/File:BsAs2012Odvstimeab.jpgFile:BsAs2012Odvstimeab.jpg2012-10-27T01:56:05Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:55:26Z<p>Vparasco: /* Secretion Rate of Trp as a function of culture growth */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
|Strain<br />
|Name<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|300px]]<br />
|YFP_TRPb_TRPZipper2<br />
|-<br />
|[[File:BsAs2012-icono-Cepa2.jpg|300px]]<br />
|YFP_TRPb_PolyWb<br />
|-<br />
|[[ |300px]]<br />
|YFP_TRPb<br />
|-<br />
|<br />
|YFP_TRPa_TRPZipper2<br />
|-<br />
|[[File:BsAs2012-icono-Cepa2.jpg|300px]]<br />
|YFP_TRPa_PolyWb<br />
|-<br />
|<br />
|YFP_TRPa<br />
|}<br />
<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimeab.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
[[File:BsAs2012-icono-Cepa3.jpg| 100px]]<br />
<br />
- YFP_TRPb_PolyWb<br />
[[File:BsAs2012-icono-Cepa4.jpg| 100px]]<br />
<br />
- YFP_TRPb (control)<br />
[[File:BsAs2012-icono-YFP-185.jpg| 100px]]<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/File:BsAs2012Odvstimea4.jpgFile:BsAs2012Odvstimea4.jpg2012-10-27T01:54:42Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:54:08Z<p>Vparasco: /* Secretion Rate of Trp as a function of culture growth */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPa_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_TRPZipper2'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''YFP_TRPb_PoliWb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM185 (TRPb) + <partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|}<br />
|}<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHa'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792009</partinfo> (PoliHa)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| '''CFP_HIS_PoliHb'''<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3128 (CFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pEG202 (HIS) + <partinfo>BBa_K792011</partinfo> (PoliHb)<br />
|}<br />
|}<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
[[File:BsAs2012-icono-YFP.jpg | 200px]]<br />
<br />
<br />
{| class="wikitable"<br />
|-<br />
|Strain<br />
|Name<br />
|-<br />
|[[File:BsAs2012-icono-Cepa1.jpg|300px]]<br />
|YFP_TRPb_TRPZipper2<br />
|-<br />
|[[File:BsAs2012-icono-Cepa2.jpg|300px]]<br />
|YFP_TRPb_PolyWb<br />
|-<br />
|[[ |300px]]<br />
|YFP_TRPb<br />
|-<br />
|<br />
|YFP_TRPa_TRPZipper2<br />
|-<br />
|[[File:BsAs2012-icono-Cepa2.jpg|300px]]<br />
|YFP_TRPa_PolyWb<br />
|-<br />
|<br />
|YFP_TRPa<br />
|}<br />
<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
{|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|<br />
[[File:BsAs2012Odvstimea4.jpg | 150]]<br />
|}<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
[[File:BsAs2012-icono-Cepa3.jpg| 100px]]<br />
<br />
- YFP_TRPb_PolyWb<br />
[[File:BsAs2012-icono-Cepa4.jpg| 100px]]<br />
<br />
- YFP_TRPb (control)<br />
[[File:BsAs2012-icono-YFP-185.jpg| 100px]]<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
FOTOS DE LAS PLACAS AQUIIII!<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. In this way cells can survive for a period of time in media defficient in amino acid (at least, during the time course of our experiment), but grow slower. Probably it would requires more time than 3 days to observe significative cell dying.<br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
[[File:BsAs2012-icono-CFP-202.jpg | 200px]]<br />
<br />
[[File:BsAs2012-icono-YFP-185.jpg | 200px]]<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T01:53:02Z<p>Vparasco: /* Lag Time */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
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[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
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= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we deviced a way to facilitate absortion. <br />
We decided to work with<br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|-<br />
|This lag time was quantified using the Third cycle as a Standard, <br />
|<br />
[[File:lagK.jpg|350px]]<br />
|<br />
|}</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:18:02Z<p>Vparasco: /* Secretion Rate of Trp as a function of culture growth */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
<br />
DOS<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
TRES<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
TCY3081 (YFP) TCY3128 (CFP) Strain Name<br />
pCM182 (TRPa) + BBa_K792010 (TRPZipper2) X YFP_TRPa_TRPZipper2<br />
pCM182 (TRPa) + BBa_K792012 (PoliWb) X YFP_TRPa_PoliWb<br />
pCM185 (TRPb) + BBa_K792010 (TRPZipper2) X YFP_TRPb_TRPZipper2<br />
pCM185 (TRPb) + BBa_K792012 (PoliWb) X YFP_TRPb_PoliWb<br />
pEG202 (HIS) + BBa_K792009 (PoliHa) X CFP_HIS_PoliHa<br />
pEG202 (HIS) + BBa_K792011 (PoliHb) X CFP_HIS_PoliHb<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. <br />
Therefore the secretion rates calculated will be higher than the actual ones. We used an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
[[File:BsAs2012Odvstime4.jpg | 150]]<br />
<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
<br />
- YFP_TRPb_PolyWb<br />
<br />
- YFP_TRPb (control)<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. <br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:16:44Z<p>Vparasco: /* Secretion Rate of Trp as a function of culture growth */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa2.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
<br />
DOS<br />
<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa3.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa4.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
TRES<br />
{|<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa5.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|<br />
{| style="width:50%"<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa6.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
|}<br />
<br />
TCY3081 (YFP) TCY3128 (CFP) Strain Name<br />
pCM182 (TRPa) + BBa_K792010 (TRPZipper2) X YFP_TRPa_TRPZipper2<br />
pCM182 (TRPa) + BBa_K792012 (PoliWb) X YFP_TRPa_PoliWb<br />
pCM185 (TRPb) + BBa_K792010 (TRPZipper2) X YFP_TRPb_TRPZipper2<br />
pCM185 (TRPb) + BBa_K792012 (PoliWb) X YFP_TRPb_PoliWb<br />
pEG202 (HIS) + BBa_K792009 (PoliHa) X CFP_HIS_PoliHa<br />
pEG202 (HIS) + BBa_K792011 (PoliHb) X CFP_HIS_PoliHb<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
NOTE: The fluorescence meausurements taken for the Tryptophan in the medium, take into account both the Amino Acid secreted by the device and the one diffused. Therefore the secretion rate calculated will be higher than the actual ones. We use an empty plasmid as control to study Tryptophan diffusion.<br />
<br />
We used a simple model to measure the secretation rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
[[File:BsAs2012Odvstime4.jpg | 150]]<br />
<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
<br />
- YFP_TRPb_PolyWb<br />
<br />
- YFP_TRPb (control)<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
<br />
'''Result'''<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
'''Table:''' Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. <br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Results/BBsTestingTeam:Buenos Aires/Results/BBsTesting2012-10-27T01:03:50Z<p>Vparasco: /* Secretion Rate of Trp as a function of culture growth */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
= After the Jamboree! =<br />
<br />
When we returned from the Latin America Jamboree we focused all our efforts on completing the neccesary transformations to test our devices and our projet as a whole. <br />
<br />
We devided this task in three sections<br />
<br />
== Week 1&2 : Yeast expression vectors & Transformations ==<br />
<br />
In order to construct the yeast expression plasmids we choosed 3 vectors, 2 with a tryptophan marker and 1 with an histidine marker:<br />
# '''pCM182/5''', which are centromeric plasmids with TRP1 marker, and with a doxycycline repressible promoter [Gari et al 1996]. <br />
# '''pEG202''', with a 2 ori, HIS3 marker and a constitutive promoter (PADH1). <br />
<br />
<br />
{| style="width:100%"<br />
|[[File:BsAs2012-plasmid-PEG202.jpg|400px]]<br />
|[[File:BsAs2012-plasmid-BPCM185.gif|340px]]<br />
|}<br />
<br />
<br />
<br />
The cloning we did was:<br />
<br />
{| class="wikitable"<br />
|<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792009</partinfo> (PoliHa)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792010</partinfo> (TRPZipper2)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792011</partinfo> (PoliHb)<br />
! scope="row" style="background: #7ac5e8"|<partinfo>BBa_K792012</partinfo> (PoliWb)<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM182 (TRPa)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pCM185 (TRPb)<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|-<br />
! scope="row" style="background: #81BEF7"|pEG202 (HIS)<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
! scope="row" style="background: #01DF01"|X<br />
|<br />
|}<br />
<br />
<br />
==== Protocol ====<br />
<br />
# Digestion of plasmids and TRP/HIS export device:<br />
##pCM182; pCM 185; BBa_K792010 y BBa_K792012 were digested with BamHI and Pst1 restriction enzymes.<br />
##pEG202; BBa_K792009 y BBa_K792011 were digested with BamHI and Not1.<br />
# Purification of digested vectors (pCM185; pCM182; pEG202) <br />
# Ligation of vectors and devices according the anterior table (T4 ligase protocol, overnight)<br />
# Transformation of E. Coli DH5a with the ligation products. Bacterias were plated on LB-agar with Ampicillin, and incubated over night at 37 °C.<br />
# Colonies were used for liquid cultures (LB + Ampicillin) and minipreps were made.<br />
# Constructions (vector + insert) were checked by digestion with restriction enzymes, and 1%-agarose gel (1kb and 100bp as markers).<br />
<br />
<br />
Once obtained the desired constructions, we transformed yeast strains:<br />
# TCY3081: W303, bar1-, ura3::PAct1-YFP<br />
# TCY3128: W303, bar1-, leu2:: Pprm1-CFP 405<br />
<br />
We got the following '''transformed strains''':<br />
<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8"| Name<br />
! scope="row" style="background: #7ac5e8"| Strain transformed<br />
! scope="row" style="background: #7ac5e8"| Plasmid<br />
|-<br />
! scope="row" style="background: #CCCCCC"| pato<br />
|<br />
|<br />
|}<br />
<br />
{|<br />
| rowspan="3" | [[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
! scope="row" style="background: #7ac5e8"| Name<br />
| YFP_TRPa_TRPZipper2<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Strain<br />
|TCY3081 (YFP)<br />
|-<br />
! scope="row" style="background: #CEE3F6"|Plasmid<br />
|pCM182 (TRPa) + BBa_K792012 (PoliWb)<br />
|}<br />
<br />
[[File:BsAs2012-icono-Cepa1.jpg | 200px]]<br />
<br />
TCY3081 (YFP) TCY3128 (CFP) Strain Name<br />
pCM182 (TRPa) + BBa_K792010 (TRPZipper2) X YFP_TRPa_TRPZipper2<br />
pCM182 (TRPa) + BBa_K792012 (PoliWb) X YFP_TRPa_PoliWb<br />
pCM185 (TRPb) + BBa_K792010 (TRPZipper2) X YFP_TRPb_TRPZipper2<br />
pCM185 (TRPb) + BBa_K792012 (PoliWb) X YFP_TRPb_PoliWb<br />
pEG202 (HIS) + BBa_K792009 (PoliHa) X CFP_HIS_PoliHa<br />
pEG202 (HIS) + BBa_K792011 (PoliHb) X CFP_HIS_PoliHb<br />
<br />
== Week 3: Synthetic Ecology Characterization ==<br />
<br />
Our task is to characterize our system including the devices functioning.<br />
We want specifically to: <br />
<br />
#Quantify the export of Trp as proof that the devices work<br />
#Determine experimentally some of the parameters that we used in the model<br />
#Characterize the growth of the transformed strains in coculture<br />
<br />
In order to characterize the devices that we used to transform our strains we came up with the series of assays that we describe below.<br />
<br />
=== Devices characterization ===<br />
<br />
==== Secretion Rate of Trp as a function of culture growth ====<br />
<br />
The first step was to actually check if the construct works: do the transformed yeast strains - with the tryptophan devices- actually secrete tryptophan into the medium?<br />
<br />
To test this we used the following strains:<br />
<br />
*YFP_TRPb_TRPZipper2<br />
*YFP_TRPb_PolyWb<br />
*YFP_TRPb<br />
*YFP_TRPa_TRPZipper2<br />
*YFP_TRPa_PolyWb<br />
*YFP_TRPa<br />
*YFP<br />
<br />
'''Protocol'''<br />
<br />
*We started 5ml cultures with 3 replica until they reached exponential phase, overnight, using a -T medium.<br />
*Starting OD for the assay 0.1 (exponential phase). <br />
*We measured OD every hour until they reached an OD: 0.8 (5 hs approximately). <br />
*We measured the Trp signal for each culture medium using the spectrofluorometer.<br />
<br />
<br />
We used a simple model to measure the export rate for all the strains. Since the cultures are in exponential phase, we take<br />
<br />
[[File:BsAs2012-eqTrp1.jpg | 225px]]<br />
<br />
After a few calculations, we find that<br />
<br />
[[File:BsAs2012-eqTrp2.jpg | 225px]]<br />
<br />
'''Results'''<br />
<br />
Next we show the average OD for each strains used, needed to calculate the export rates of Trytophan.<br />
<br />
[[File:BsAs2012Odvstime4.jpg | 150]]<br />
<br />
Figure X. check<br />
<br />
[[File:BsAs2012rate2.jpg| 150]]<br />
<br />
Figure X. check<br />
<br />
==== Tryptophan secretion at increasing histidine concentrations ====<br />
<br />
We asked ourselves which was the dependance of tryptophan secretion on the amount of histidine in medium. We carried on this test in order to determine wether the secretion of tryptophan depends on the concentration of another aminoacid in the media, such as histidine and what would be the necessary amount of histidine in medium for the start of our system. <br />
<br />
In this experiment we used strains: <br />
<br />
- YFP_TRPb_TRPZipper2<br />
<br />
- YFP_TRPb_PolyWb<br />
<br />
- YFP_TRPb (control)<br />
<br />
<br />
'''Protocol'''<br />
<br />
# Starters of each strain used were grown over night in -T media, at 30 °C in shaker.<br />
# After 12 hs, cells were pelleted and washed with -HT media.<br />
# Cultures with increasing concentrations of histidine (0X, 1X, 1/4X and 1/16X) were set at an initial OD: 0.1, for each strain with 2 replica.<br />
# We left the cultures in shaker at 30ºC for 5 hours. After that time, we measured the final OD reached by cultures with the use of a spectrophotometer and the amount of tryptophan present in medium with a spectrofluorometer.<br />
<br />
'''Results'''<br />
<br />
[[File: BsAs2012TrpvHis.jpg]]<br />
<br />
[[File: BsAs2012ratioTrpvHisbypromotor.jpg]]<br />
<br />
=== Strain characterization ===<br />
==== Experimental determination of strains death rate====<br />
<br />
We set out to determine how long can auxotroph cells[link] survive in media that lacks both Trytophan and Histidine. These values are the '''death''' parameters for CFP and YFP strains used in our model[link]. These were taken as equal in the mathematical analysis for simplicity but now we would like to test whether this approximation is accurate.<br />
<br />
Given that our system most likely will present a lag phase until a certain amount of both AmioAcids is accumulated in the media, will the cells be viable until this occurs? This is a neccesary check of our '' system's feasability''.<br />
<br />
'''Protocol'''<br />
<br />
*We set cultures of the two auxotroph strains without being transformed (YFP and CFP) in medium –HT at an initial OD of 0.01. <br />
*Each day we plated the same amount of µl of the culture and counted the number of colonies obtain in each plate. We set 3 replica of each strain.<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
! scope="row" style="background: #7ac5e8" |Strain<br />
! scope="row" style="background: #7ac5e8" |Replica<br />
! scope="row" style="background: #7ac5e8" |Monday<br />
! scope="row" style="background: #7ac5e8" |Tuesday<br />
! scope="row" style="background: #7ac5e8" |Wednesday<br />
|-<br />
|CFP<br />
|1<br />
|260<br />
|320<br />
|285<br />
|-<br />
|CFP<br />
|2<br />
|267<br />
|314<br />
|76<br />
|-<br />
|CFP<br />
|3<br />
|413<br />
|362<br />
|278<br />
|-<br />
|YFP<br />
|1<br />
|230<br />
|316<br />
|688<br />
|-<br />
|YFP<br />
|2<br />
|291<br />
|194<br />
|524<br />
|-<br />
|YFP<br />
|3<br />
|449<br />
|344<br />
|725<br />
|}<br />
<br />
Table: Number of colonies counted per plate.<br />
<br />
We expect to see a decrease in the number of colonies - because of cell death. We found that this was not the case, in the experiment's time lapse. However we observed that the size of the colonies was smaller everyday as can be seen in the following pictures.<br />
<br />
<br />
<br />
<br />
We can infer from this data that though they have not died, they may have enter into a '''...Alan state'''. <br />
<br />
<br />
{|<br />
|[[File:BsAs2012_celldeath.png | 100px]]<br />
|[[File:BsAs2012_celldeath2.png| 100px]]<br />
|<br />
|}<br />
FigureX.<br />
<br />
==== Growth dependence on the Trp and His concentration====<br />
<br />
An important thing in order to characterize the system is the dependence of the growth rate on the culture with the concentration of the crossfeeding aminoacids, tryptophane (Trp) and histidine (His).<br />
<br />
This would allow us to estimate one of the parameters used in our model (the EC50, which is the amount of aminoacid at which the culture reaches half of the maximum growth).<br />
<br />
<br />
===== Protocol=====<br />
<br />
1. For this experiment we would use strains YFP and CFP (non-transformed, without devices).<br />
We started cultures of 5 ml of initial OD: 0.025 for:<br />
<br />
{| class="wikitable"<br />
| Strain YFP at the following media [Trp] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain CFP at the following media [His] = 1x; 0.5x; 0.25x; 0.125x; 0.0625x, 0.03125x<br />
|-<br />
| Strain YFP at Synthetic Complete media<br />
|-<br />
| Strain CFP at Synthetic Complete media<br />
|}<br />
<br />
2. Cultures would be left overnight (12 hs) at 30°C with agitation and we measured OD reached with the use of spectrophotometer.<br />
<br />
===== Results ===== <br />
To be done!<br />
<br />
=== Coculture of transformed strains ===<br />
<br />
We did the first experiment to test whether our system works and how two transformed strains grow together.<br />
<br />
We designed an assay to do so; following the growth of these strains:<br />
<br />
{|<br />
|<br />
{| class="wikitable"<br />
|+ Transformed cells coculture and controls.<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Treatment'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain A'''<br />
|! scope="row" align="center" style="background: #7ac5e8"| '''Strain B'''<br />
|-<br />
|1<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS_PolyHa<br />
|-<br />
|2<br />
|YFP_TRPb_TRPZipper2<br />
|CFP_HIS<br />
|-<br />
|3<br />
|YFP_TRPb_TRPZipper2<br />
|! scope="row" style="background: #CCCCCC"|<br />
|-<br />
|4<br />
|YFP_TRPb<br />
|CFP_HIS_PolyHa<br />
|-<br />
|5<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS_PolyHa<br />
|-<br />
|6<br />
|YFP_TRPb<br />
|CFP_HIS<br />
|-<br />
|7<br />
|! scope="row" style="background: #CCCCCC"|<br />
|CFP_HIS<br />
|-<br />
|8<br />
|YFP_TRPb<br />
|! scope="row" style="background: #CCCCCC"|<br />
|}<br />
|}<br />
<br />
==== Protocol ====<br />
{|<br />
|<br />
# Starters of strains were grown over night at 30°C, according the scheme showed in the table<br />
# The next day cultures were sonicated briefly in low power, and OD was measured in order to check they were in exponential phase.<br />
# Cells were centrifugated and then washed with medium –HT.<br />
# We set the culture of strains at OD: 0.02 in 5 ml of medium –HT with 3 replica, according to Table 1. <br />
# At 0, 1, 2, 3, 4, 5, 6, 7, 8 and 22 hours we took samples of 20 µl.<br />
# Samples were placed in a 384 wells plate, with 20 µl of cyclohexamide 2x (final concentration 1x) in each of the wells.<br />
# We used epifluorescence microscope in order to determinate the strain proportion of each coculture. The density of the culture was calculated based on the cell density at in each wells.<br />
|<br />
{|class="wikitable"<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Strain'''<br />
|! scope="row" align="center" style="background: #7ac5e8"|'''Media'''<br />
|-<br />
|YFP_TRPb_TRPZipper2<br />
|'''-T'''<br />
|-<br />
|YFP_TRPb<br />
|'''-T'''<br />
|-<br />
|CFP_HIS_PolyHa<br />
|'''-H'''<br />
|-<br />
|CFP_HIS<br />
|'''-H'''<br />
|}<br />
|}<br />
<br />
{| class="wikitable" style="width:50%"<br />
| align="center" | [[File:Bsas2012-Wells.png|500px]]<br />
|-<br />
| 384 wells plate to be used for epifluorescence microscope.<br />
|}<br />
<br />
<br />
==== Results ====</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:54:41Z<p>Vparasco: /* Lag Time */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
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[[File:BsAs2012diapi.jpg|450px]]<br />
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|-<br />
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[[File:BsAs2012diapii.jpg|350px]]<br />
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[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
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[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
|-<br />
|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
<br />
{|<br />
|Let's finally look at some numerical simulations to see how the system evolves in time. We present a sample simulation with parameters from Region III to the rigth. There's a new characeristic that our previous analysis didn't show: the system reaches the desired steady state, however there will be significant lag phase.<br />
<br />
We found numerically that it's related to time it takes for the Amino Acids in the medium to reach a certain concentration; one similar to the parameters '''Kaa''' and '''Kbb''' respectively. To this effect we note that it's possible to reduce this ''lag time'' by<br />
<br />
*Using higher initial concentration for each population.<br />
<br />
*Lowering parameters '''Kaa''' and '''Kbb'''.<br />
<br />
Given the relationship between these parameters and the AA absortion rates, we decided to device a way to facilitate absortion. <br />
<br />
'''Troyan Peptides'''<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:45:00Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
|-<br />
|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:44:32Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
|<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|600px]]<br />
|expli<br />
|-<br />
|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012diap2.jpgFile:BsAs2012diap2.jpg2012-10-27T00:43:51Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:34:38Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
|<br />
|<br />
[[File:BsAs2012diapi.jpg|450px]]<br />
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[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
[[File:BsAs2012diapiii.jpg|200px]]<br />
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[[File:BsAs2012diap2.jpg|350px]]<br />
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|expli<br />
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|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012diapiii.jpgFile:BsAs2012diapiii.jpg2012-10-27T00:34:03Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:33:48Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
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= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012diapi.jpgFile:BsAs2012diapi.jpg2012-10-27T00:23:47Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:23:24Z<p>Vparasco: /* Overview */</p>
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<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
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[[File:BsAs2012diapi.jpg|350px]]<br />
|-<br />
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[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
|bbb<br />
|-<br />
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[[File:BsAs2012diap2.jpg|350px]]<br />
[[File:BsAs2012diap3.jpg|350px]]<br />
|expli<br />
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|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparascohttp://2012.igem.org/File:BsAs2012diapii.jpgFile:BsAs2012diapii.jpg2012-10-27T00:21:24Z<p>Vparasco: </p>
<hr />
<div></div>Vparascohttp://2012.igem.org/Team:Buenos_Aires/Project/ModelTeam:Buenos Aires/Project/Model2012-10-27T00:19:19Z<p>Vparasco: /* Overview */</p>
<hr />
<div>{{:Team:Buenos_Aires/Templates/menu}}<br />
<br />
= Overview =<br />
<br />
<br />
mathematical model<br />
<br />
{|<br />
|<br />
[[File:BsAs2012diapi.jpg|350px]]<br />
|-<br />
[[File:BsAs2012diapii.jpg|350px]]<br />
|<br />
|<br />
|bbb<br />
|-<br />
|<br />
[[File:BsAs2012diap2.jpg|350px]]<br />
[[File:BsAs2012diap3.jpg|350px]]<br />
|expli<br />
|-<br />
|explic<br />
|}<br />
<br />
= Modeling a synthetic ecology =<br />
To gain insight into the behavior of our crossfeeding design, to understand which parameters of the system are important, and to study the feasibility of the project, we decided to implement a model of the system. We found this interesting per se, as the model we need is that of a microbial community and ecology. <br />
<br />
The mathematical modeling of ecological system is an active field of research with a very rich and interesting history; from the works of Lotka and Volterra, who modeled predator-prey dynamics with ordinary differential equations, to Robert May’s chaotic logistic maps. In fact a lot of synthetic systems of interacting bacteria created in recent years were used to study these sort of models.<br />
<br />
== The crossfeeding model ==<br />
<br />
In the crossfeeding design, each strain produces and releases to the medium an aminoacid the other strain(s) need to grow. The growth rate of each strain depends on the aminoacid (AA) concentration of those AA it can’t produce. In turn these concentrations depend on the abundance of the other strains. Therefore the growth of the strains is interdependent.<br />
<br />
For simplicity and to be consistent with the experimental work, we decided to model two interacting strains, one that produces tryptophan (Trp) but requires histidine (His), and another that produces His but requires Trp. <br />
<br />
We decided to use ordinary differential equations to model the system. This is a normal approach when studying population dynamics of this kind. <br />
<br />
The model has four variables:<br />
*[Nhis-] : the concentration of histidine dependent (Trp producing) yeast cells, in cells per ml<br />
*[Ntrp-] : the total amount of tryptophan dependent (His producing) yeast cells, in cell per ml<br />
*[his]: the concentration of histidine in the medium, in molecules per ml<br />
*[trp]: the concentration of tryptophan in the medium, in molecules per ml.<br />
<br />
To build the model we did the following assumptions:<br />
* The growth rate of each strain depends on the concentration in the medium of the AA they can’t produce. As the concentration of this AA in the medium increases, so does the growth rate of the strain, until it settles at the growth rate observed in optimal conditions (doubling time of 90 min for yeast).<br />
* There is a maximal density of cells the medium can support (carrying capacity)<br />
* Each cell has a fixed probability of dying per time interval<br />
* Each cell releases to the medium the AA it produces at a fixed rate<br />
* Each strain only consumes the AA it doesn't produce<br />
* The system reaches steady state.<br />
<br />
[[File:Bsas2012-model1.png]] (model)<br />
<br />
In the equation for the temporal evolution of each population we take the growth rate as a Hill function of the amount of AA to which the strain is auxotrophic (it can't produce). The function captures the increase of the growth rate with the relevant AA concentration, until it reaches a plateau at the maximal growth rate, that corresponds to a doubling time of 90 minutes (doubling time = ln(2)/kmax). These functions are of the form<br />
<br />
[[File:bsas2012-modeling-eq1.png|200px]](1)<br />
<br />
where '''Kaa''' is the effective concentration of AA at which half maximal growth rate is obtained, and '''l''' is the Hill coefficient, that describes how "steep" the curve is. <br />
<br />
The term (1-(Nhis+Ntrp)/Cc) of the model accounts for other factors, not explicit in our model that can limit the concentration of cells in a given volume (carrying capacity), enabling the population to reach equilibrium. We included a term related to cell death (- death Ntrp), which is makes biologically sense (cell do die) and is critical for a correct behavior of the model.<br />
<br />
The terms in the equations for the evolution of each [AA] in the medium are the fluxes of AA entering and leaving the medium. The first term (Ptrp*Nhis-) is a measure of the AA produced and exported in the form of peptides by a cell, for example the rate of tryptophan secretion by the histidine dependent cell. <br />
<br />
The second term is the flux leaving the medium and entering the auxotrophic cells. Each cell has a more or less fixed amount of each amino acid, which we call '''d'''. If a cell is to replicate itself and cannot produce and amino acid, it will have to absorb it from the medium. Therefore the flux of AA entering the cell, is '''d''' divided by the doubling time &tau; (the time it takes to "construct" a new cell). <br />
One of the hypotheses built into our model is that &tau; will vary greatly with the concentration of nutrients available. We've used <br />
<br />
[[File:bsas2012-modeling-eq2.png|200px]](2)<br />
<br />
The amount of AA entering the cells that produce it was considered negligible. This means that a cell that produces Trp doesn't import it from the medium in significant quantities. This is likely to hold when AA concentrations are limiting. <br />
<br />
=== Steady State Solution ===<br />
<br />
The 4 equations in the model were equaled to zero and the non-linear algebraic system solved using [http://www.wolfram.com/mathematica/ Mathematica] to find their equilibrium values.<br />
<br />
Here we change the notation a little bit to two generic strains '''a''' and '''b''' where population '''Na''' produces amino acid '''a''' and requires '''b''', and population '''Nb''' produces '''b''' and requires '''a'''. We are interested in the value of the cell populations in equilibrium, or more importantly the fraction of each population in steady state. Thus a change was made to more convenient variables: the sum of both population and a strain's fraction.<br />
<br />
Nt = Na + Nb<br />
<br />
Xa = Na / Nt<br />
<br />
Only 3 fixed points were found for the system (See [[Team:Buenos_Aires/Project/ModelAdvance#Appendix | Appendix]]). There are some solutions for which it isn't true that the four variables reach a steady state (SS) or equilibrium. There are initial conditions for which the AA concentrations will not stop growing! So caution is required when assuming steady state. <br />
<br />
*In the first solution we found the culture doesn't thrive, for example because one strain was missing or the initial density was to low.<br />
<br />
*The second one has no biological relevance since it yields negative concentrations for the Amino Acids.<br />
<br />
*The third one is the significant one (see equations below). However for some parameters the concentrations of Nt and AA can be negative, therefore restricting the parameter space in which the model works. <br />
<br />
<br />
[[File:bsas2012-modeling-eqsol3.png]](3)<br />
<br />
=== Regulation ===<br />
<br />
Note that the fraction of each strain in the community is a function of the AA secretion rates ('''pa''' and '''pb''') and the amount of AA required to "construct" a cell ('''da''' and '''db''').<br />
<br />
[[File:bsas2012-modeling-eq4.png]] (4)<br />
<br />
For positive values of '''d''' and '''p''' the range of the function is (0; 1), consistent with what we expect for a fraction.<br />
<br />
The fraction of each strain in the culture in equilibrium are regulated by the production and export of each AA – represented in the model through '''pa''' and '''pb'''. These fractions are independent of initial conditions! This means that the system auto-regulates itself, as intended. <br />
<br />
In fact we only need to control the ratio between these parameters to control the culture composition: <br />
<br />
[[File:bsas2012-modeling-eq5revised.png]](5)<br />
<br />
The next figure illustrates how the fraction Xa varies with the variable &epsilon;.<br />
<br />
[[File:bsas2012-modeling-fig1revised.png]]<br />
<br />
Figure 1. Fraction Xa as a fuction of the ratio of protein export for values of D=0.1,1,10 (in green, purple and red).<br />
<br />
To programme the percentage we need a second set of biobricks that can sense an external stimulus and transduce this signal to modify &epsilon;. The range of percentages we can control is determined by the range of &epsilon; accessible with this second device and the ratio D that is set for any two A.A.<br />
<br />
=== Parameters ===<br />
<br />
The parameter estimation process is detailed in [[Team:Buenos_Aires/Project/Model#Parameter_selection | parameter selection]]<br />
<br />
{| class="wikitable"<br />
|+ align="top" style="color:#e76700;" |''Parameters selected''<br />
|-<br />
|<br />
|style="color:white; background-color: purple;"|'''Value'''<br />
|style="color:white; background-color: purple;"|'''Units'''<br />
|-<br />
|style="color:white; background-color: purple;"|kmax<br />
|0.4261<br />
|1/hr<br />
|-<br />
|style="color:white; background-color: purple;"|K his<br />
|2.588e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|K trp<br />
|1.041e16<br />
|AA/ml<br />
|-<br />
|style="color:white; background-color: purple;"|n his<br />
|1.243<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|n trp<br />
|1.636<br />
|<br />
|-<br />
|style="color:white; background-color: purple;"|Cc<br />
|3.0 10^7<br />
|cell/ml<br />
|-<br />
|style="color:white; background-color: purple;"|death<br />
|3 to 7<br />
|days<br />
|-<br />
|style="color:white; background-color: purple;"|p his<br />
|p 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|p trp<br />
|p &epsilon; 2.16e8<br />
|AA/ cell hr<br />
|-<br />
|style="color:white; background-color: purple;"|d his<br />
|6.348e8<br />
|AA/cell<br />
|-<br />
|style="color:white; background-color: purple;"|d trp<br />
|2.630e7 <br />
|AA/cell<br />
|}<br />
<br />
Table 1. Model parameters used for the simulations<br />
<br />
=== Parameter selection ===<br />
<br />
We estimatated values for all the parameter in the model, doing dedicated experiments or using values from the literature. This allowed to check the feasibility of the system.<br />
<br />
*The '''Kaa''' found in the equations are related to the concentration of AAs in the medium required to reach half the maximum rate of growth. Curves of OD600 vs [AA](t=0) were measured experimentally for each amino acid and the data fitted to a Hill equation (6) using MATLAB’s TOOLBOX: Curve Fitting Tool.<br />
<br />
[[File:Bsas2012-modeling-eqfit.png|200px]](6)<br />
<br />
This data from [[Team:Buenos_Aires/Results/Strains#Growth dependence on the Trp and His concentrations | experimental results]] and the best fit obtained for each are shown below in Figure 2.<br />
<br />
[[File:Bsas2012-modeling-fig_aux1.png]]<br />
[[File:Bsas2012-modeling-fig_aux2.png]]<br />
Figure 2. Single strain culture density after over night growth vs the initial concentration of AA in the medium (dilutions 1:X).<br />
The best fit to the data is also shown.<br />
<br />
The values taken from the fits are <br />
<br />
His- :<br />
K_dil = 0.2255 <br />
n = 1.52<br />
R-square: 0.997 <br />
<br />
Trp- :<br />
K_dil = 0.0469<br />
n = 1.895 <br />
R-square: 0.998<br />
<br />
<br />
The results were then converted to the units chosen for the simulations.<br />
<br />
K = K_dil * [AA 1x] * Navog / (Molar mass AA) <br />
<br />
where [AA 1x] = 0.02 mg/ml is the concentration of the AA (His or Trp) in the 1x medium and Navog is Avogadro's number. We get<br />
<br />
*K trp= .0469* 5.88e16 AA / ml = 2.76e15 molecules/ml <br />
<br />
*K his= 0.2255* 7.8e16 AA / ml = 1.76e16 molecules /ml<br />
<br />
<br />
The competition within a strain and with the other were taken as equal. The system's general ''carrying capacity'' considered in the model is the one often used here, in a lab that works with these yeast strains:<br />
<br />
**Cc= 3e7 cell/ml.<br />
<br />
<br />
*The death rate was taken between 3 and 7 days.<br />
<br />
<br />
*The rate of “production and export” was given an upper bound value (P_MAX) of 1% of the maximum estimated number of protein elongation events (peptidil transferase reactions) for a yeast cell per hour. That is, if all the biosynthetic capacity of the cell was used to create the AA rich exportation peptide, the export rate would equal P_MAX. Of course this is not possible because the cell has to do many other things, therefore we considered 1% of P_MAX as a reasonable upper bound for '''p'''.<br />
<br />
From [http://www.biomedcentral.com/1752-0509/2/87| von der Haar 2008] we get an estimate for the total number of elongation events (peptidil transferase reactions): 6e6 1 / cell sec [ ]<br />
<br />
* P_MAX = 2.16e8 1/ cell hour <br />
<br />
These parameters will be regulated in the simulation by &epsilon; and '''p''', to alter the fraction between populations.<br />
<br />
*p trp = '''p'''* '''&epsilon;'''*2.16e8 AA / cell hour<br />
<br />
*p his = '''p'''*2.16e8 AA / cell hour<br />
<br />
where '''p''' < 1 controls the fraction of the P_MAX value and &epsilon; the ratio between the export of each amino acid.<br />
<br />
<br />
'''d''' is the total number of amino acids in a yeast cell –same as the ones needed to create a daughter -per cell: <br />
<br />
'''d''' = # A.A. per cell = (mass of protein per yeast cell ) * relative abundance of AA * Navog / AA's molar mass.<br />
<br />
*d trp= 2.630e7 AA / cell <br />
<br />
*d his= 6.348e8 AA / cell<br />
<br />
==Numerical Simulations==<br />
:Initially we relied on numerical simulations (NS) performed with [http://www.mathworks.com/products/matlab/| MATLAB] to explore possible behaviors of the model, ODEs rarely have solutions that can be expressed in a closed form.<br />
<br />
:To run the simulations all that is left is to choose values {p, &epsilon;, initial conditions}.<br />
<br />
* Since this is merely a framewok we have taken values '''p''' from a log scale from -3 to 1. <br />
* '''&epsilon;''' was ranged from 0.0001 to 4; which varies the fraction of each population from 10% to 90%. <br />
* Cells initial concentration (i.c.c.): dilutions from 1:10000 to 10x of the carrying capacity (Cc). <br />
* Amino acids (AA) initial concentration: null, unless stated otherwise.<br />
<br />
== Die or thrive?==<br />
:Some basic properties were observed by simplifying the system; we wanted to check that our model was sound. We considered a "symmetric interaction" in which both secretion rates and amino acid requirement were equivalent. <br />
<br />
[[File:bsas2012-modeling-eq6.png]](7)<br />
<br />
where we can define <br />
<br />
[[File:bsas2012-modeling-eq7.png]] (8)<br />
<br />
:This parameter &lambda; has an intuitive interpretation. The ratio '''d'''/'''p''' is the time it takes a cell to export enough AA for a cell of the other strain to build a daughter. On the other hand, 1/death is the average life span of a cell. Therefore &lambda; is the ratio between the "life span" of a cell and the time it takes to export sufficient AA to build a cell, thus &lambda; represents the amount of cells that can be constructed with the AA secreted by a cell in its lifetime. If this value is grated than one (&lambda; &gt; 1) the culture grows, otherwise it dies (This is completely analogous to the "force of infection" as defined in epidemiology). <br />
<br />
:Keeping '''d''' and '''death''' constant, the total steady state number of cells in the culture depends on the secretion rate '''p''' as shown in the following figure 3. There is a threshold value p given by &lambda;=1; with lower values the culture dies.<br />
<br />
[[File:bsas2012-modeling-fig3revised.png]] <br />
<br />
Figure 3. Total number of cells in the mix vs the strengh '''p''' of the production and export of AAs for a set of parameters Cc,d, death. <br />
<br />
<br />
:Another condition is related to extra-cellular concentration of amino acids. Looking at the equations for the evolution of the AA in the model, we can identify the parameter &delta; as follows<br />
<br />
[[File:bsas2012-modeling-eq8.png]](9)<br />
<br />
: As before, the ratio '''&radic;(da db)/&radic;(pa pb)''' is the average time required for a cell to export enough AA to construct another cell. '''1/kmax''' is the time it takes a cell to replicate in optimal growth conditions. &delta; can be interpret as the amount of cells that can be made with the material secreted a by a single cell before it divides (in optimal conditions). If &delta; &gt; 1 the amount of nutrients produced exceeds the consumption, the medium gets saturated with AA and the regulation fails. So the system is auto-regulated only if &delta; &lt; 1.<br />
<br />
:Combining these two conditions (&lambda; &gt; 1 and &delta; &lt; 1), we conclude that the production rate has to be in a defined region for the system to work. To low and the culture dies out, to big and it gets out of control.<br />
<br />
== Parameter Space and Solutions ==<br />
:Uniting the conditions for &lambda; and &delta; we see that in general '''p''' and &epsilon; must be bound for our solution to make sense (i.e. all concentrations &gt; 0):<br />
<br />
[[File:bsas2012-modeling-eq14.png]](10)<br />
<br />
<br />
[[File:bsas2012-modeling-fig3.png]]<br />
Figure 4. Regions in the parameter space that present different types of solutions. Only in Region III the system works as intended.<br />
<br />
<br />
:Now, let's classify these regions numerically to see whether the ideas we just presented are supported. Taking random values from each region we found that all four variables are always positive, but each region is associated with a different kind of solution. The conditions shape the behavior and not the existence of a solution.<br />
<br />
:Taking AA(t=0)=0:<br />
<br />
::I. The culture doesn't grow, it decays with varying velocities for any initial concentration of cells (i.c.c.). This is consistent with solution 1, where Nt= 0 as t &rarr; &infin;. This is the &lambda; &lt; 1 case.<br />
<br />
<br />
::II. The extracellular AA concentration keeps growing and the medium gets saturated. The culture reaches equilibrium for every i.c.c. no matter how low, but there is no regulation of the composition of the culture. This is the &delta; &gt; 1 case. <br />
<br />
::The growth rate tends to the theoretical 90 min and the AA dependence disappears from the equations for each population. Remarkably the fraction of each strain is still independent of the i.c.c.<br />
<br />
<br />
::III. The four variables reach SS. The mole fraction is solely dependent on &epsilon; according to the formula on equation (5). The total population of the community (Nt) is the same as in Region II.<br />
<br />
::'''This is the region where the auxotrophy leads to regulation of the community.''' However the culture doesn’t grow for all i.c.c. – will get back to this point shortly.<br />
<br />
===Conclusions===<br />
::Some conclusions we've drawn from these numerical simulations:<br />
<br />
# We had postulated that the solution doesn't hold in region II and expected a dramatic change in the system’s behavior. However there is a smooth transition between regions II and III. For a fixed &epsilon; we can go from region III to region II by increasing '''p'''. Once we cross the threshold we notice that the total population of cells (Nt) doeen't vary from one region to the next. Though the AA continues to grow over time (and accumulate) it does so slowly; more so than we'd expect for a vertical asymptote. <br />
# More so, the formula (5) is a good approximation for the fraction of each strain in the region II close to the limit with region III; the difference between the two increases gradually as '''p''' gets further away from this threshold value. The formula is not true in II; thus regulation fails.<br />
# There is no dramatic change caused by the asymptote, in fact the two regions can't be distinguished experimentally through a strain's fraction measurement in each side of the frontier; so small is the difference between the values across. <br />
# Taking into account that the threshold is based on estimations; perhaps is safer to choose points well inside Region III to ensure proper regulation. This has a cost, for a fixed percentage the production and export of AAs is now lower and the dynamic of the culture slower.<br />
<br />
:The original purpose of this analysis was to undertand '''under which initial conditions do the populations thrive or die'''. This has to be analyzed in terms of Figure 4, not merely the conditions for &lambda;.<br />
<br />
:We noticed that the culture's survival in region III also depends on the values of '''Kaa''', even though is not explicit in any formula so far. Remember that '''Kaa''' is the concentration of an AA in the medium required for half maximal growth rate. For a fixed value of '''Kaa''' there is a critical initial concentration of cells below which the culture doesn't prosper. This effect is important when the percentage desired is extreme (close 100%), where the '''p''' value required for the strain gets really low. <br />
<br />
:This is reasonable considering that another time scale is introduced. Not only have the cells to produce and absorb the required amounts of AA before they die, they also need to modify the AA concentration of the medium. The cells must produce enough amino acids so that the concentration of AA approximates '''Kaa'', before the original cells die out. If the initial cell density is to low, this won't happen.<br />
<br />
<br />
== Lag Time ==<br />
{|<br />
|xxoo<br />
|<br />
[[File:timeevol.jpg|350px]]<br />
|}<br />
<br />
[[File:lagK.jpg|500px]]</div>Vparasco