http://2012.igem.org/wiki/index.php?title=Special:Contributions/Af.simbaqueba218&feed=atom&limit=50&target=Af.simbaqueba218&year=&month=2012.igem.org - User contributions [en]2020-11-27T16:41:19ZFrom 2012.igem.orgMediaWiki 1.16.0http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:05:04Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team - Grand Prize Winner<br />
[[File:Photo2.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team <br />
[[File:Photo3.jpg|600x600px|thumb|center]]<br />
Teams that advace to championship<br />
[[File:Photo4.jpg|600x600px|thumb|center]]<br />
Colombia iGEM Team - Best Model</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:53Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|600x600px|thumb|center]]<br />
[[File:Photo2.jpg|600x600px|thumb|center]]<br />
[[File:Photo3.jpg|600x600px|thumb|center]]<br />
[[File:Photo4.jpg|600x600px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:24Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|1024x682px|thumb|center]]<br />
[[File:Photo2.jpg|1024x682px|thumb|center]]<br />
[[File:Photo3.jpg|1024x682px|thumb|center]]<br />
[[File:Photo4.jpg|1024x682px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:02:02Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|1024x682|thumb|center]]<br />
[[File:Photo2.jpg|1024x682|thumb|center]]<br />
[[File:Photo3.jpg|1024x682|thumb|center]]<br />
[[File:Photo4.jpg|1024x682|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/File:Photo4.jpgFile:Photo4.jpg2012-10-27T04:01:18Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photo3.jpgFile:Photo3.jpg2012-10-27T04:00:57Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photo2.jpgFile:Photo2.jpg2012-10-27T04:00:38Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/File:Photoone.jpgFile:Photoone.jpg2012-10-27T04:00:19Z<p>Af.simbaqueba218: </p>
<hr />
<div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T04:00:07Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photoone.jpg|400px|thumb|center]]<br />
[[File:Photo2.jpg|400px|thumb|center]]<br />
[[File:Photo3.jpg|400px|thumb|center]]<br />
[[File:Photo4.jpg|400px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/GalleryTeam:Colombia/Gallery2012-10-27T03:59:32Z<p>Af.simbaqueba218: /* Gallery */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Gallery ==<br />
<br />
[[File:video.jpg|400px|thumb|center]]<br />
Making the presentation video of our project.<br />
<br />
[[File:foro.jpg|400px|thumb|center]]<br />
After the forum: [http://2012.igem.org/Team:Colombia/Human/Research "Research in Colombia: Obtaining Research Permits, Contracts for Access to Genetic Resources and Biological Collections"] All of us so elegant for this important date!<br />
<br />
[[File:1110249.jpg|400px|thumb|center]]<br />
During one of our human practices activities with presentations in rural schools.<br />
<br />
[[File:colviv.jpg|400px|thumb|center]]<br />
Children from the school learning while playing<br />
<br />
[[File:jul.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Notebook/Protocols Minipreps!!!]<br />
<br />
[[File:claslab.jpg|400px|thumb|center]]<br />
During the [http://2012.igem.org/Team:Colombia/Notebook/Classes laboratory classes] at the beginning of our project.<br />
<br />
[[File:cafe.jpg|400px|thumb|center]]<br />
Taking care of coffee plants: So important for testing our design. Not everything is laboratory!<br />
<br />
[[File:chit.jpg|400px|thumb|center]]<br />
[http://2012.igem.org/Team:Colombia/Project/Experiments/Aliivibrio_and_Streptomyces Chitin!!] Getting it from shrimps.. Poor shrimps!<br />
</div><br />
<br />
[[File:Photo1.jpg|400px|thumb|center]]<br />
[[File:Photo2.jpg|400px|thumb|center]]<br />
[[File:Photo3.jpg|400px|thumb|center]]<br />
[[File:Photo4.jpg|400px|thumb|center]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/StochasticTeam:Colombia/Modeling/Stochastic2012-10-27T03:51:31Z<p>Af.simbaqueba218: /* Stochastic Model */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== '''Stochastic Model''' ==<br />
<br />
<p align="justify"><br />
<br />
The previous sections showed how to know the mean behavior of the system for one cell, but this is just an average of the total proteins within the cell. All the biological systems are controlled by probability events. The cell is a huge space where there are a lot of small molecules. If we want a biological process to happen, two of these molecules have to find each other among millions in a huge pool. The differential equations do not take into account these uncontrollable events that can change the response dramatically. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
If we look only at one cell, it may not behave like we want and the system may not respond. Even worse, the probability of dying exist and our cell may die. But dealing with one cell is not real and we always work with hundreds of cells. Within this population, some cells may not behave as expected but others will and the average of cells would be able to respond to the presence of the pest.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
The stochastic algorithms are a way to model these probability events within a population. This simulation is made in order to confirm that the system dynamics are robust, consistent and show us if the response is still behaving like we want (taking probabilities into consideration). We use the Gillespie algorithm to develop our model. Here is a brief explanation of how it works: <br />
<br />
The complete method consists of eight steps.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::#Define the number of cells.<br />
::#Define the number of steps<br />
::#Define and name all the constants involved.<br />
::#Define creation and destruction events for each substance involved: The differential equations in this part have to be divided in two, the creation and the destruction expression. <br />
::#Apply [http://www.annualreviews.org/doi/pdf/10.1146/annurev.physchem.58.032806.104637 Gilliespie algorithm:] <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::• Calculate the sample space of the analyzed system: This is the sum of all the changes presented at specific time "t". <br />
<br />
[[File:sampspa.png|center|200x100pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate time distribution that depends on a random number between 0 and 1.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:sampspa1.png|center|600x200pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate which event occurs: The Gillespie algorithm does not consider simultaneous events, this is that in each time only one event occurs. In this case, the events are the creation or destruction of one protein. Each event has a probability of occurrence within the sample space between 0 and 1. To know which event occurs at the time "t+1", we take into account the random number use for the time distribution and look for the event that has this probability of occurrence . For example, if you see the sample space figure below, there are 5 possible events with their probability; if the random number is 0.4 then A is going to be destructed but if the random number is 0.55. then B will be created. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:sampspa2.png|center|500x300pxpx]]<br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::6. Take the outputs from the simulation and convert them into regular interval vectors.<br />
::7. Obtain the Gillespie function mean values.<br />
::8. Plot the obtained functions.<br />
<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/StochasticTeam:Colombia/Modeling/Stochastic2012-10-27T03:51:08Z<p>Af.simbaqueba218: /* Stochastic Model */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== '''Stochastic Model''' ==<br />
<br />
<p align="justify"><br />
<br />
The previous sections showed how to know the mean behavior of the system for one cell, but this is just an average of the total proteins within the cell. All the biological systems are controlled by probability events. The cell is a huge space where there are a lot of small molecules. If we want a biological process to happen, two of these molecules have to find each other among millions in a huge pool. The differential equations do not take into account these uncontrollable events that can change the response dramatically. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
If we look only at one cell, it may not behave like we want and the system may not respond. Even worse, the probability of dying exist and our cell may die. But dealing with one cell is not real and we always work with hundreds of cells. Within this population, some cells may not behave as expected but others will and the average of cells would be able to respond to the presence of the pest.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
The stochastic algorithms are a way to model these probability events within a population. This simulation is made in order to confirm that the system dynamics are robust, consistent and show us if the response is still behaving like we want (taking probabilities into consideration). We use the Gillespie algorithm to develop our model. Here is a brief explanation of how it works: <br />
<br />
The complete method consists of eight steps.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::#Define the number of cells.<br />
::#Define the number of steps<br />
::#Define and name all the constants involved.<br />
::#Define creation and destruction events for each substance involved: The differential equations in this part have to be divided in two, the creation and the destruction expression. <br />
::#Apply [[http://www.annualreviews.org/doi/pdf/10.1146/annurev.physchem.58.032806.104637 Gilliespie algorithm:]] <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::• Calculate the sample space of the analyzed system: This is the sum of all the changes presented at specific time "t". <br />
<br />
[[File:sampspa.png|center|200x100pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate time distribution that depends on a random number between 0 and 1.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:sampspa1.png|center|600x200pxpx]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
:::•Calculate which event occurs: The Gillespie algorithm does not consider simultaneous events, this is that in each time only one event occurs. In this case, the events are the creation or destruction of one protein. Each event has a probability of occurrence within the sample space between 0 and 1. To know which event occurs at the time "t+1", we take into account the random number use for the time distribution and look for the event that has this probability of occurrence . For example, if you see the sample space figure below, there are 5 possible events with their probability; if the random number is 0.4 then A is going to be destructed but if the random number is 0.55. then B will be created. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:sampspa2.png|center|500x300pxpx]]<br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::6. Take the outputs from the simulation and convert them into regular interval vectors.<br />
::7. Obtain the Gillespie function mean values.<br />
::8. Plot the obtained functions.<br />
<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/AttributionsTeam:Colombia/Attributions2012-10-27T03:47:43Z<p>Af.simbaqueba218: /* Attributions */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''Attributions''' =<br />
<br />
'''1.'''We would like to thank iGEM Colombia Team 2011*. Their original idea of sensing a fungal plant pathogen through a system of two transgenic bacterial variants is extended our the actual project, facilitating and improving key aspects of part design and modeling. Their experience contributed not only with concepts and strategies, but also by aiding to prevent and/or address several issues and pitfalls we have come across in the development of our work. We want to briefly mention some aspects that makes our project different from the 2011's. The idea to use genetically modified bacteria to detect pathogen molecules in an early stage of pathogen invasion is maintained this year, however, no parts from the previous project were used in this year project. iGEM Colombia team 2011 aimed to detect coffee rust fungus ''Hemileia vastatrix'' only. This year's team extends the idea of pathogen detection to detect also a bacterial pathogen, ''Ralstonia solanacearum'', which is a vascular pathogen of tomato ''Solanum lycopersicum'' and potato ''Solanum tuberosum'', as well as other crop plants. Another key feature introduced this year is the toxin-antitoxin modules which will be used to control the bacterial population density, prevent horizontal gene transfer and plasmid curing (in an antibiotic free strategy).<br />
<br />
The full list of team members can be found at http://2011.igem.org/Team:Colombia/Team.<br />
<br />
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<body><br />
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<br />
'''2.'''The protocol for the persisters issolation we used is from the research work of Silvia Cañas (S. Cañas et al., manuscript in preparation, 2012). We thank Juan Manuel Pedraza, Silvia Restrepo and Sivia Cañas for lending us the protocol.<br />
<br />
'''3.'''We want to thank Lina Cabal for her help and advices to develop the layout of this page.<br />
<br />
'''4.'''Special thanks to Silvia Restrepo; her help, advices and accompaniment have been invaluable for this team.<br />
<br />
'''5.'''Special thanks to [http://medmicro.wisc.edu/people_faculty_profile.php?id=egruby&view=intro Dr. Edward Ruby] and [http://labs.medmicro.wisc.edu/ruby/members/ziegelhoffer/index.html Dr. Eva Ziegelhoffer] for gently providing the ''Aliivibrio fischeri'' ES114.<br />
<br />
'''6.'''Thanks also to [http://www.med.und.edu/microbiology/thomas-hill.cfm Dr. Thomas M. Hill] and [http://www.biology.neu.edu/faculty03/lewis03.html Dr. Kim Lewis] for providing us the ''E. coli'' strains: TH1269 and TH1268.<br />
<br />
'''7.''' We thank [http://lamfu/HOME/Home.html LAMFU] [http://cimic/Investigadores/jenny_dussan.htm CIMIC] and [http://biofisica.uniandes.edu.co/ Biophysics] labs for hosting our team!!! Thanks for the patience and collaboration!!<br />
<br />
'''8.''' For their collaboration with the organization of the Forum Research in Colombia: Obtaining Research Permits (Human Practice), Contracts for Access to Genetic Resources and Biological Collections, we want to thank:<br />
- Prof. Gonzalo Andrade, Universidad Nacional de Colombia.<br />
- Prof. Silvia Restrepo, Universidad de los Andes<br />
- Adriana Sierra, Public Relations, Universidad de los Andes.<br />
- Luisa Fernanda Bastidas, Public Relations, Universidad de los Andes.<br />
- Paola Pardo, Universidad de los Andes<br />
- Juan Gabriel Sutachan, Universidad de los Andes<br />
- Adriana Rosillo, Universidad de los Andes<br />
- Audiovisual Production – DTI, Universidad de los Andes<br />
- Facultad de Ciencias, Universidad de los Andes<br />
<br />
'''9.'''For their collaboration with the Social Schools and Coffee growers activities (Human Practice), we want to thank:<br />
- Federación Nacional de Cafeteros de Colombia<br />
- Dr. Fernando Gast, Federación Nacional de Cafeteros<br />
- Dr. Luis Francisco Useche Barbosa, Federación Nacional de Cafeteros<br />
- Mr. Leonardo Rojas, Federación Nacional de Cafeteros<br />
- Coffee Growers from Gualivá Region (Sasaima and Supatá)<br />
- Mrs. Patricia Méndez, Institución Educativa Rural San Bernardo, Sasaima.<br />
- Students and educational community of Institución Educativa Rural San Bernardo, Sasaima.<br />
<br />
'''10.'''Special thanks to Dr. Felipe Munoz Giraldo and all his research group to provide us computational resources (http://ingenieria.uniandes.edu.co/profesores/fmunoz/doku.php).<br />
<br />
'''11.'''Special thanks to Dr. Harold Castro and all his research group to provide us computational resources (http://sistemas.uniandes.edu.co/~hcastro/dokuwiki/doku.php).</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/AttributionsTeam:Colombia/Attributions2012-10-27T03:47:25Z<p>Af.simbaqueba218: /* Attributions */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
= '''Attributions''' =<br />
<br />
'''1.'''We would like to thank iGEM Colombia Team 2011*. Their original idea of sensing a fungal plant pathogen through a system of two transgenic bacterial variants is extended our the actual project, facilitating and improving key aspects of part design and modeling. Their experience contributed not only with concepts and strategies, but also by aiding to prevent and/or address several issues and pitfalls we have come across in the development of our work. We want to briefly mention some aspects that makes our project different from the 2011's. The idea to use genetically modified bacteria to detect pathogen molecules in an early stage of pathogen invasion is maintained this year, however, no parts from the previous project were used in this year project. iGEM Colombia team 2011 aimed to detect coffee rust fungus ''Hemileia vastatrix'' only. This year's team extends the idea of pathogen detection to detect also a bacterial pathogen, ''Ralstonia solanacearum'', which is a vascular pathogen of tomato ''Solanum lycopersicum'' and potato ''Solanum tuberosum'', as well as other crop plants. Another key feature introduced this year is the toxin-antitoxin modules which will be used to control the bacterial population density, prevent horizontal gene transfer and plasmid curing (in an antibiotic free strategy).<br />
<br />
The full list of team members can be found at http://2011.igem.org/Team:Colombia/Team.<br />
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'''2.'''The protocol for the persisters issolation we used is from the research work of Silvia Cañas (S. Cañas et al., manuscript in preparation, 2012). We thank Juan Manuel Pedraza, Silvia Restrepo and Sivia Cañas for lending us the protocol.<br />
<br />
'''3.'''We want to thank Lina Cabal for her help and advices to develop the layout of this page.<br />
<br />
'''4.'''Special thanks to Silvia Restrepo; her help, advices and accompaniment have been invaluable for this team.<br />
<br />
'''5.'''Special thanks to [http://medmicro.wisc.edu/people_faculty_profile.php?id=egruby&view=intro Dr. Edward Ruby] and [http://labs.medmicro.wisc.edu/ruby/members/ziegelhoffer/index.html Dr. Eva Ziegelhoffer] for gently providing the ''Aliivibrio fischeri'' ES114.<br />
<br />
'''6.'''Thanks also to [http://www.med.und.edu/microbiology/thomas-hill.cfm Dr. Thomas M. Hill] and [http://www.biology.neu.edu/faculty03/lewis03.html Dr. Kim Lewis] for providing us the ''E. coli'' strains: TH1269 and TH1268.<br />
<br />
'''7.''' We thank [http://lamfu/HOME/Home.html LAMFU] [http://cimic/Investigadores/jenny_dussan.htm CIMIC] and [http://biofisica.uniandes.edu.co/ Biophysics] labs for hosting our team!!! Thanks for the patience and collaboration!!<br />
<br />
'''8.''' For their collaboration with the organization of the Forum Research in Colombia: Obtaining Research Permits (Human Practice), Contracts for Access to Genetic Resources and Biological Collections, we want to thank:<br />
- Prof. Gonzalo Andrade, Universidad Nacional de Colombia.<br />
- Prof. Silvia Restrepo, Universidad de los Andes<br />
- Adriana Sierra, Public Relations, Universidad de los Andes.<br />
- Luisa Fernanda Bastidas, Public Relations, Universidad de los Andes.<br />
- Paola Pardo, Universidad de los Andes<br />
- Juan Gabriel Sutachan, Universidad de los Andes<br />
- Adriana Rosillo, Universidad de los Andes<br />
- Audiovisual Production – DTI, Universidad de los Andes<br />
- Facultad de Ciencias, Universidad de los Andes<br />
<br />
'''9.'''For their collaboration with the Social Schools and Coffee growers activities (Human Practice), we want to thank:<br />
- Federación Nacional de Cafeteros de Colombia<br />
- Dr. Fernando Gast, Federación Nacional de Cafeteros<br />
- Dr. Luis Francisco Useche Barbosa, Federación Nacional de Cafeteros<br />
- Mr. Leonardo Rojas, Federación Nacional de Cafeteros<br />
- Coffee Growers from Gualivá Region (Sasaima and Supatá)<br />
- Mrs. Patricia Méndez, Institución Educativa Rural San Bernardo, Sasaima.<br />
- Students and educational community of Institución Educativa Rural San Bernardo, Sasaima.<br />
<br />
'''10.'''Special thanks to Dr. Felipe Munoz Giraldo and all his research group to provide us computational resources (http://ingenieria.uniandes.edu.co/profesores/fmunoz/doku.php).<br />
<br />
'''10.'''Special thanks to Dr. Harold Castro and all his research group to provide us computational resources (http://sistemas.uniandes.edu.co/~hcastro/dokuwiki/doku.php).</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:40:44Z<p>Af.simbaqueba218: /* Mathematical Model Description */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|500px|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/Ecological_ModelTeam:Colombia/Modeling/Ecological Model2012-10-27T03:40:19Z<p>Af.simbaqueba218: /* Mathematical Model Description */</p>
<hr />
<div><html><br />
<br><br />
</br><br />
</html><br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Implementation Model=<br />
<br />
'''General objective'''<br />
<br />
To generate a computational model that simulates the most relevant relationships between our engineered system and the plant pathogens inside the appropriate habitat for the Rust control.<br />
<br />
'''Specific Objectives'''<br />
<br />
- To limit the multifactorial ecological problem in a way that a simple mathematical model may be proposed. Such model should be able to answer relevant questions regarding the implementation method.<br />
<br />
- To find the populational proportions between our organism and the plant pathogens that optimize our biological control.<br />
<br />
- To generate hypotheses for future experimental confirmations.<br />
<br />
==Biological Panorama==<br />
<br />
Coffee Rust dispersion is based on the generation of [http://botanydictionary.org/uredospore.html uredospores]. These are dispersed by wind and water predominantly, as well as by active animal or human dispersion. These spores require about 24 to 48 hours of free continuous humidity, so the infection process usually occur only during rainy seasons. The fungus grows as a [http://en.wikipedia.org/wiki/Mycelium mycelium] on the leaves of the plant, and the generation of new spores takes about 10 to 14 days. Since leaves drop prematurely, this effectively removes important quantities of epidemic potential inoculum; nevertheless, a few green leaves will survive through the dry season. Dry uredospores may live for about 6 weeks. In this way, there is always a viable inoculum capable of infecting new leaves ath the beginning of the next rainy season.<br />
<br />
In this year's iGEM, our main goal is to significatively reduce the mycelial form of the fungus in order to control inocula from a season to the next. The way this works is by spraying bacteria on top of the leaves of the plants, however, the amount and concentration of bacteria are not known. Thanks to a [http://2012.igem.org/Team:Colombia/Project/Experiments/Our_Design population control system by toxin-antitoxin modules], a small fraction (near 15%) of the bacterial population will live in a persistant state. Persister cells have very low metabolic rates. Non-persister active cells, even though more sensitive to environmental hazards, readily detect fungal infections. If a determined chitin profile (based on our [http://2012.igem.org/Team:Colombia/Modeling/Paramterers molecular mathematical models]) is detected, active bacteria are stimulated in a way that they are capable of secreting a plant hormone to induce its natural defense responses.<br />
<br />
==Mathematical Model Description==<br />
<br />
Let's begin with the expected dynamics for the inoculated bacteria in absence of a fungal infection (''R'' variable). An initial number of bacteria (''B'' variable) are sprayed on the leaf. As mentioned earlier, these may be in a persistant (''I'' variable) or active (''A^--'' variable) state in a 15:85 ratio. By assuming persistence as a static metabolic state, persister death rate is neglected. On the other hand, active bacteria die with a given rate (''delta_A'' parameter per active bacterium). However, these populations are maintained through a dynamic equilibrium with a persistance transition rate (''gamma_1'' parameter per active bacterium), and another one in the reverse direction (''alpha(R)'' parameter per persister bacterium). The ''alpha(R)'' parameter should, in principle, have a term independant of ''R'' in order to maintain the described equilibrium. If this were not true, ''A^-'' would have no population inputs and would decay to zero in steady state.<br />
<br />
In the presence of fungi, cells should wake up more often (which should be included in the ''alpha(R)'' parameter). Additionally, the ''A^--'' population should generate a stimulated cell population (''A^+'' variable) at a certain rate (''sigma(R)'' parameter per inactive bacterium). Stimulated bacteria are capable of producing salycilic acid, a plant hormone that induces plant defense mechanisms that should decrease fungal populations at a given rate (''delta_R(A^+)'' per fungus). The only fungi relevant to our model are those who already germinated from the uredospores and are infecting the plant (i.e., that are in a mycelial form). Taking this into account, their random removal and natural death rates are neglected. In the same fashion as with the active cell population, stimulated once are capable of returning to a persister state with a certain rate (''gamma_2'' parameter per stimulated bacterium) and also eventually die at a given rate (which we approximated to be comparable to the active one's). Persister state stimulating toxins act at a intercellular level, so cell cross-activation/inactivation phenomena are discarded. The following schematic represents the expected population dynamics for this model for a single infection cycle. Subsequent cycles should work in a similar fashion, where the next cycle's inputs are the previous cycle's outputs.<br />
<br />
[[File:ecomoda.png|thumb|center|Figure 1. Expected population dynamics ]]<br />
<br />
The following table indicates the different parameters and variables of our system, together with its units and explanation.<br />
<br />
[[File:ecotabla.png|center|thumb|700px|Table 1. Parameters and variables of this system ]]<br />
<br />
=== Differential Equations ===<br />
<br />
From the schematic above the following ordinary differential equations were constructed:<br />
<br />
[[File:ecodif.png|center]]<br />
<br />
As well as the following initial conditions:<br />
<br />
[[File:ecocondin.png|center]]<br />
<br />
=== Inferences from the Molecular Mathematical Model===<br />
<br />
First of all we had to find our parameters' values, as well as define some of those more thoroughly.<br />
<br />
- ''alpha(R)'': As mentioned earlier, this parameter should have both ''R'' dependent and independent terms. The independent term was searched for in literature, where we found it to be 0.1 h^-1 (Balaban et al, 2004). For the ''R'' dependent term, we thought of two possibilities. The first one that it may be aproximated as a line in the form of ''beta*R'', and the second one as a heaviside function (step function). In order to answer this, we went back to our original mathematical molecular model and plotted chitin concentration against the difference between toxin and antitoxin concentrations. This should give us an idea of the shape of the function we are looking for. The following figure shows how ''alpha(R)'' heavily resembles a line, so we went for the linear option (''beta'' slope = 0.103562).<br />
<br />
[[File:figuraalfa.png|center|500px|thumb|Figure 2. Toxin-Antitoxin levels as a function of chitin concentration ]]<br />
<br />
- ''sigma(R)'': Because of the way that we defined our bacterial states, there is no way that there are intermediate states between our activated and stimulated populations. With this in mindo we decided that the stimulation transition state was to be described with a heaviside step function. This function's value is zero until a certain criterion is met. In our case, that is that the R value surpasses a given threshold. Since we were not able to measure how much chitin in a Coffee Rust sample, we decided to transform our ''R'' function to a chitin function. This should not be a problem since their relationship should behave linearly. As a way to define an ''Rnot'', that is, the chitin threshold for successful stimulation, we went back to our molecular mathematical model and plotted chitin concentration against salycilic acid. The chitin concentration that gave us half the maximum production of salycilic acid would be the value chosen for ''Rnot''. We successfully estimated ''Rnot'' = 0.19124 mM from the following figure.<br />
<br />
[[File:figurarnot.png|center|500px|thumb|Figure 3. Salycilic acid level as a function of chitin concentration]]<br />
<br />
- ''gamma_1'': We looked for persistence transition rates in the literature and found that ''gamma_1'' = 1.2e-6 h^-1(Balaban et al, 2004).<br />
<br />
- ''gamma_2'': Since we haven't measured our own final stimulated bacteria persistence transition rate, we estimated it to be about 5% of ''gamma_1''. We have engineered our system in such a way that ''gamma_1'' should be a lot greater that ''gamma_2'', so 5% is actually an overestimation.<br />
<br />
- ''delta_A'': [http://2011.igem.org/Team:Colombia Last year's Colombia iGEM team] measured the ''Escherichia coli'' DH5alpha and ''E. coli'' K12 survival on top of the coffee plants for 48 hours (measurements not in wiki). They inoculated a total of 500 UFC/leaf at the starting time and observed the remaining UFC/leaf 24 aand 48 hours later. The following graph shows their results. We fitted the average of both columns into an exponential distribution and estimated ''delta_A'' = 0.035 h^-1.<br />
<br />
[[File:leafcount.png|center|500px|thumb|Figure 4. E. coli survival in coffee leaves]]<br />
<br />
- ''delta_R(A^+)'': Since the plant's response is the disposal of the whole leaf, and we are currently modeling a single leaf, we decided to use an inverse heaviside step function for this parameter. In words, once the stimulated bacterial cell population reaches a certain threshold, all living fungi will die off the leaf, because the Coffee Rust needs its host to be alive in order to live. We named this threshold ''Anot''. Ideally, we need to estimate, given our current molecular constructions, how much Salycilic Acid is produced per stimulated cell in order to determine ''Anot'', as well as what is the minumum amount of salycilic acid the plant needs to optimize its defense response. Unfortunately, such measurements have not been made yet. In the next sections we check that our model works correctly and discuss a method to calculate the optimal amount of bacteria to spray onto the leaf for optimal implementation.<br />
<br />
=== Implementation Model scripting check ===<br />
<br />
As mentioned earlier, we are one parameter short (''Anot'') to be able to objectively minimize the number of bacteria needed to be sprayed onto the leaves for a successful biological control. However, we guesstimated both ''B'' and ''Anot'' in order to see how our model's results should look like. We wrote the following two codes that solve our differential equations:<br />
<br />
% Differential Equations<br />
<br />
function output = ode(dt, v)<br />
<br />
%% Biological Parameters<br />
<br />
alpha = 0.1; % basal wake up rate Balaban et al [1/h]<br />
beta = 0.103562; % chitin induced wake up rate<br />
Rnot = 0.19124; % The amount of chitin necessary to activate 'a'<br />
gamma1 = 1.2e-6; % 'a'sleep rate [1/h]<br />
gamma2 = 0.05*gamma1; % 'A' sleep rate [1/h]<br />
deltaA = 0.035; % E.coli death rate in leaves [1/h]<br />
Anot = 3500; % 'A' cells required for effective plant defense induction<br />
<br />
%% Differential Equations<br />
<br />
I = v(1); % Import 'I' cell number<br />
a = v(2); % Import 'a' cell number<br />
A = v(3); % Import 'A' cell number<br />
R = v(4); % Import 'R' chitin concentration<br />
<br />
dI = gamma1*a + gamma2*A - (alpha + beta*R)*I;<br />
% 'I' cell ODE<br />
<br />
da = (alpha + beta*R)*I - gamma1*a - heaviside(R - Rnot)*a - deltaA*a;<br />
% 'a' cell ODE<br />
<br />
dA = heaviside(R - Rnot)*a - gamma2*A - deltaA*A;<br />
% 'A' cell ODE<br />
<br />
if A < Anot % Plant Defense check<br />
dR = 0;<br />
else dR = -R;<br />
end<br />
<br />
output1(1) = dI;<br />
output1(2) = da;<br />
output1(3) = dA;<br />
output1(4) = dR;<br />
<br />
output = output1';<br />
<br />
end<br />
<br />
%Solver Implementation model<br />
<br />
clear; clc; close all;<br />
<br />
%% Biological Parameters<br />
<br />
B = 5e3; % Number of initial bacteria<br />
a0 = 0.85*B; % Estimated basal 'a' cell proportion<br />
I0 = 0.15*B; % Estimated basal persister proportion<br />
R0 = 0.2; % Successful Pestbuster response chitin concentration<br />
A0 = 0; % Initial activated 'a' cells<br />
<br />
%% Solver Parameters<br />
<br />
h = 50; % Maximum Time<br />
<br />
m = 0.01; % Time step [h]<br />
<br />
t = 0:m:h; % Time Vector<br />
<br />
l = (0:m:h)'; % Column time vector<br />
<br />
x = zeros(length(l), 4); % Result matriz initialization<br />
% Columns represent I, a, A, and R quantities<br />
% Rows represent each time step<br />
<br />
x(1,:) = [I0 a0 A0 R0]; % Initial conditions<br />
<br />
%% Differential equation 4th order Runge-Kutta method (RK4)<br />
<br />
for k = 1:length(l) - 1<br />
<br />
xk = x(k,:); % Extract most recent population numbers<br />
<br />
k1 = ode(l(k),xk); % First RK4 slope<br />
k2 = ode(l(k) + m/2,xk + (m/2*k1)'); % Second RK4 slope<br />
k3 = ode(l(k) + m/2,xk + (m/2*k2)'); % Third RK4 slope<br />
k4 = ode(l(k) + m,xk + (m*k3)'); % Fourth RK4 slope<br />
<br />
xk1 = xk + m/6*(k1 + 2*k2 + 2*k3 + k4)';<br />
% New population numbers calculation<br />
<br />
xk2 = zeros(1,length(xk1));<br />
% Row vector initialization<br />
<br />
for p = 1:length(xk1)<br />
<br />
if(xk1(p) < 0.00000001) % Tolerance check<br />
<br />
xk2(p) = 0;<br />
else<br />
xk2(p) = xk1(p);<br />
end<br />
end<br />
<br />
x(k + 1,:) = xk2(:);<br />
end<br />
<br />
%% Plots<br />
<br />
I = x(:,1); % 'I' cell vector<br />
a = x(:,2); % 'a' cell vector<br />
A = x(:,3); % 'A' cell vector<br />
R = x(:,4); % Chitin vector<br />
<br />
figure<br />
subplot(2,2,1)<br />
P1 = plot(l,I);<br />
set(P1,'LineWidth',2)<br />
title('Persister Cells [I]')<br />
xlabel('Time [h]')<br />
ylabel('Persister Cell Number')<br />
<br />
subplot(2,2,2)<br />
P2 = plot(l,a);<br />
set(P2,'LineWidth',2)<br />
title('Unstimulated Woken up Cells [a]')<br />
xlabel('Time [h]')<br />
ylabel('Unsitmulated Woken up Cell Number')<br />
<br />
subplot(2,2,3)<br />
P3 = plot(l,A);<br />
set(P3,'LineWidth',2)<br />
title('Activated Cells [A]')<br />
xlabel('Time [h]')<br />
ylabel('Activated Cell Number')<br />
<br />
subplot(2,2,4)<br />
P4 = plot(l,R);<br />
set(P4,'LineWidth',2)<br />
title('Rust fungi [R]')<br />
xlabel('Time [h]')<br />
ylabel('Leaf Chitin Concentration')<br />
<br />
If you run these codes you get the following plots:<br />
<br />
[[File:elcheck.jpg|center|700px|thumb|Figure 5. Model check results]]<br />
<br />
== Model Results ==<br />
<br />
While we are waiting for experimental results to be able to infer the minimum Bacterial numbers to spray into the plant, we have deviced a method to calculate this number once we know ''Anot''.<br />
<br />
==References==<br />
#Balaban, N. Q., Merrin, J., Chait, R., Kowalik, L., & Leibler, S. (2004). Bacterial persistence as a phenotypic switch. Science (New York, N.Y.), 305(5690), 1622–5. doi:10.1126/science.1099390</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:33:30Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Toxin/Antitoxin module substances]] [[File: rust5.png|center|thumb|450x450pxpx|Figure 12. CI and Salycilic Acid response]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:58Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Toxin/Antitoxin module substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:29Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Lux I - LuxR system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Detection system substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:32:02Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx|Figure 10. Detection system substances]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx|Figure 11. Detection system substances]] [[File: rust5.png|center|450x450pxpx|Figure 12. Detection system substances]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:30:58Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system substances]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:30:44Z<p>Af.simbaqueba218: /* Rust: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx|thumb|Figure 9. Detection system]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|thumb|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|thumb|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:29:57Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. CI and Salycilic Acid response ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:29:28Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|Figure 7. Toxin/Antitoxin response]] [[File: ral5.png|center|thumb|450x450pxpx|Figure 8. ]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:28:40Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR response ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|thumb|450x450pxpx|]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:27:45Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. Behavior of the LuxI - LuxR ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:27:10Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the activator response ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|thumb|450x450pxpx|Figure 6. ]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:26:26Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor phcS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|Figure 5. Behavior of the ]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:25:54Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure 4. Behavior of the sensor PchS ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:25:17Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|Figure ]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:24:49Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|thumb|450x450pxpx|]] <br />
[[File: ral2.png|center|thumb|450x450pxpx|]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:23:55Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
<br />
[[File:Ral1.png|center|450x450pxpx]] <br />
[[File: ral2.png|center|450x450pxpx]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T03:23:41Z<p>Af.simbaqueba218: /* Ralstonia: */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Results ==<br />
<br />
<br />
<p align="justify"><br />
<br />
<br />
The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
The new system is showed in the figure below: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
<br />
</p> <br />
<br />
<br><br />
<br><br />
<br />
== Differential equations results ==<br />
<br />
<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br><br />
<br />
===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
[[File:Ral1.png|center|450x450pxpx]] <br />
[[File: ral2.png|center|450x450pxpx]]<br />
<br />
<br />
<br><br />
<br />
The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
<br />
[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
<br />
[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
<br />
<br><br />
<br />
===='''Rust:'''====<br />
<br />
When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
<br />
Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
<br />
[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/TeamTeam:Colombia/Team2012-10-27T03:22:13Z<p>Af.simbaqueba218: /* Diana Sanchez */</p>
<hr />
<div>{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
=The Team=<br />
<br />
Our team is comprised by students from the biological sciences, chemical and biomedical engineering, physics, and mathematics departments at the Universidad de Los Andes at Bogotá, Colombia.<br />
<br />
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[[File:Colombia_iGE.JPG|650px|thumb|center]]<br />
<br />
<br />
-----<br />
<br />
==Undergrads==<br />
<br />
===Daniel Giraldo===<br />
[[File:Daniel Giraldo.jpg|200px|thumb|right]] Daniel is an undergraduate Chemistry and Chemical Engineering double major senior at Universidad de los Andes. Although he decided to study Chemistry, he has always had an interest for science and is always eager to learn about other fields. He is very interested in learning more about organic chemistry applied to biological systems, which is why iGem is the perfect opportunity for him to explore a little bit into microbiology and synthetic biology. His very passionate about research and working at the lab. Currently he is working in the Ralstonia group at iGem Colombia.<br />
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===Daniela Olivera===<br />
<br />
[[File:DOM1.jpg|thumb|left|130px]]<br />
Daniela is an undergraduate student in Chemical engineering and Microbiology at the Universidad de los Andes. She is interested in bioinformatic and biomedical engineering research. Currenly, she is one of the outstanding students in chemical engineering department and there are too many proffesors that wants her in their research groups. She loves to spend her little free time playing with her cat (named Anastasia), working on iGEM with her lucky friends, going to cinema and burning calories in the gym.<br />
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===David A. Ayala-Usma===<br />
<br />
[[File:david_ayala_2012.jpg|200px|thumb|right]] David is an undergraduate senior of Biology and Microbiology that, one day, simply was in the right place to get involved with iGEM and Synthetic Biology. He likes Molecular Cell Biology, Paleoecology, Geosciences, Astronomy, and some other science stuff. Also, he loves reading all kinds of tales and stories for children (like him), eating desserts, looking at the sky, taking pictures, playing at the PC, sleeping a lot, and talking, and talking, and talking... xD<br />
<br />
He expects to eventually become a Ph.D. in Cell Biology, Earth Sciences, both or something in between, just to make a life and a living out of his passions, his favorite molecules, and discovering new exciting things.<br />
He also likes to be in contact with people around the world, and invites people with his same interests to add him on [http://www.twitter.com/EstadoAlternado Twitter] or [http://www.facebook.com/ayala.usma Facebook].<br />
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===Juanita Lara===<br />
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[[File:Juana.jpeg|150px|thumb|left]]<br />
Juanita is a biology and physics undergraduate student. She is very passionate about science and unveiling the mechanisms underlying biological systems is what she wants to do in life. For that reason she joined the Biophysics Group at Universidad de Los Andes, and is currently working on the characterization of thermosensors in ''Bacillus subtilis'' using molecular biology techniques and biophysical approaches. She sees in iGEM a great opportunity to meet new people and have the chance to learn from them. <br />
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===Laura Rodriguez===<br />
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[[File:Laura.jpg|150px|thumb|right]]<br />
<br />
Laura is an undergraduate student in Chemistry and Microbiology at Universidad de los Andes. She is passionate about science, likes organic chemistry and loves bacteria! She is also curious and a realll hard worker. For her, iGEM has been an opportunity to learn, practice lab skills and making good friends! Currently she is working in the Ralstonia group at iGEM Colombia. She is really excited to meet people involved in science from another countries, this will give her a perspective of science outside her country and will also be a cultural enriching experience.<br />
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=== '''Javier E. Vargas'''===<br />
[[File:javier.JPG|150px|thumb|left]]Javier already finished his thesis for the B.Sc. in Microbiology, but also is currently a senior student of Design at the Universidad de Los Andes. During his Microbiology thesis, he worked with the S-layer protein of [http://microbewiki.kenyon.edu/index.php/Lysinibacillus_sphaericus_C3-41 ''Lysinibacillus sphaericus''] applied to bioremediation of chromium using an immobilization matrix to improve the protein stability. In general, He is interested in molecular biology, synthetic biology, experience design and design of narratives. Also, he practices soft combat, fencing, climbing and enjoys painting (a lot).<br />
<br />
iGEM is a great opportunity to apply his knowledge and creative instinct to demonstrate him self their capacities, gaining more lab experience while doing what he likes the most.<br />
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===David Alejandro García===<br />
<br />
[[File:deivid_alejandrou.JPG|150px|thumb|right]]David is pursuing a degree in physics and mathematics as a member of the University of the Andes` class of 2014. David decided to participate in iGEM because he felt it would be an excellent opportunity to understand and manipulate the brick of the life to solve a big spectrum of problems. Outside the lab, David spends his free time playing the piano, reading some philosophy and literature, swimming. David also participates in a wide variety of academic activities such as in the “problem clinic” where he helps other students to solve difficulties in the resolution of problems in physics and being a prefect in a class of nanotechnology. After graduation, he wants to pursue a PhD in theoretical physics or nanotechnology<br />
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===César Augusto Quintana===<br />
<br />
[[File:Cesitar.JPG|150px|thumb|left]]Cesar was born in Popayan (Cauca), he is a Physics and mathematics undergraduate student at the “Universidad de los Andes”. He began participating in this project because of an enormous interest in life systems founding along this time a crescent fascination about the theme. Beside science he likes a lot to play the acoustic guitar and watch movies.<br />
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===Luis Alberto Gutiérrez López===<br />
[[File:Luis.JPG|150px|thumb|right]]Luis is an undergraduate Physics student at the Universidad de los Andes. Since his school years he’s been interested in science, deeply fascinated by the way our Universe works and particularly by the mechanisms of life. His interest in biology led him to explore other fields like physics. This passion for science and knowledge made him a very devoted student which enabled him to be awarded as Best High School Graduate of Colombia in 2011.<br />
<br />
Besides his enthusiasm for study, he loves physical activity, especially swimming and jogging. He also enjoys literature.<br />
<br />
He decided to join iGEM because he considers it an excellent opportunity to become familiar with research and learn many useful things about molecular biology, mathematics and programming.<br />
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===Roberto Moran Tovar===<br />
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[[File:561311_3727288733798_169786548_n.jpg|thumb|left|150px]]<br />
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Roberto is a second year undergraduate Physics and Mathematics student at Los Andes University. He loves physics since he was at high school and thinks that the science ( specially physics) is the most amazing thing that could exist. Recently, he has been interested in the study of life, evolution and in general the whole biology. He thinks his best quality is the curiosity because lets him to explore the universe in a very funny way! He is a good soccer player, likes to play video games and likes good Rock&Roll.<br />
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===Diana Wilches===<br />
[[File:dianaw.jpg|thumb|right|150px]]<br />
Diana is a B.Sc in Biology and a last year Microbiology undergraduate student of the Universidad de los Andes. She is highly interested in Environmental Science and Biotechnology, mainly in the development of strategies and alternatives that could allow to reduce the impact of the human being in the world. With this aim, she has worked in biological control of insects, bioremediation and with this iGEM project she wants to help in the development of new alternatives to the use of chemicals products in agriculture. Furthermore, Diana is passionate for traveling, old history, languages and cultural exchange.<br />
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===[https://www.facebook.com/ksk89 Gabriel Martínez-Gálvez]===<br />
<br />
[[File:GMG.jpg|thumb|left|150px]]<br />
<br />
Gabriel is a B.Sc. in microbiology and last year student in biomedical engineering (minor in physics). He is also a gamer to the bone, and a heavy soccer and basketball fan. Since high school he found it fascinating and exciting to think about programming cells into living bio-robots automated to perform specific actions inside the human body. For that matter he found systems biology and synthetic biology to be his main motivations for his studies and graduation thesis with the [http://openwetware.org/wiki/Biophysics Biophysics Lab] at the [http://www.uniandes.edu.co/component/content/article/656-about-uniandes Universidad de los Andes].<br />
<br />
He is very interested in the design of new biological processes through synthetic biology, [http://en.wikipedia.org/wiki/Dendritic_cell dendritic cell] information integration towards specific immune response coordination in humans as well as [http://pubs.acs.org/doi/abs/10.1021/ed042p49?journalCode=jceda8 molecular psychology] for a better understanding of emotions and aging phenomena. Feel free to follow him on [https://twitter.com/ksk_89 twitter] or challenge him in [http://us.playstation.com/psn/#?psnId=network_psn PSN] (PSN ID: ksk_89)!<br />
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===Diana Sanchez===<br />
[[File:ds.jpg|thumb|right|150px]]<br />
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Diana is a design student with emphasis on communication design and textile design. She has high interest in the dialogue between arts and science. Especially in biodesign, perception, interaction design, and art direction.<br />
Her projects focus on the boundaries between the biological and the technological and how this changes our perception. She has also worked as a Field Researcher at future trends in the Observatorio de Tendencias de la Cámara de Comercio de Bogotá and Future Concept Lab Milan.<br />
She is interested in how science can bring metaphores and processes to design manifestations that allow us to experience the world in a more significant way.<br />
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===Luz Alba Gallo===<br />
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Luz is a last year Design student. Her focus is on social innovation and strategy. In the last year she had the opportunity to work on a project named "Let's meet your baby!" that was related with maternal health in low income communities. Also she is an active participant in Design communities such as OpenIdeo and TechoLab. She is interested in the posssiblities that the Design offers to all the other areas of knowledge to improve the life quality and the world. <br />
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==Grad Students==<br />
===Silvia J. Cañas===<br />
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[[File:SilviaC.jpg|thumb|left|180px]] Silvia is a M.Sc student in Biological Sciences (Microbiology) at the Biophysics Laboratory and the Mycology and Phytopathology Laboratory (LAMFU) at the Universidad de los Andes. She is a B. Sc in Microbiology and B. Sc in Chemical Engineering of the Universidad de los Andes (Minors in ''Bioinformatics'' and ''Bioengineering''), where she worked with Metabolic engineering. Her main areas of interest are '''Molecular Cell Biology''' and '''Systems & Synthetic Biology'''. She is currently investigating the effect of Sigma factors transitivity on persisters generation in ''Escherichia coli K12'' . Some of the approaches she is using are based on Molecular Biology, Systems Biology & Epifluorescence Microscopy<br />
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===Vivian Bernal Galeano===<br />
[[File:Vivian.jpg|thumb|right|140px]] Vivian is a M.Sc student in Biological Sciences at the Laboratory of Mycology and Phytopathology at the Universidad de los Andes. She is a Bachelor in Biology of the Universidad Nacional de Colombia. She has worked in the area of molecular phytopathology, in the pathosystem Cassava-''Xanthomonas axonopodis'' pv. manithotis (''Xam''), for two and half years and currently she has studied the small ncRNA of ''Xam''. Her role in the iGEM Team is to participate in the lab activities and to coordinate, plan and develop, with her teammates, the activities related to the human practices, she enjoys that!!<br />
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===Paola Reyes===<br />
[[File:379523 128088457300454 728084190 n.jpeg|150px|thumb|left]]Paola is a pretty enthusiastic Master Student at the Laboratory of Mycology and Phytopathology of Universidad de los Andes. She has been working in molecular biology for more than two years now. Her research interest is the molecular interaction between plants and phytopathogenic bacteria. Her role in the iGEM team has been to help undergraduate students on wet lab activities and in diverse areas. She loves drama but she is kind of cool most of the time.<br />
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===Laura Avelleneda Franco===<br />
[[File:avefra.JPG|150px|thumb|right]]Laura holds a B.Sc in Chemical Engineer, and a B.Sc in Microbiology, both from Universidad de los Andes. She is a second year M.Sc student of Biological Sciences at the Center of Microbiology Research (CIMIC) at the Universidad de los Andes. She is interested in biotechnology from molecular scale to industrial scale. She is excited for new branches of biotechnology such as synthetic and systems biology. She believes that the deciphering of new biological pathways from genes to signal cascades are highly important for the research and development of new products and processes.<br />
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===Andrés Felipe Simbaqueba Sánchez===<br />
[[File:me.jpg|thumb|left|150px]] Andrés Felipe was born in Florencia (and that’s at Colombia) and he is a Chemical Engineer and M.Sc student in Chemical Engineering at Universidad de los Andes. Actually, he has been researching in bioindustrial processes in order to produce biofuels from cellulosic biomass. He thinks that iGEM is a good opportunity to understand biological processes from a more scientific point of view. However, his life is not reduced only to full-time researching... also he spends his little free time going to the cinema, hanging out with some lucky friends, meeting new people and traveling around the whole world. Feel free to follow him on [https://https://twitter.com/TheWhiteLion89 twitter]<br />
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===Estefanía Luengas===<br />
[[File:StefL20.JPG|thumb|right|150px]]I am interested in the geographic referencing and analysis of biological data. I have worked in landscape transformation for a coffee certificate, databases development for social cartography and development and standardization of cartographic databases of administrative data for social processes. Currently, I am working in early stages on climatic modeling of ''Phytophthora infestans'', the causal agent of potato late blight, involving collection to determinate severity curves.<br />
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===Juan Enciso===<br />
[[File:enciso.png|thumb|left|150px]] Juan is a M.Sc. student in Biological Sciences at Universidad de los Andes. His interests lie in the fields of bioinformatics and molecular evolution. He's currently searching novel groups of Oomycetes, organisms which include several important animal and plant pathogens such as ''Phytophthora sp.'' and ''Saprolegnia sp.'', among others.<br />
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== Instructors ==<br />
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==='''Silvia Restrepo Restrepo, Ph. D.===<br />
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[[image:Silvia_restrepo_restrepo.PNG|left|none|thumb|Silvia Restrepo, Ph. D.]] Dr. Restrepo is the leader and main researcher at the [http://lamfu.uniandes.edu.co Laboratory of Mycology and Phytopathology] of the [http://www.uniandes.edu.co Universidad de los Andes]. Additionally, she is the dean of the [http://cienciasbiologicas.uniandes.edu.co Department of Biological Sciences].Her main research topic is phytopathology, and her favorite organism is ''Phytophthora infestans'', of course!. <br />
'''Website''': [http://lamfu.uniandes.edu.co/RESEARCH/Silvia_Restrepo.html Lab Page]<br />
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==='''Juan Manuel Pedraza, Ph. D.'''===<br />
[[image:JuanPedraza.jpg|right|none|thumb|Juan Manuel Pedraza, Ph. D.]]<br />
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Dr. Pedraza leads the Systems/Synthetic Biology division of the Biophysics Laboratory at Uniandes. His specialty is stochasticity in gene expression, but is getting more and more interested in evolution and the consequences of phenotypic variability.<br />
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==='''Adriana Bernal, Ph. D.'''===<br />
[[image:Adriana_Bernal.JPG|left|none|thumb|Adriana Bernal, Ph. D.]]<br />
Dr. Bernal is a Associated Proessor at the Universidad de los Andes, her main research topic is the Plant-Pathogen interactions of ''Xanthomonas axonopodis pv. manihotis'' with its main host. She is the co-director of LAMFU with Dr. Silvia Restrepo.<br />
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Webpage: [http://lamfu.uniandes.edu.co/RESEARCH/Adriana_Bernal.html LAMFU Webpage]<br />
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</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/TeamTeam:Colombia/Team2012-10-27T03:21:15Z<p>Af.simbaqueba218: /* The Team */</p>
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<div>{{http://2012.igem.org/User:Tabima}}<br />
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=The Team=<br />
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Our team is comprised by students from the biological sciences, chemical and biomedical engineering, physics, and mathematics departments at the Universidad de Los Andes at Bogotá, Colombia.<br />
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==Undergrads==<br />
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===Daniel Giraldo===<br />
[[File:Daniel Giraldo.jpg|200px|thumb|right]] Daniel is an undergraduate Chemistry and Chemical Engineering double major senior at Universidad de los Andes. Although he decided to study Chemistry, he has always had an interest for science and is always eager to learn about other fields. He is very interested in learning more about organic chemistry applied to biological systems, which is why iGem is the perfect opportunity for him to explore a little bit into microbiology and synthetic biology. His very passionate about research and working at the lab. Currently he is working in the Ralstonia group at iGem Colombia.<br />
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===Daniela Olivera===<br />
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Daniela is an undergraduate student in Chemical engineering and Microbiology at the Universidad de los Andes. She is interested in bioinformatic and biomedical engineering research. Currenly, she is one of the outstanding students in chemical engineering department and there are too many proffesors that wants her in their research groups. She loves to spend her little free time playing with her cat (named Anastasia), working on iGEM with her lucky friends, going to cinema and burning calories in the gym.<br />
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===David A. Ayala-Usma===<br />
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[[File:david_ayala_2012.jpg|200px|thumb|right]] David is an undergraduate senior of Biology and Microbiology that, one day, simply was in the right place to get involved with iGEM and Synthetic Biology. He likes Molecular Cell Biology, Paleoecology, Geosciences, Astronomy, and some other science stuff. Also, he loves reading all kinds of tales and stories for children (like him), eating desserts, looking at the sky, taking pictures, playing at the PC, sleeping a lot, and talking, and talking, and talking... xD<br />
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He expects to eventually become a Ph.D. in Cell Biology, Earth Sciences, both or something in between, just to make a life and a living out of his passions, his favorite molecules, and discovering new exciting things.<br />
He also likes to be in contact with people around the world, and invites people with his same interests to add him on [http://www.twitter.com/EstadoAlternado Twitter] or [http://www.facebook.com/ayala.usma Facebook].<br />
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===Juanita Lara===<br />
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[[File:Juana.jpeg|150px|thumb|left]]<br />
Juanita is a biology and physics undergraduate student. She is very passionate about science and unveiling the mechanisms underlying biological systems is what she wants to do in life. For that reason she joined the Biophysics Group at Universidad de Los Andes, and is currently working on the characterization of thermosensors in ''Bacillus subtilis'' using molecular biology techniques and biophysical approaches. She sees in iGEM a great opportunity to meet new people and have the chance to learn from them. <br />
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===Laura Rodriguez===<br />
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Laura is an undergraduate student in Chemistry and Microbiology at Universidad de los Andes. She is passionate about science, likes organic chemistry and loves bacteria! She is also curious and a realll hard worker. For her, iGEM has been an opportunity to learn, practice lab skills and making good friends! Currently she is working in the Ralstonia group at iGEM Colombia. She is really excited to meet people involved in science from another countries, this will give her a perspective of science outside her country and will also be a cultural enriching experience.<br />
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=== '''Javier E. Vargas'''===<br />
[[File:javier.JPG|150px|thumb|left]]Javier already finished his thesis for the B.Sc. in Microbiology, but also is currently a senior student of Design at the Universidad de Los Andes. During his Microbiology thesis, he worked with the S-layer protein of [http://microbewiki.kenyon.edu/index.php/Lysinibacillus_sphaericus_C3-41 ''Lysinibacillus sphaericus''] applied to bioremediation of chromium using an immobilization matrix to improve the protein stability. In general, He is interested in molecular biology, synthetic biology, experience design and design of narratives. Also, he practices soft combat, fencing, climbing and enjoys painting (a lot).<br />
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iGEM is a great opportunity to apply his knowledge and creative instinct to demonstrate him self their capacities, gaining more lab experience while doing what he likes the most.<br />
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===David Alejandro García===<br />
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[[File:deivid_alejandrou.JPG|150px|thumb|right]]David is pursuing a degree in physics and mathematics as a member of the University of the Andes` class of 2014. David decided to participate in iGEM because he felt it would be an excellent opportunity to understand and manipulate the brick of the life to solve a big spectrum of problems. Outside the lab, David spends his free time playing the piano, reading some philosophy and literature, swimming. David also participates in a wide variety of academic activities such as in the “problem clinic” where he helps other students to solve difficulties in the resolution of problems in physics and being a prefect in a class of nanotechnology. After graduation, he wants to pursue a PhD in theoretical physics or nanotechnology<br />
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===César Augusto Quintana===<br />
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[[File:Cesitar.JPG|150px|thumb|left]]Cesar was born in Popayan (Cauca), he is a Physics and mathematics undergraduate student at the “Universidad de los Andes”. He began participating in this project because of an enormous interest in life systems founding along this time a crescent fascination about the theme. Beside science he likes a lot to play the acoustic guitar and watch movies.<br />
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===Luis Alberto Gutiérrez López===<br />
[[File:Luis.JPG|150px|thumb|right]]Luis is an undergraduate Physics student at the Universidad de los Andes. Since his school years he’s been interested in science, deeply fascinated by the way our Universe works and particularly by the mechanisms of life. His interest in biology led him to explore other fields like physics. This passion for science and knowledge made him a very devoted student which enabled him to be awarded as Best High School Graduate of Colombia in 2011.<br />
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Besides his enthusiasm for study, he loves physical activity, especially swimming and jogging. He also enjoys literature.<br />
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He decided to join iGEM because he considers it an excellent opportunity to become familiar with research and learn many useful things about molecular biology, mathematics and programming.<br />
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===Roberto Moran Tovar===<br />
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Roberto is a second year undergraduate Physics and Mathematics student at Los Andes University. He loves physics since he was at high school and thinks that the science ( specially physics) is the most amazing thing that could exist. Recently, he has been interested in the study of life, evolution and in general the whole biology. He thinks his best quality is the curiosity because lets him to explore the universe in a very funny way! He is a good soccer player, likes to play video games and likes good Rock&Roll.<br />
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===Diana Wilches===<br />
[[File:dianaw.jpg|thumb|right|150px]]<br />
Diana is a B.Sc in Biology and a last year Microbiology undergraduate student of the Universidad de los Andes. She is highly interested in Environmental Science and Biotechnology, mainly in the development of strategies and alternatives that could allow to reduce the impact of the human being in the world. With this aim, she has worked in biological control of insects, bioremediation and with this iGEM project she wants to help in the development of new alternatives to the use of chemicals products in agriculture. Furthermore, Diana is passionate for traveling, old history, languages and cultural exchange.<br />
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===[https://www.facebook.com/ksk89 Gabriel Martínez-Gálvez]===<br />
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Gabriel is a B.Sc. in microbiology and last year student in biomedical engineering (minor in physics). He is also a gamer to the bone, and a heavy soccer and basketball fan. Since high school he found it fascinating and exciting to think about programming cells into living bio-robots automated to perform specific actions inside the human body. For that matter he found systems biology and synthetic biology to be his main motivations for his studies and graduation thesis with the [http://openwetware.org/wiki/Biophysics Biophysics Lab] at the [http://www.uniandes.edu.co/component/content/article/656-about-uniandes Universidad de los Andes].<br />
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He is very interested in the design of new biological processes through synthetic biology, [http://en.wikipedia.org/wiki/Dendritic_cell dendritic cell] information integration towards specific immune response coordination in humans as well as [http://pubs.acs.org/doi/abs/10.1021/ed042p49?journalCode=jceda8 molecular psychology] for a better understanding of emotions and aging phenomena. Feel free to follow him on [https://twitter.com/ksk_89 twitter] or challenge him in [http://us.playstation.com/psn/#?psnId=network_psn PSN] (PSN ID: ksk_89)!<br />
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===Diana Sanchez===<br />
[[File:ds.jpg|thumb|right|150px]]<br />
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Diana is a design student with emphasis on communication design and textile design. She has high interest in the dialogue between arts and science. Especially in biodesign, perception, interaction design, and art direction.<br />
Her projects focus on the boundaries between the biological and the technological and how this changes our perception. She has also worked as a Field Researcher at future trends in the Observatorio de Tendencias de la Cámara de Comercio de Bogotá and Future Concept Lab Milan.<br />
She is interested in how science can bring metaphores and processes to design manifestations that allow us to experience the world in a more significant way.<br />
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===Luz Alba Gallo===<br />
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Luz is a last year Design student. Her focus is on social innovation and strategy. In the last year she had the opportunity to work on a project named "Let's meet your baby!" that was related with maternal health in low income communities. Also she is an active participant in Design communities such as OpenIdeo and TechoLab. She is interested in the posssiblities that the Design offers to all the other areas of knowledge to improve the life quality and the world. <br />
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==Grad Students==<br />
===Silvia J. Cañas===<br />
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[[File:SilviaC.jpg|thumb|left|180px]] Silvia is a M.Sc student in Biological Sciences (Microbiology) at the Biophysics Laboratory and the Mycology and Phytopathology Laboratory (LAMFU) at the Universidad de los Andes. She is a B. Sc in Microbiology and B. Sc in Chemical Engineering of the Universidad de los Andes (Minors in ''Bioinformatics'' and ''Bioengineering''), where she worked with Metabolic engineering. Her main areas of interest are '''Molecular Cell Biology''' and '''Systems & Synthetic Biology'''. She is currently investigating the effect of Sigma factors transitivity on persisters generation in ''Escherichia coli K12'' . Some of the approaches she is using are based on Molecular Biology, Systems Biology & Epifluorescence Microscopy<br />
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===Vivian Bernal Galeano===<br />
[[File:Vivian.jpg|thumb|right|140px]] Vivian is a M.Sc student in Biological Sciences at the Laboratory of Mycology and Phytopathology at the Universidad de los Andes. She is a Bachelor in Biology of the Universidad Nacional de Colombia. She has worked in the area of molecular phytopathology, in the pathosystem Cassava-''Xanthomonas axonopodis'' pv. manithotis (''Xam''), for two and half years and currently she has studied the small ncRNA of ''Xam''. Her role in the iGEM Team is to participate in the lab activities and to coordinate, plan and develop, with her teammates, the activities related to the human practices, she enjoys that!!<br />
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===Paola Reyes===<br />
[[File:379523 128088457300454 728084190 n.jpeg|150px|thumb|left]]Paola is a pretty enthusiastic Master Student at the Laboratory of Mycology and Phytopathology of Universidad de los Andes. She has been working in molecular biology for more than two years now. Her research interest is the molecular interaction between plants and phytopathogenic bacteria. Her role in the iGEM team has been to help undergraduate students on wet lab activities and in diverse areas. She loves drama but she is kind of cool most of the time.<br />
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===Laura Avelleneda Franco===<br />
[[File:avefra.JPG|150px|thumb|right]]Laura holds a B.Sc in Chemical Engineer, and a B.Sc in Microbiology, both from Universidad de los Andes. She is a second year M.Sc student of Biological Sciences at the Center of Microbiology Research (CIMIC) at the Universidad de los Andes. She is interested in biotechnology from molecular scale to industrial scale. She is excited for new branches of biotechnology such as synthetic and systems biology. She believes that the deciphering of new biological pathways from genes to signal cascades are highly important for the research and development of new products and processes.<br />
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===Andrés Felipe Simbaqueba Sánchez===<br />
[[File:me.jpg|thumb|left|150px]] Andrés Felipe was born in Florencia (and that’s at Colombia) and he is a Chemical Engineer and M.Sc student in Chemical Engineering at Universidad de los Andes. Actually, he has been researching in bioindustrial processes in order to produce biofuels from cellulosic biomass. He thinks that iGEM is a good opportunity to understand biological processes from a more scientific point of view. However, his life is not reduced only to full-time researching... also he spends his little free time going to the cinema, hanging out with some lucky friends, meeting new people and traveling around the whole world. Feel free to follow him on [https://https://twitter.com/TheWhiteLion89 twitter]<br />
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===Estefanía Luengas===<br />
[[File:StefL20.JPG|thumb|right|150px]]I am interested in the geographic referencing and analysis of biological data. I have worked in landscape transformation for a coffee certificate, databases development for social cartography and development and standardization of cartographic databases of administrative data for social processes. Currently, I am working in early stages on climatic modeling of ''Phytophthora infestans'', the causal agent of potato late blight, involving collection to determinate severity curves.<br />
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===Juan Enciso===<br />
[[File:enciso.png|thumb|left|150px]] Juan is a M.Sc. student in Biological Sciences at Universidad de los Andes. His interests lie in the fields of bioinformatics and molecular evolution. He's currently searching novel groups of Oomycetes, organisms which include several important animal and plant pathogens such as ''Phytophthora sp.'' and ''Saprolegnia sp.'', among others.<br />
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== Instructors ==<br />
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==='''Silvia Restrepo Restrepo, Ph. D.===<br />
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[[image:Silvia_restrepo_restrepo.PNG|left|none|thumb|Silvia Restrepo, Ph. D.]] Dr. Restrepo is the leader and main researcher at the [http://lamfu.uniandes.edu.co Laboratory of Mycology and Phytopathology] of the [http://www.uniandes.edu.co Universidad de los Andes]. Additionally, she is the dean of the [http://cienciasbiologicas.uniandes.edu.co Department of Biological Sciences].Her main research topic is phytopathology, and her favorite organism is ''Phytophthora infestans'', of course!. <br />
'''Website''': [http://lamfu.uniandes.edu.co/RESEARCH/Silvia_Restrepo.html Lab Page]<br />
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==='''Juan Manuel Pedraza, Ph. D.'''===<br />
[[image:JuanPedraza.jpg|right|none|thumb|Juan Manuel Pedraza, Ph. D.]]<br />
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Dr. Pedraza leads the Systems/Synthetic Biology division of the Biophysics Laboratory at Uniandes. His specialty is stochasticity in gene expression, but is getting more and more interested in evolution and the consequences of phenotypic variability.<br />
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==='''Adriana Bernal, Ph. D.'''===<br />
[[image:Adriana_Bernal.JPG|left|none|thumb|Adriana Bernal, Ph. D.]]<br />
Dr. Bernal is a Associated Proessor at the Universidad de los Andes, her main research topic is the Plant-Pathogen interactions of ''Xanthomonas axonopodis pv. manihotis'' with its main host. She is the co-director of LAMFU with Dr. Silvia Restrepo.<br />
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Webpage: [http://lamfu.uniandes.edu.co/RESEARCH/Adriana_Bernal.html LAMFU Webpage]<br />
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</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Human/Social:_SchoolsTeam:Colombia/Human/Social: Schools2012-10-27T03:01:19Z<p>Af.simbaqueba218: /* Social: Schools and Coffee Growers */</p>
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<div>{{http://2012.igem.org/User:Tabima}}<br />
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= '''Social: Schools and Coffee Growers''' =<br />
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The basic objectives of the social activities are the integration of the team with the community as well as the divulgation and teaching of basic concepts in synthetic biology through our project’s idea.<br />
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[http://issuu.com/dianasanchezbarrios/docs/hp-igem-print]<br />
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==The Stakeholder diagram==<br />
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The different problems associated with bad cultural practices and excessive use of pesticides in coffee agriculture result in great economic losses. The stakeholders diagram proposes an important interaction to establish a possible community service model. The service model suggests that the coffee growers should work together to acquire the different crop materials at a lower price. However, the interaction of different institutions in charge of providing technical and educational support on synthetic biology to the community is necessary. This support will help the coffee growers have a better understanding of the strategy designed by iGem Colombia team, which will function as a pest control in crops. Pest busters helps coffee growers grow an eco-friendly coffee based on the lower use of pesticides. The main idea of creating these interactions is to encourage teamwork among coffee growers, which will help them to generate an additional income. Focusing on teamwork culture, the additional incomes would go to a community fund that will help funding the next generation of Pest Busters. Having a common fund enables different interactions in the community and helps creating a savings culture among the coffee growers to secure materials needed for later sowings.<br />
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[[File:diagram.jpg|thumb|center|927x663px|frame|Figure 1.The Stakeholder diagram shows how different actors involved in a community service model can interact exchanging different contributions. With the arrows are showed the donors and the receptors.]]</div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ResultsTeam:Colombia/Modeling/Results2012-10-27T02:55:43Z<p>Af.simbaqueba218: /* Results */</p>
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<div>{{http://2012.igem.org/User:Tabima}}<br />
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== Results ==<br />
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The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The figure below shows the original design of the circuit.<br />
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[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
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Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
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1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
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2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
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3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
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The new system is showed in the figure below: <br />
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[[File:modelocorr.jpg|thumb|500px|center|Figure 2. Detection module located in the plasmid I]]<br />
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[[File:p2corr.png|250px|center|thumb|Figure 3. Alert system and toxin/antitoxin system located in the plasmid II ]]<br />
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== Differential equations results ==<br />
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Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
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===='''Ralstonia:'''====<br />
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As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
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[[File:Ral1.png|center|450x450pxpx]] [[File: ral2.png|center|450x450pxpx]]<br />
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The LuxI- LuxR system increases its activations by phcsA<br />
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[[File: ral3.png|center|450x450pxpx]]<br />
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Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
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[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
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===='''Rust:'''====<br />
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When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
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[[File: rust1.png|center|450x450pxpx]]<br />
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Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
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[[File: rust2.png|center|450x450pxpx]]<br />
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The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
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[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
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<div>{{http://2012.igem.org/User:Tabima}}<br />
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== Results ==<br />
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<p align="justify"><br />
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The mathematical model should help the experimental design to optimize the circuit. This case was not the exception. The picture below shows the original design of the circuit.<br />
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[[File:toget.png|600px|thumb|center|Figure 1. Our desing before modeling results]]<br />
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<br />
Once results from simulations were obtained ,we had to make little changes to the proposed system: <br />
<br />
<br />
1. As it is shown, before results of simulations, there was an unknown promoter for LuxR. In the beginning, it was established that this promoter must had been constitutive. From simulations results we conclude that response curves of the system were not consistent with the reality (LuxR had giant concentrations and the salicylic acid never went up). In the designed system, LuxR had to interact with LuxI and turn on the response. Thus, it was thought that LuxR must had been in a similar concentration of LuxI. Consequently, LuxI was putted under the same promoter of LuxR, hence the two proteins will be promoted at the same time. <br />
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</br><br />
</html><br />
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2. The desired response is to increase Salicylic Acid levels when a pest gets near the bacteria. With the original system, salicylic acid increased but not as much as required. Thus, we tried putting the promoter activated by Lux next to the CI promoter in order to see if an increase was observed. With results of simulations, it was discovered that this solution optimized the increase of salicylic acid in the response. <br />
<br />
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</br><br />
</html><br />
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3. Looking for the right set of parameters, it was possible conclude that Hill constant "k" (Concentration of the substrate when the rate of production is half of the maximum production rate) for the promoter activated by Lux '''had''' to be four times greater than the Hill constant for CI promoter. This results are based on biological reasons; the Lux promoter came from a quorum sensing system, then it needs high concentration of activator. Biologically, this is because it informs the promoter that there is high cell density. On the other hand, the CI promoter box came from a bacteriophage and it is used to attack the bacteria as quickly as possible, then it needs small quantities of protein to fully activate this system.<br />
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The new system is showed in the picture below: <br />
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[[File:p2corr.png|250px|center]]<br />
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== Differential equations results ==<br />
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<p align="justify"><br />
<br />
Although the screening of the parameters could not be completely done, we made a manual search for them and found a set that makes the system behave as expected. Here we present the mean response of all the substances in our biological system for one cell. The impulse of the pest was made during the times 10-20. <br />
<br />
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<html><br />
<br><br />
</br><br />
</html><br />
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<br><br />
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===='''Ralstonia:'''====<br />
<br />
As it is shown below, when the system is under the presence of 3-OH-PAME the sensor is quickly phosphorylated and the complex phcR-phcA liberates the activator. This activator has a peak and then decrease softly because it is bound with the promoter. Once the impulse is gone, everything goes back to normality.<br />
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[[File:Ral1.png|center|450x450pxpx]] [[File: ral2.png|center|450x450pxpx]]<br />
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The LuxI- LuxR system increases its activations by phcsA<br />
<br />
<br />
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[[File: ral3.png|center|450x450pxpx]]<br />
<br />
Looking the behavior of the species of interest, it possible to conclude that the antitoxin has greater concentration than the toxin when the 3-OH-PAME appears. This means that the cell is awake and can produce proteins. On the other hand, the Salicylic Acid has an increase of almost two times than observed before. <br />
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[[File:Ral4.png|center|450x450pxpx]] [[File: ral5.png|center|450x450pxpx]]<br />
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===='''Rust:'''====<br />
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When the system is under the presence of chitin, it possible to see how the positive feedback of the chitoporin and chitinase works making their concentration increase. Consequently, it results in level increase of chitin monomers and release of the sensor which is going to activate the LuxI and LuxR promoter.<br />
<br />
[[File: rust1.png|center|450x450pxpx]]<br />
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Like it was shown in Ralstonia system, the Lux system concentrations increase when their promoter is activated. The complex LuxI-LuxR has a peak and then decrease because it is delay activation of CI and Salicylic Acid. <br />
<br />
[[File: rust2.png|center|450x450pxpx]]<br />
<br />
The substances of interest behave just like expected. As in Ralstonia, the cell is awake when the chitin is present and the Salicylic Acid has folded its level of concentration. It is important to conclude that this system takes more time to go back to the steady state than Ralstonia's system.<br />
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[[File:Rust4.png|center|450x450pxpx]] [[File: rust5.png|center|450x450pxpx]]<br />
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<div>== Team Colombia @ 2012 iGEM ==<br />
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{{http://2012.igem.org/User:Tabima}}<br />
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== Parameters of the equations ==<br />
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When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
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There are three possible ways to find this parameters: <br />
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::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
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::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
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::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
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== How did we do it? ==<br />
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'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
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For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
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[[File:tabla2.png|center|300x250pxpx]]<br />
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'''''a.Basal levels of the proteins:'''''<br />
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Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
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[[File:alfbsal1.png|center|120x120px]]<br />
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Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
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[[File:alfbasal2.png|center|80x60pxpx]]<br />
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But γ is approximately 1/T, then:<br />
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[[File:alfbasal3.png|center|80x60pxpx]]<br />
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Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
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Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
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[[File:range1.png|center|156x104pxpx]]<br />
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Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
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[[File:z.png|center|153x105pxpx]]<br />
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By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
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'''b.Protein degradation:'''<br />
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The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
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[[File:degrada.png|center|100x80pxpx]]<br />
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Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
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'''c. Reaction constant:'''<br />
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This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
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[[File:reactioncte.png|center|186x126pxpx]]<br />
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'''d. Hill coefficients k:'''<br />
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We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
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[[File:zzzzzzz.png|center|145x95pxpx]]<br />
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'''e. Hill coefficients n:'''<br />
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We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
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[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
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'''f. Maximum cell production (β):'''<br />
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Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
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[[File:RRMoizzz.png|center|136x90pxpx]]<br />
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'''CI PARAMETERS'''<br />
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All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
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[[File:CI.png|center|150x150pxpx]]<br />
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Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
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:'''Step 1: Objective function: Define your desired behavior'''<br />
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First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
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[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
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:'''Step 2. Optimization of parameters: A point within an area'''<br />
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Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
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[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
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Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
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[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
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A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
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In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
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This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
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Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
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:'''Step 3: Sensitivity anlysis''' <br />
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In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
[[File:luxi.png|center|thumb|350x350pxpx|Figure 4. LuxI, maximal production rate. Range: 0-22. Step size: 0.5 ]]<br />
<br />
<br><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br />
----<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the fungal detection module. The following table shows the different parameters involved in the system with the fungal detection module. Besides, it shows how they affect the final behavior. <br />
<br />
[[File:resultsab.png|center|thumb|480x650pxpx|Table 1. Parameters involved in the fungal detection module]]<br />
<br />
Here we present some of the graphics found in the analysis. The figures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|thumb|650x380pxpx|Figure 5. Parameters that do not have influence in the response]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|thumb|650x380pxpx|Figure 6. Parameters that have influence in the response ]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|thumb|650x380pxpx|Figure 7. Parameters that affect the final response]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|thumb|480x650pxpx|Table 2. Parameters involved in Ralstonia detection module]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|thumb|650x380pxpx|Figure 8. Behavior of relevant parameters for Ralstonia detection module]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|thumb|650x380pxpx|Figure 9. Parameters that had a significant influence ]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|thumb|650x380pxpx|Figure 10. Parameters with significant influence]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|thumb|400x200pxpx|Figure 11. Size of the steep for screening ]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|thumb|500x300pxpx|Figure 12. Optimum solution for a system]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:29:01Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
<br><br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
[[File:luxi.png|center|thumb|350x350pxpx|Figure 4. LuxI, maximal production rate. Range: 0-22. Step size: 0.5 ]]<br />
<br />
<br><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br />
----<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:28:15Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
<br><br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
[[File:luxi.png|center|thumb|350x350pxpx|Figure 4. LuxI, maximal production rate. Range: 0-22. Step size: 0.5 ]]<br />
<br />
<br><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:27:41Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
<br><br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
[[File:luxi.png|center|thumb|350x350pxpx|Figure 4. LuxI, maximal production rate. Range: 0-22. Step size: 0.5 ]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:27:14Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
<br><br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
[[File:luxi.png|center|thumb|350x350pxpx|LuxI Figure 4. LuxI, maximal production rate. Range: 0-22. Step size: 0.5 ]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:23:02Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
<br><br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:22:03Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|thumb|400x200pxpx|Figure 3. A point in parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:20:48Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|thumb|400x200pxpx|Figure 2. Parameter space for a system ]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|400x200pxpx|Figure 2. Parameter space for a system]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:19:06Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|thumb|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|400x200pxpx]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|400x200pxpx]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:18:30Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|480x450pxpx|Figure 1. Objective function and desired behavior]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|400x200pxpx]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|400x200pxpx]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/ParamterersTeam:Colombia/Modeling/Paramterers2012-10-27T02:16:32Z<p>Af.simbaqueba218: /* How did we do it? */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
== Parameters of the equations ==<br />
<br />
When we want to model a biological process, it is necessary to write the differential equation that model the system which requires a number of constants. If the real value for the constants are unknown, the system can not have any biological sense. These entries are called parameters and they are crucial elements in the mathematical model made in this project.<br />
<br />
There are three possible ways to find this parameters: <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::i) Literature. There are a lot of studies trying to find biological parameters, such as basal rate of protein production, kinetic constants, Monod's constants, etc. Moreover, there are so many biological systems and only a few of them have been characterized. Thus, it is difficult to find the parameters that are needed. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
::ii) Experimental way. If an experiment is made using the biological system of interest, it is possible to find the parameters for the equations that models the whole system. For this project, it was necessary to model the biological system first. Thus, experiments couldn't be performed to find the constant for the differential equations. <br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
::iii) Screening of parameters. Sometimes we don't have the exact number that we need, but we have a rank where it could be or the parameter for a similar biological system, then we can perfom a screening of parameter, where we try to find the value that perfectly fits the reponse of our circuit.<br />
<br />
== How did we do it? ==<br />
<br />
<br />
<p align="justify"><br />
<br />
'''As said above finding the right set of parameters for a system is a headache for all the synthetic biologists. That is why we developed a standard procedure that can be use any synthetic biology mathematical model. It has four main steps. But before starting to work in it we need to find as much information in literature as possible.''' <br />
<br />
<br />
<br> <br />
<br><br />
<br />
For our particular case, ee found all the CI promoter box parameters, we normalized all the degradation terms with the cell division time and for the other we found acceptable ranges. We used a lot of resources and methods to approximate the limits for this ranges. Here we show an explanation:<br />
<br />
[[File:tabla2.png|center|300x250pxpx]]<br />
<br />
'''''a.Basal levels of the proteins:'''''<br />
<br />
Determining a rank which this value could be, we described mathematically a very simple process. Suppose there is a usual differential equation:<br />
<br />
[[File:alfbsal1.png|center|120x120px]]<br />
<br />
Where αo is the basal level, γ is the protein parameter for degradation and P is the protein concentration. Thus, we can assume that in steady state conditions we have that dP/dt= 0:<br />
<br />
[[File:alfbasal2.png|center|80x60pxpx]]<br />
<br />
But γ is approximately 1/T, then:<br />
<br />
[[File:alfbasal3.png|center|80x60pxpx]]<br />
<br />
Establishing the rank, we assumed T as φ and we looked for a normal rank of concentration of a protein in a cell [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=104520&ver=10&trm=protein]. Another important aspect is that there were constitutive proteins and inducible proteins. Thus, we divided the basal levels in two class: i) one for basal proteins and ii) one for constitutive proteins. Finally, following ranges were defined: <br />
<br />
Basal proteins range (LuxR, LuxI, HipB and Salicylic Acid):<br />
<br />
[[File:range1.png|center|156x104pxpx]]<br />
<br />
Constitutive proteins range (HipA7,Sensor, Chitinase, Chitoporin and CBP):<br />
<br />
[[File:z.png|center|153x105pxpx]]<br />
<br />
By the other hand, the basal production of HipA has to be constitutive and inducible because the cell has to have three stages. The first stage is always sleep (constitutive) due to HipA effect. Once an impulse of chitin or 3-OH-PAME is presented, it is going to awake the cell due to concentration decrease of HipA . This is the second stage of the cell. The third stage is when cell is slept again which it is achieve through a positive control (inducible). The basal concentration used in the equations was the constitutive one because it is going to have more effect in the response. <br />
<br />
'''b.Protein degradation:'''<br />
<br />
The chosen unit of time was the bacteria life time because it represents when the proteins are diluted and decrease in the cell. We can establish easily the protein degradation using values related to life time of E.Coli. We defined the protein degradation for almost all values as follows: <br />
<br />
[[File:degrada.png|center|100x80pxpx]]<br />
<br />
Again, we found a special case. Degradation of HB is greater, then we assigned it a value of 4/φ. <br />
<br />
'''c. Reaction constant:'''<br />
<br />
This value can vary depending of the described process. Fortunately, we found in literature how to approximate this value [http://www.biokin.com/dynafit/scripting/html/node23.html#SECTION00431000000000000000]. However, we took the approximation and turned it into units described above. <br />
<br />
[[File:reactioncte.png|center|186x126pxpx]]<br />
<br />
'''d. Hill coefficients k:'''<br />
<br />
We looked for some reference in different data sources and we found the coefficient of CI ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). Then, we decided to approximate a rank taking this value as a reference.<br />
<br />
[[File:zzzzzzz.png|center|145x95pxpx]]<br />
<br />
'''e. Hill coefficients n:'''<br />
<br />
We based on the value "n" found for CI( [http://www.sciencemag.org/content/307/5717/1962.short NItzal et al.2005]). In this case, there was an analysis that took in account the number of molecules that interfere with gene activation.<br />
<br />
[[File:zzzzRRzzz.png|center|260x172pxpx]]<br />
<br />
'''f. Maximum cell production (β):'''<br />
<br />
Considering the concentration of Rubisco, which is about 20 times the average concentration and rate of production of a protein, [http://bionumbers.hms.harvard.edu/bionumber.aspx?&id=107431&ver=1&trm=rubisco], we assign the limits for this range as follows.<br />
<br />
[[File:RRMoizzz.png|center|136x90pxpx]]<br />
<br />
'''CI PARAMETERS'''<br />
<br />
All the parameters for CI activation system were found in the literature. ([http://www.sciencemag.org/content/307/5717/1962.short Nitzal et al.2005]). We only made a change of units. <br />
<br />
[[File:CI.png|center|150x150pxpx]]<br />
<br />
<br />
----<br />
<br />
Once the ranges of the parameters were set, we proceed to develop the standard method. Here we show the steps proposed with the obtained results for Pest-busters as an example.<br />
<br />
<br />
:'''Step 1: Objective function: Define your desired behavior'''<br />
<br />
First of all, it is necesary to define the desired response, in this case the Salicylic Acid. Thus, we stablished some ranges where concentration supposed to be. This response depends on the chitin or 3-OH-PAME impulse. Besides, the system is preferable to respond if the signal is long and intense. On the other hand, we don't want our cells to be "awake". The figure below shows this: <br />
<br />
[[File:param4.png|center|480x450pxpx]] <br />
<br />
<br />
:'''Step 2. Optimization of parameters: A point within an area'''<br />
<br />
Within the parameter space, there are many sets of them that make the system behaves just like expected; and these can be represented as an area. The main objective is to find this area. Suppose you only have two parameters. The plane represents the parameter space and the green area is where the system works. <br />
<br />
[[File:param.png|center|400x200pxpx]]<br />
<br />
Now we want a point within these area to begin the screening. It seems easy to identify in two dimensions, but this process can take a lot of time (weeks or even months) when it is a space of more than 10 parameters. So, one way to achieve this process is making an optimization. <br />
<br />
[[File:param2.png|center|400x200pxpx]]<br />
<br />
A process of optimization takes a function and found maximum or minimum values changing some variables of it. The changing variables are named optimization variables and function is called objective function. If we have some limitations, it is possible to add restrictions to the system, and the function will be optimized without breaking them.<br />
<br />
In this case, the objective function is a minimum difference of squares between the points of the expected behavior and the response of the equations with a set of optimization variables. When the distance between these points is minimum, the parameters are found. <br />
<br />
This optimization process was done discretizing the differential equations and putting them as restrictions. The same procedure was made for the stable state concentration where the differential equation must be equal to zero (when there is no signal). This algorithm was programmed in a specialized software. <br />
<br />
Unfortunately the firsts results were not satisfactory and a new code it is being developed. <br />
<br />
:'''Step 3: Sensitivity anlysis''' <br />
<br />
In this step the importance of each parameters in the main outputs behavior (Our case: Salicylic Acid, the toxin HipA7 and the antitoxin HipB) is tested. The objective is to find how much each parameter affect the desired response.<br />
<br />
This test considered the following stages: i.) Establish the ranges of the parameters (see above), ii) Determine appropriate division for the ranges, iii) Iterate each parameter while leaving the others fixed in the MATLAB code. iv) See how the difference between the steady state's concentrations and the concentrations during the impulse of the pathogen changed with the change of each parameter.<br />
<br />
<br><br />
<br />
'''Note: the exact value for each parameter is not important. It is important their relevance and how they change the response.'''<br />
<br />
<br><br />
<br />
Here is an example:<br />
<br />
</p><br />
<br />
<p align="center"><br />
<br />
Parameter: LuxI Maximal production rate<br />
<br><br />
<br />
Range: 0-22 <br />
<br />
<br><br />
<br />
Step size: 0.5<br />
<br />
[[File:luxi.png|center|350x350pxpx]]<br />
<br />
</p><br />
<br />
<p align="justify"><br />
<br />
The figure above shows how the HipB, HipA7 and Salicylic Acid concentration change during the presence of the pathogen is significantly influenced by the maximal production rate of LuxI protein. We make this procedure for all the parameters in both systems (Ralstonia and Fungus). The results are shown below:<br />
<br />
<br><br />
<br><br />
<br />
<br />
'''Fungus:'''<br />
<br />
The sensitivity analysis was performed for the system with the detection module for fungus. The following table shows the different parameters involved in the system with the fungal detection system and how they affect the final behavior <br />
<br />
[[File:resultsab.png|center|480x650pxpx]]<br />
<br />
Here we present some of the graphics found in the analysis. The pictures below show two parameters that do not have significant influence in the desired response:<br />
<br />
[[File:funnochange.png|center|650x380pxpx]] <br />
<br />
<br><br />
<br />
We also found some parameters that have a significant influence in one of the main outputs but were not sensitive to the rest:<br />
<br />
[[File:funnochangeone.png|center|650x380pxpx]] <br />
<br />
Finally, we found some parameters that affect the final response of all the main outputs of interest: <br />
<br />
[[File:funnochangetwo.png|center|650x380pxpx]] <br />
<br />
<br />
'''Ralstonia'''<br />
<br />
Below, it is exposed the results obtained from sensitivity test for Ralstonia. The next table identifies those parameters that make a relevant change in the model from those that do not. The main outputs tested were the HipB, HipA7 and the salicylic acid change in concentration due to the impulse. <br />
<br />
[[File:resultsabn3.png|center|480x650pxpx]]<br />
<br />
The following figures show the results obtained for almost all the relevant parameters. Like in the previous case we found some parameters that had no effect at all in the response and others than only had effect in one of the main outputs. <br />
<br />
[[File:ralchangeone.png|center|650x380pxpx]]<br />
<br />
We also found some interesting results, there were some parameters that had a significant influence in a small range, but when the rest of the range was evaluated the response was not sensitive to these parameters: <br />
<br />
[[File:ralchangetwo.png|center|650x380pxpx]]<br />
<br />
Finally we found parameters that had significant influence in the response of the three main outputs and in the complete range of the parameter. Here we present some of the most interesting behaviors of these kind of parameters: <br />
<br />
[[File:ralchange3.png|center|650x380pxpx]]<br />
<br />
<br />
Using this results it is possible to know the parameters that affect the response in a major way. Although it is still unknown the exact value of the parameter, it is possible predict how the system is supposed to response. Then, we could proceed to the final step.<br />
<br />
<br><br />
<br />
:'''Step 4: Screening'''<br />
<br />
::''If we have a set of parameters, why do we do a screening?''<br />
<br />
In the second step we found a set of parameters that give the expected response of the system. But this is only a point. What does happen with the rest of points of the area? Does the optimization method “know” if these parameters are real or have biological sense? As long as we specified one single response for the parameters, we don’t know if there are other possible responses of valid solutions. Do they exist?<br />
<br />
To answer these questions we performed a screening of the parameters. Beginning at the resulting point of the optimization, we started to move in all directions in a fixed range and then we examined when the acceptable area ends. <br />
<br />
How much do we move depends on the sensitivity analysis. If the response is not very sensitive to the parameter, we take longer steps than the case which the response is more sensitive. <br />
<br />
[[File:param3.png|center|400x200pxpx]]<br />
<br />
There are some parameters that can me modified experimentally like the maximal rate production but most of them depend on molecular details, are unchangeable and can only be known with experiments. The final goal of these standard procedure is to set the changeable parameters in such a way that the cross sectional area of the area of parameters that has desired response is maximized. <br />
<br />
Suppose you only have two parameters, one that can be changed and one that does not. If you set the first parameter in a black dot (see figure below), a small change of the uncontrollable parameter would take the system out of its working area. The optimum solution is to set the first parameter in the red line, so the probability of going out of the working area is smaller. <br />
<br />
[[File:param5.png|center|500x300pxpx]]<br />
<br />
<br />
<br />
-Note: Due to long computational time, the code is being parallelized <br> and we expect to run the tests shortly. <br />
<br />
</p> <br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/DiffTeam:Colombia/Modeling/Diff2012-10-27T01:57:39Z<p>Af.simbaqueba218: /* RALSTONIA */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Differential equations=<br />
<br />
<p align="justify"><br />
<br />
Before starting to work at the lab with the designed bacteria and plants, we can check if this design works through a mathematical model. The first step is to develop a deterministic model based in differential equations. This type of equations are deterministic because they describe the behavior for each of the substances in the synthetic circuit over time. However, they do not take into account the probabilities involved in each of the events described, the population interactions and the noise of the system. <br />
<br />
All of these equations are based on the law of mass conservation: <br />
<br />
[[File:Mass balance1.png|center|530px]]<br />
<br />
In a biological system, the accumulation stands for the concentration changes over time, the input and output are related with the processes of export and import of a molecule into the cell, the generation is related to the production by a gene or a chemical reaction, and the consumption is related to chemicals reactions too. All these terms depend on reaction kinetics that could be expressed as a simple multiplication or a complex expression like a Hill equation.<br />
<br />
<br />
Below it is shown an example to understand the previous ideas:<br />
<br />
'''Example:'''<br />
<br />
[[File:difeq.png|thumb|center|530px| Figure 1. Biological system interacting]]<br />
<br />
<br />
The molecule W activates de promoter for the production of A, which is used in a reaction with B for producing C and for the activation of the D's promoter. <br />
<br />
To describe the changes over time of the protein A it is possible to see that there is not export or import; as a consequence, there is not input or output term. The generation term is the production by the gene promoted by W, and it can be expressed with a Hill type equation:<br />
<br />
<br />
[[File:hil1l.png|center|80x80px]]<br />
<br />
The consumption term is divided in two: first the reaction with B, that can be expressed as a first order reaction with a kinetic constant m and the activation of the promoter of D; however this activation is an event that occurs in a short time scale so it can be removed<br />
<br />
<br />
[[File:consumption12.png|center|80x80px]]<br />
<br />
<br />
Writing the complete mass balance equation for substance A:<br />
<br />
[[File:eqq1.png|center|280x100px]]<br />
<br />
<br />
This procedure was made for each of substances in the designed circuit. As shown above, Hill type equations were used to describe the production by the activation of a promoter and the reactions terms followed the law of mass action. Once all the equations are describe and the constants are set we can solve the differential equation with specialized software like MATLAB and its tools such as ODE.<br />
<br />
<br />
== '''Differential equations for Pest-busters''' ==<br />
<br />
==='''''FUNGAL INFECTION'''''===<br />
<br />
Below it is shown how differential equations for Pest-busters were made. However, before describing the modeled system ,it is necessary to know all the symbols that will be use in the documents and the simulation. The following table contains all the substances involved in the processes and the constants required for the simulation.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:tablerust.png|thumb|center|500x1000px|Table 1. Symbols used in the document and simulation ]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
'''''CBP:''''' The Chitin binding protein participates in two major processes. First, it binds to the sensor. then, when the chitin is in the cell, the CBP binds to it.<br />
<br />
[[File:reactionCBP.png|center|200x150px]]<br />
<br />
This set of equations involves de change of CBS free in the cell and the change of the complex C.S. With the production, the destruction rate and the reactions describe above the equations are: <br />
<br />
[[File:eq12.png|center|400x280px]]<br />
<br />
'''''ChiP:''''' The chitioporin is the protein that allows the entrance of the chitin monomers into the cell. Its production is regulated by the sensor (S), this regulation is expressed as a hill type equation. The differential expression also includes the basal production and the rate of destruction; it is assumed that all the chitoporin produced goes to the membrane.<br />
<br />
[[File:eq3.png|center|280x170px]]<br />
<br />
'''''ChiA : The Chitinase'''''<br />
inside the cell depends of its basal production and the induction made by the sensor protein (S) as a positive feedback. The exportation of this enzyme is also involved in the equation. <br />
<br />
[[File:eq4.png|center|380x200px]]<br />
<br />
The chitinase outside the cell depends of the export rate of the chitinase inside, the diffusion in the environment and the reaction with the dimers of chitin. <br />
<br />
[[File:eq5.png|center|400x280px]]<br />
<br />
'''''Chitin:''''' This equation measures the chitin oligomers inside the cell. These depends of a function of importation that depends on the quantity of chitoporins and the creation of chitin monomers outside the cell. This oligomers are consumed in the reaction made with the complex C.S. <br />
<br />
[[File:eq6.png|center|400x200px]]<br />
<br />
'''''Sensor:''''' This protein is one of the most important in the detection system, its function is to activate the promoters of P,A and I. Once the chitin enters to the cell S is is freed from the complex C.S and starts activating promoters.<br />
<br />
This protein has two equations, the first one is an expression that shows the total of S in the cell, and suppose that it remains constant. The second one shows the terms involved in the formation of the complex C.S and the liberation of S after the chitin enters into the cell. It also includes terms associated to binding of the S protein with promoters regions and its reverse reaction, the unbinding of the promoter site. This expression was not taken into account, because the activation of the promoters are insignificant in the scale of time we are using. <br />
<br />
[[File:eq7.png|center|210x200px]]<br />
<br />
'''''LuxI:''''' The I protein inside the cell depends on the basal production and normal degradation rate. Also, its promotion by the S protein, export and import from the cell and the reaction with R to make the I.R complex.<br />
<br />
[[File:eq9.png|center|530x280px]]<br />
<br />
The I protein outside the cell only depends on the rates of exportation and importation of the cells and the diffusion in the environment. <br />
<br />
[[File:eq10.png|center|400x280px]]<br />
<br />
The complex I.R creation depends of the concentration of I and R. It activates the production of HipB, CI and Salicylic acid. <br />
<br />
[[File:eq11b.png|center|300x280px]]<br />
<br />
'''''LuxR:''''' The R protein is only involved in the creation of the complex L.R. It is downstream the I protein so its production also depends on the activation of the promoter by S <br />
<br />
[[File:eq12r.png|center|350x280px]] <br />
<br />
'''''CI and HipB: ''''' The same promoters produce these two proteins downstream. Its creation depends on the activation of the promoters, the basal production and rate of destruction. Although, CI promoter has three boxes, it was found in the literature that can be modeled as a simple box and the experimental parameters are known. HipB forms dimers and interact with HipA7 to "awake" the cell<br />
<br />
[[File:eq1314.png|center|400x280px]] <br />
<br />
[[File:eq14.png|center|550x280px]] <br />
<br />
'''''HipA7 ''''' This protein is activated by CI. Its concentration on the cell depends of the basal production, the rate of production when it is activated and the rate of destruction. The toxin HA reacts with the antitoxin to awake the cell. <br />
<br />
[[File:eq1516.png|center|430x280px]]<br />
<br />
''' Salicylic Acid: The desired response'''<br />
<br />
The salicylic acid is produced when the IR and the CI promoters are activated. It also is exported outside the cell because it works as a phytohormone that alerts the plant. <br />
<br />
[[File:eq16b.png|center|450x280px]]<br />
<br />
<br />
----<br />
<br />
==='''''RALSTONIA'''''===<br />
<br />
For this mathematical model the only thing that changes is the detection system. Now we want to sense 3-OH-PAME instead of Chitin. All the system involving CBP, chitinase and chitoporin is replaced with the sensor pchS and the transcription activator pchA. Thus, differences in the differential equations are in the first part only. The following table presents all the new substances involved in the process:<br />
<br />
[[File:tableralstonia.png|thumb|center|380x350px|Table 2. Substances involved in Ralstonia detection]]<br />
<br />
<br />
<br />
'''''phcS:''''' This molecule is the sensor of the OH. When the OH is in the environment, sensor is phosphorylated and phosphorylates the phcR-phcA complex. This set of equations includes the basal production and normal degradation of the sensor and the phosphorylation processes.<br />
<br />
[[File:eq1ral.png|center|280x180px]]<br />
<br />
'''''phcR:''''' This complex is normally in the cell with a rate of basal production and destruction. It is broken when the Sf phosphorylates it and the phcA is released.<br />
<br />
[[File:eq2ral.png|center|230x200px]]<br />
<br />
<br />
'''''phcA:''''' This protein is the activator and its released after the phosphorylation of R. It binds to a promoter, in this case the CI and HipB promoter.<br />
<br />
[[File:eq3ralb.png|center|230x280px]]<br />
<br />
<br />
The equations of the second part are the same as in the rust model (Equations 9-16). The difference is that promoter of the LuxI-LuxR system is now induced by A:<br />
<br />
[[File:eqchangral.png|center|510x280px]]<br />
<br />
[[File:eqchangra2l.png|center|385x280px]]<br />
<br />
<br />
</p><br />
<br />
<br />
</div></div>Af.simbaqueba218http://2012.igem.org/Team:Colombia/Modeling/DiffTeam:Colombia/Modeling/Diff2012-10-27T01:56:30Z<p>Af.simbaqueba218: /* FUNGAL INFECTION */</p>
<hr />
<div>== Team Colombia @ 2012 iGEM ==<br />
<br />
{{http://2012.igem.org/User:Tabima}}<br />
<br />
<div class="right_box"><br />
<br />
=Differential equations=<br />
<br />
<p align="justify"><br />
<br />
Before starting to work at the lab with the designed bacteria and plants, we can check if this design works through a mathematical model. The first step is to develop a deterministic model based in differential equations. This type of equations are deterministic because they describe the behavior for each of the substances in the synthetic circuit over time. However, they do not take into account the probabilities involved in each of the events described, the population interactions and the noise of the system. <br />
<br />
All of these equations are based on the law of mass conservation: <br />
<br />
[[File:Mass balance1.png|center|530px]]<br />
<br />
In a biological system, the accumulation stands for the concentration changes over time, the input and output are related with the processes of export and import of a molecule into the cell, the generation is related to the production by a gene or a chemical reaction, and the consumption is related to chemicals reactions too. All these terms depend on reaction kinetics that could be expressed as a simple multiplication or a complex expression like a Hill equation.<br />
<br />
<br />
Below it is shown an example to understand the previous ideas:<br />
<br />
'''Example:'''<br />
<br />
[[File:difeq.png|thumb|center|530px| Figure 1. Biological system interacting]]<br />
<br />
<br />
The molecule W activates de promoter for the production of A, which is used in a reaction with B for producing C and for the activation of the D's promoter. <br />
<br />
To describe the changes over time of the protein A it is possible to see that there is not export or import; as a consequence, there is not input or output term. The generation term is the production by the gene promoted by W, and it can be expressed with a Hill type equation:<br />
<br />
<br />
[[File:hil1l.png|center|80x80px]]<br />
<br />
The consumption term is divided in two: first the reaction with B, that can be expressed as a first order reaction with a kinetic constant m and the activation of the promoter of D; however this activation is an event that occurs in a short time scale so it can be removed<br />
<br />
<br />
[[File:consumption12.png|center|80x80px]]<br />
<br />
<br />
Writing the complete mass balance equation for substance A:<br />
<br />
[[File:eqq1.png|center|280x100px]]<br />
<br />
<br />
This procedure was made for each of substances in the designed circuit. As shown above, Hill type equations were used to describe the production by the activation of a promoter and the reactions terms followed the law of mass action. Once all the equations are describe and the constants are set we can solve the differential equation with specialized software like MATLAB and its tools such as ODE.<br />
<br />
<br />
== '''Differential equations for Pest-busters''' ==<br />
<br />
==='''''FUNGAL INFECTION'''''===<br />
<br />
Below it is shown how differential equations for Pest-busters were made. However, before describing the modeled system ,it is necessary to know all the symbols that will be use in the documents and the simulation. The following table contains all the substances involved in the processes and the constants required for the simulation.<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
[[File:tablerust.png|thumb|center|500x1000px|Table 1. Symbols used in the document and simulation ]]<br />
<br />
<html><br />
<br><br />
</br><br />
</html><br />
<br />
<br />
'''''CBP:''''' The Chitin binding protein participates in two major processes. First, it binds to the sensor. then, when the chitin is in the cell, the CBP binds to it.<br />
<br />
[[File:reactionCBP.png|center|200x150px]]<br />
<br />
This set of equations involves de change of CBS free in the cell and the change of the complex C.S. With the production, the destruction rate and the reactions describe above the equations are: <br />
<br />
[[File:eq12.png|center|400x280px]]<br />
<br />
'''''ChiP:''''' The chitioporin is the protein that allows the entrance of the chitin monomers into the cell. Its production is regulated by the sensor (S), this regulation is expressed as a hill type equation. The differential expression also includes the basal production and the rate of destruction; it is assumed that all the chitoporin produced goes to the membrane.<br />
<br />
[[File:eq3.png|center|280x170px]]<br />
<br />
'''''ChiA : The Chitinase'''''<br />
inside the cell depends of its basal production and the induction made by the sensor protein (S) as a positive feedback. The exportation of this enzyme is also involved in the equation. <br />
<br />
[[File:eq4.png|center|380x200px]]<br />
<br />
The chitinase outside the cell depends of the export rate of the chitinase inside, the diffusion in the environment and the reaction with the dimers of chitin. <br />
<br />
[[File:eq5.png|center|400x280px]]<br />
<br />
'''''Chitin:''''' This equation measures the chitin oligomers inside the cell. These depends of a function of importation that depends on the quantity of chitoporins and the creation of chitin monomers outside the cell. This oligomers are consumed in the reaction made with the complex C.S. <br />
<br />
[[File:eq6.png|center|400x200px]]<br />
<br />
'''''Sensor:''''' This protein is one of the most important in the detection system, its function is to activate the promoters of P,A and I. Once the chitin enters to the cell S is is freed from the complex C.S and starts activating promoters.<br />
<br />
This protein has two equations, the first one is an expression that shows the total of S in the cell, and suppose that it remains constant. The second one shows the terms involved in the formation of the complex C.S and the liberation of S after the chitin enters into the cell. It also includes terms associated to binding of the S protein with promoters regions and its reverse reaction, the unbinding of the promoter site. This expression was not taken into account, because the activation of the promoters are insignificant in the scale of time we are using. <br />
<br />
[[File:eq7.png|center|210x200px]]<br />
<br />
'''''LuxI:''''' The I protein inside the cell depends on the basal production and normal degradation rate. Also, its promotion by the S protein, export and import from the cell and the reaction with R to make the I.R complex.<br />
<br />
[[File:eq9.png|center|530x280px]]<br />
<br />
The I protein outside the cell only depends on the rates of exportation and importation of the cells and the diffusion in the environment. <br />
<br />
[[File:eq10.png|center|400x280px]]<br />
<br />
The complex I.R creation depends of the concentration of I and R. It activates the production of HipB, CI and Salicylic acid. <br />
<br />
[[File:eq11b.png|center|300x280px]]<br />
<br />
'''''LuxR:''''' The R protein is only involved in the creation of the complex L.R. It is downstream the I protein so its production also depends on the activation of the promoter by S <br />
<br />
[[File:eq12r.png|center|350x280px]] <br />
<br />
'''''CI and HipB: ''''' The same promoters produce these two proteins downstream. Its creation depends on the activation of the promoters, the basal production and rate of destruction. Although, CI promoter has three boxes, it was found in the literature that can be modeled as a simple box and the experimental parameters are known. HipB forms dimers and interact with HipA7 to "awake" the cell<br />
<br />
[[File:eq1314.png|center|400x280px]] <br />
<br />
[[File:eq14.png|center|550x280px]] <br />
<br />
'''''HipA7 ''''' This protein is activated by CI. Its concentration on the cell depends of the basal production, the rate of production when it is activated and the rate of destruction. The toxin HA reacts with the antitoxin to awake the cell. <br />
<br />
[[File:eq1516.png|center|430x280px]]<br />
<br />
''' Salicylic Acid: The desired response'''<br />
<br />
The salicylic acid is produced when the IR and the CI promoters are activated. It also is exported outside the cell because it works as a phytohormone that alerts the plant. <br />
<br />
[[File:eq16b.png|center|450x280px]]<br />
<br />
<br />
----<br />
<br />
==='''''RALSTONIA'''''===<br />
<br />
For this mathematical model the only thing that changes is the detection system. Now we want to sense 3-OH-PAME instead of Chitin. All the system involving CBP, chitinase and chitoporin is replaced with the sensor pchS and the transcription activator pchA. Thus, differences in the differential equations are in the first part only. The following table presents all the new substances involved in the process:<br />
<br />
[[File:tableralstonia.png|center|380x350px]]<br />
<br />
<br />
<br />
'''''phcS:''''' This molecule is the sensor of the OH. When the OH is in the environment, sensor is phosphorylated and phosphorylates the phcR-phcA complex. This set of equations includes the basal production and normal degradation of the sensor and the phosphorylation processes.<br />
<br />
[[File:eq1ral.png|center|280x180px]]<br />
<br />
'''''phcR:''''' This complex is normally in the cell with a rate of basal production and destruction. It is broken when the Sf phosphorylates it and the phcA is released.<br />
<br />
[[File:eq2ral.png|center|230x200px]]<br />
<br />
<br />
'''''phcA:''''' This protein is the activator and its released after the phosphorylation of R. It binds to a promoter, in this case the CI and HipB promoter.<br />
<br />
[[File:eq3ralb.png|center|230x280px]]<br />
<br />
<br />
The equations of the second part are the same as in the rust model (Equations 9-16). The difference is that promoter of the LuxI-LuxR system is now induced by A:<br />
<br />
[[File:eqchangral.png|center|510x280px]]<br />
<br />
[[File:eqchangra2l.png|center|385x280px]]<br />
<br />
<br />
</p><br />
<br />
<br />
</div></div>Af.simbaqueba218