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Team:Grenoble/Modeling/Amplification/Sensitivity
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<section> | <section> | ||
<h1><img src="https://static.igem.org/mediawiki/2012/4/49/1_mod.png" alt="" /> Classic Odes Parameters </h1> | <h1><img src="https://static.igem.org/mediawiki/2012/4/49/1_mod.png" alt="" /> Classic Odes Parameters </h1> | ||
| + | |||
</br> | </br> | ||
| - | <center><img src="https://static.igem.org/mediawiki/2012/4/44/Tab_parameters.png" alt="" /></center> | + | |
| + | <!--<center><img src="https://static.igem.org/mediawiki/2012/4/44/Tab_parameters.png" alt="" /></center>--> | ||
| + | |||
| + | <table id="param"> | ||
| + | <thead> | ||
| + | <tr> | ||
| + | <th class="colonne1"><b>Parameter Name</b></th> | ||
| + | <th class="colonne2"><b>Value</b></th> | ||
| + | <th class="colonne3"><b>Unit</b></th> | ||
| + | <th class="colonne4"><b>Source</b></th> | ||
| + | </tr> | ||
| + | </thead> | ||
| + | <tbody> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">AraC synthesis rate <i>v<span class="indice">mAraC</span></i></td> | ||
| + | <td class="colonne2">12 10<span class="exposant">-8</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span>.min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[1]</a> and <a href="#exp1">explanation 1</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Ca synthesis rate <i>v<span class="indice">mAraC</span></i></td> | ||
| + | <td class="colonne2">2 10<span class="exposant">-9</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span>.min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp2">explanation 2</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">AraC threshold <i>K<span class="indice">AraC</span></i></td> | ||
| + | <td class="colonne2">0.310<span class="exposant">-6</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp3">explanation 3</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Ca threshold <i>K<span class="indice">Ca</span></i> (for (CRP-cAMP) activation)</td> | ||
| + | <td class="colonne2">0.6 10<span class="exposant">-6</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp3">explanation 3</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Ca threshold <i>K'<span class="indice">Ca</span></i> (for AraC* activation)</td> | ||
| + | <td class="colonne2">0.6 10<span class="exposant">-6</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp3">explanation 3</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Dissociation constant of cAMP and CRP <i>K<span class="indice">c</span></i></td> | ||
| + | <td class="colonne2">10<span class="exposant">-5</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[2]</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Dissociation of arabinose with AraC <i>K<span class="indice">c1</span></i></td> | ||
| + | <td class="colonne2">2 10<span class="exposant">-13</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[3]</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Degradation rate of AraC <i>α<span class="indice">AraC</span></i></td> | ||
| + | <td class="colonne2">6 10<span class="exposant">-3</span></td> | ||
| + | <td class="colonne3">min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[1]</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Degradation rate of Ca <i>α<span class="indice">Ca</span></i></td> | ||
| + | <td class="colonne2">6 10<span class="exposant">-3</span></td> | ||
| + | <td class="colonne3">min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp4">explanation 4</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Degradation/exports rate of cAMP <i>α<span class="indice">cAMP</span></i></td> | ||
| + | <td class="colonne2">2.1</td> | ||
| + | <td class="colonne3">min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[4]</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Arabinose concentration</td> | ||
| + | <td class="colonne2">10<span class="exposant">-6</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Chosen by the team</td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">CRP concentration</td> | ||
| + | <td class="colonne2">10<span class="exposant">-6</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes <a href="#ref">[5]</a> and <a href="#exp1">explanation 1</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">cAMP import constant η</td> | ||
| + | <td class="colonne2">6 10<span class="exposant">-1</span></td> | ||
| + | <td class="colonne3">min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp5">explanation 5</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Catalysis constant <i>k<span class="indice">cat</span></i></td> | ||
| + | <td class="colonne2">810</td> | ||
| + | <td class="colonne3">min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp6">explanation 6</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Hill cooperativity n, <i>η<span class="indice">1</span></i>, <i>η<span class="indice">2</span></i></td> | ||
| + | <td class="colonne2">1.5</td> | ||
| + | <td class="colonne3">/</td> | ||
| + | <td class="colonne4">No, explanation 7</td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">AraC basal value <i>p<span class="indice">AraC</span></i></td> | ||
| + | <td class="colonne2">12 10<span class="exposant">-11</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></i>.<i>min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp1">explanation 1</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Ca basal value <i>p<span class="indice">AraC</span></i></td> | ||
| + | <td class="colonne2">2 10<span class="exposant">-12</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></i>.<i>min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">No, <a href="#exp1">explanation 1</a></td> | ||
| + | </tr> | ||
| + | </tbody> | ||
| + | </table> | ||
| + | |||
</br> | </br> | ||
</br> | </br> | ||
| - | <h2>Explanation 1</h2> | + | |
| + | <h2 id="exp1">Explanation 1</h2> | ||
| + | |||
</br> | </br> | ||
| - | <ul><li><u> | + | |
| + | <ul><li><u>AraC and Ca:</u></li></ul> | ||
| + | |||
</br> | </br> | ||
| - | Once the production of | + | |
| + | Once the production of AraC has been activated, we have: | ||
</br> | </br> | ||
<center><img src="https://static.igem.org/mediawiki/2012/f/f6/Eq_sens_1.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/f/f6/Eq_sens_1.png" alt="" /></center> | ||
<center><img src="https://static.igem.org/mediawiki/2012/1/11/Eq_sens_2.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/1/11/Eq_sens_2.png" alt="" /></center> | ||
</br> | </br> | ||
| - | In addition, we assume that | + | In addition, we assume that p_AraC ≪v_mAraC thus, we get: |
</br> | </br> | ||
<center><img src="https://static.igem.org/mediawiki/2012/3/38/Eq_sens_3.png" alt="" /></center> | <center><img src="https://static.igem.org/mediawiki/2012/3/38/Eq_sens_3.png" alt="" /></center> | ||
</br> | </br> | ||
| - | In addition we know that the maximum number of copies per cell of | + | In addition we know that the maximum number of copies per cell of AraC is 40, thus<img src="https://static.igem.org/mediawiki/2012/0/09/Eq_sens_4.png" alt="" />where<img src="https://static.igem.org/mediawiki/2012/3/35/Eq_sens_5.png" alt="" />Avogadro number and<img src="https://static.igem.org/mediawiki/2012/6/64/Eq_sens_6.png" alt="" />is E. coli volume. Thus, we have <img src="https://static.igem.org/mediawiki/2012/9/97/Eq_sens_7.png" alt="" />. Then, we get the value of <img src="https://static.igem.org/mediawiki/2012/2/2b/Eq_sens_8.png" alt="" />. |
| + | </br> | ||
| + | </br> | ||
| + | For the adenylate cyclase, but we assumed that there is less adenylate cyclase in the cell than AraC. Indeed, when there is too much cAMP is inhibits the production of the adenylate cyclase <a href="#ref">[6]</a>. | ||
| + | </br> | ||
| + | </br> | ||
| + | <ul><li><u>CRP:</u></li></ul> | ||
| + | </br> | ||
| + | We have 1000 copies per cell of CRP, and it’s a constant. Then by the same computation, we make the conversion into mol.L<span class="exposant">-1</span>, and we get the value of CRP. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="exp2">Explanation 2</h2> | ||
| + | </br> | ||
| + | We do not know the value of the synthesis rate of adenylate cyclase, but we assume that there is less adenylate cyclase, because if there is a huge amont of adenylate cyclase, there will too much cAMP, and then cAMP will repress the adenylate cyclase production <a href="#ref">[6]</a>. For the basal production, we make the same assumption as for AraC. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="exp3">Explanation 3</h2> | ||
| + | </br> | ||
| + | <ul><li><u>Activations by (CRP-cAMP):</u></li></ul> | ||
| + | </br> | ||
| + | To set the value of this parameter, we plotted the concentration of (CRP-cAMP) at t=2000 min as we varied the initial concentration of cAMP: | ||
| + | </br> | ||
| + | </br> | ||
| + | <center><img src="https://static.igem.org/mediawiki/2012/4/46/Graph_sens_1.png" alt="" /></center> | ||
| + | </br> | ||
| + | <center>Evolution of (CRP-cAMP) concentration at t=2000 minutes in function of the initial concentration of cAMP.</center> | ||
| + | </br> | ||
| + | </br> | ||
| + | We could notice that the maximum value of (CRP-cAMP) varied between 0 and 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. The value of the threshold had to be in this range of concentration. Not too low, else it would have meant that the proteins are always produced, and not to high, else the genes would never be expressed. In addition we assumed that AraC had to be activated first and without amplification of cAMP, seing that it is only when arac is expressed the adenylate cyclase is produced. | ||
| + | </br> | ||
| + | </br> | ||
| + | Remark: when we have [cAMP]>> 10<SUP>-6</SUP> mol/L=[CRP], we have by the same reasoning as for AraC: | ||
| + | </br> | ||
| + | </br> | ||
| + | <center><img src="https://static.igem.org/mediawiki/2012/a/a0/Eq_sens_9.png" alt="" /></center> | ||
| + | and we have<img src="https://static.igem.org/mediawiki/2012/f/f7/Eq_sens_10.png" alt="" />when [cAMP] increases. Thus, in this case we could be sure that the concentration of (CRP-cAMP) wouldn’t exceed 10<SUP>-6</SUP> mol.L<span class="exposant">-1</span>. | ||
| + | In addition, when [cAMP]≤10<SUP>-6</SUP> mol/L, we also know that because of the value of [CRP], [(CRP-cAMP)] wouldn’t exceed this threshold. | ||
| + | </br> | ||
| + | </br> | ||
| + | <ul><li><u>Activation by AraC*:</u></li></ul> | ||
| + | </br> | ||
| + | Same reasoning, we give the same type of graph: | ||
| + | </br> | ||
| + | </br> | ||
| + | <center><img src="https://static.igem.org/mediawiki/2012/6/69/Graph_sens_2.png" alt="" /></center> | ||
| + | </br> | ||
| + | We could set the value of K'<SUB>Ca</SUB>. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="exp4">Explanation 4</h2> | ||
| + | </br> | ||
| + | Inspired from AraC. By discussing with the biologists we concluded that Ca is also a stable protein. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="exp5">Explanation 5</h2> | ||
| + | </br> | ||
| + | By discussing with the biologists, we assumed that there is around 10 times more cAMP out of the cell than inside the cell. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="exp6">Explanation 6</h2> | ||
| + | </br> | ||
| + | In the reference <a href="#ref">[6]</a>, we have k<SUB>cat</SUB>=100 min<SUP>-1</SUP> in vitro. However, by discussing with the biologists, we assumed that in vivo this value was higher. | ||
| + | </br> | ||
| + | </section> | ||
| + | <section> | ||
| + | <h1><img src="https://static.igem.org/mediawiki/2012/1/1e/2_mod.png" alt="" /> Quorum sensing parameters </h1> | ||
| + | </br> | ||
| + | |||
| + | <!--<center><img src="https://static.igem.org/mediawiki/2012/1/1f/Tab_par_2.png" alt="" /></center>--> | ||
| + | |||
| + | <table id="param_2"> | ||
| + | <thead> | ||
| + | <tr> | ||
| + | <th class="colonne1"><b>Parameter Name</b></th> | ||
| + | <th class="colonne2"><b>Value</b></th> | ||
| + | <th class="colonne3"><b>Unit</b></th> | ||
| + | <th class="colonne4"><b>Source</b></th> | ||
| + | </tr> | ||
| + | </thead> | ||
| + | <tbody> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">cAMP diffusion coefficient <i>D<span class="indice">diff</span></i></td> | ||
| + | <td class="colonne2">2.66 10<span class="exposant">-4</span></td> | ||
| + | <td class="colonne3">cm<span class="exposant">2</span>.min<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">Yes, <a href="#ref">[8]</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1"><i>E. coli</i> volume <i>v<span class="indice">c</span></i></td> | ||
| + | <td class="colonne2">10<span class="exposant">-12</span></td> | ||
| + | <td class="colonne3">cm<span class="exposant">3</span></td> | ||
| + | <td class="colonne4">Yes, <a href="#ref">[9]</a></td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1"><i>E. coli</i> number by <i>cm<span class="exposant">3</span> ρ</i></td> | ||
| + | <td class="colonne2">0.5 10<span class="exposant">-12</span></td> | ||
| + | <td class="colonne3">cm<span class="exposant">-3</span></td> | ||
| + | <td class="colonne4">No, <a href="#ex1">explanation 1</a></td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">lenght and width <i>l<span class="indice">x</span> = l<span class="indice">y</span></i></td> | ||
| + | <td class="colonne2">2</td> | ||
| + | <td class="colonne3">cm</td> | ||
| + | <td class="colonne4">chosen</td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Number of points <i>N<span class="indice">x</span> </span> = N<span class="indice">y</span></i></td> | ||
| + | <td class="colonne2">20</td> | ||
| + | <td class="colonne3">/</td> | ||
| + | <td class="colonne4">chosen</td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Time <i>Δt</i></td> | ||
| + | <td class="colonne2">1000</td> | ||
| + | <td class="colonne3">min</td> | ||
| + | <td class="colonne4">chosen</td> | ||
| + | </tr> | ||
| + | <tr class="pair"> | ||
| + | <td class="colonne1">Number of time <i>N<span class="indice">t</span></i></td> | ||
| + | <td class="colonne2">1000</td> | ||
| + | <td class="colonne3">/</td> | ||
| + | <td class="colonne4">chosen</td> | ||
| + | </tr> | ||
| + | <tr class="impair"> | ||
| + | <td class="colonne1">Initial concentration of cAMP <i>N<span class="indice"></span></i></td> | ||
| + | <td class="colonne2">10<span class="exposant">-4</span></td> | ||
| + | <td class="colonne3">mol.L<span class="exposant">-1</span></td> | ||
| + | <td class="colonne4">chosen, <a href="#ex2">explanation 2</a></td> | ||
| + | </tr> | ||
| + | </tbody> | ||
| + | </table> | ||
| + | |||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="ex1">Explanation 1</h2> | ||
| + | </br> | ||
| + | We assumed that they would not be glued together, but not too far at the same time. | ||
| + | </br> | ||
| + | </br> | ||
| + | <h2 id="ex2">Explanation 2</h2> | ||
| + | </br> | ||
| + | We work above the threshold, because we want to know the speed of the diffusion when we have a detection. | ||
| + | </section> | ||
| + | <section> | ||
| + | <h1 id="ref">References</h1> | ||
| + | <ul><li>[1] Bionumbers. <a href="http://bionumbers.hms.harvard.edu/search.aspx?log=y&task=searchbytrmorg&trm=arac&org=" target="_blank">http://bionumbers.hms.harvard.edu/search.aspx?log=y&task=searchbytrmorg&trm=arac&org=</a> </li></ul> | ||
| + | <ul><li>[2] <u>Purification of and properties of the cyclic adenosine 2' ,5'-monophosphate receptor which mediates cyclic adenosine 3',5'-monophosphate dependent gene transcription in E. Coli.</u> </br>W.B. Aderson, A. B. Schneider, M. Emmer, R.L. Perlman, and I. Pasta</li></ul> | ||
| + | <ul><li>[3] <u>AraC protein, regulation of the L-arabinose operon inEscherichiacoli, and the light switch mechanism of AraC action.</u> </br>Robert Schleif Biology Department, Johns Hopkins University, Baltimore, MD, USA. </li></ul> | ||
| + | <ul><li>[4] Epstein et Hesse 1975. </li></ul> | ||
| + | <ul><li>[5] <u>Transcriptional regulation shapes the organization of genes on bacterial chromosomes.</u></br>Sarath Chandra Janga, Heladia Salgado, Augustino Martinez. </br><a href="http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2699516/ " target="_blank">http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2699516/ </a> </li></ul> | ||
| + | <ul><li>[6] <u>Regulation of adenylate cyclase in E. coli.</u> </br>Edith Gstrein-Reider and Manfred Schweiger, Institut fur Biochemie (nat. Fak.), UniversitAt Innsbruck, A-6020 Innsbruck, Austria. </li></ul> | ||
| + | <ul><li>[7] <u>Purification and characterization of adenylate cyclase from E. coli K12.</u> </br>Yang and Epstein 1983. </li></ul> | ||
| + | <ul><li>[8] <u>Solubility and diffusion coefficient of adenosine 3’ :5’ – monophosphate.</u> </br>Martin Dworkin and Kenneth H. Keller, 1976. </li></ul> | ||
| + | <ul><li>[9] <a href="http://ccdb.wishartlab.com/CCDB/cgi-bin/STAT_NEW.cgi" target="_blank">http://ccdb.wishartlab.com/CCDB/cgi-bin/STAT_NEW.cgi</a> </li></ul> | ||
</section> | </section> | ||
</div> | </div> | ||
Latest revision as of 20:45, 26 September 2012
Classic Odes Parameters
| Parameter Name | Value | Unit | Source |
|---|---|---|---|
| AraC synthesis rate vmAraC | 12 10-8 | mol.L-1.min-1 | Yes [1] and explanation 1 |
| Ca synthesis rate vmAraC | 2 10-9 | mol.L-1.min-1 | No, explanation 2 |
| AraC threshold KAraC | 0.310-6 | mol.L-1 | No, explanation 3 |
| Ca threshold KCa (for (CRP-cAMP) activation) | 0.6 10-6 | mol.L-1 | No, explanation 3 |
| Ca threshold K'Ca (for AraC* activation) | 0.6 10-6 | mol.L-1 | No, explanation 3 |
| Dissociation constant of cAMP and CRP Kc | 10-5 | mol.L-1 | Yes [2] |
| Dissociation of arabinose with AraC Kc1 | 2 10-13 | mol.L-1 | Yes [3] |
| Degradation rate of AraC αAraC | 6 10-3 | min-1 | Yes [1] |
| Degradation rate of Ca αCa | 6 10-3 | min-1 | No, explanation 4 |
| Degradation/exports rate of cAMP αcAMP | 2.1 | min-1 | Yes [4] |
| Arabinose concentration | 10-6 | mol.L-1 | Chosen by the team |
| CRP concentration | 10-6 | mol.L-1 | Yes [5] and explanation 1 |
| cAMP import constant η | 6 10-1 | min-1 | No, explanation 5 |
| Catalysis constant kcat | 810 | min-1 | No, explanation 6 |
| Hill cooperativity n, η1, η2 | 1.5 | / | No, explanation 7 |
| AraC basal value pAraC | 12 10-11 | mol.L-1.min-1 | No, explanation 1 |
| Ca basal value pAraC | 2 10-12 | mol.L-1.min-1 | No, explanation 1 |
Explanation 1
- AraC and Ca:
where
Avogadro number and
is E. coli volume. Thus, we have 
. Then, we get the value of 
.
For the adenylate cyclase, but we assumed that there is less adenylate cyclase in the cell than AraC. Indeed, when there is too much cAMP is inhibits the production of the adenylate cyclase [6].
- CRP:
Explanation 2
We do not know the value of the synthesis rate of adenylate cyclase, but we assume that there is less adenylate cyclase, because if there is a huge amont of adenylate cyclase, there will too much cAMP, and then cAMP will repress the adenylate cyclase production [6]. For the basal production, we make the same assumption as for AraC.Explanation 3
- Activations by (CRP-cAMP):
when [cAMP] increases. Thus, in this case we could be sure that the concentration of (CRP-cAMP) wouldn’t exceed 10-6 mol.L-1.
In addition, when [cAMP]≤10-6 mol/L, we also know that because of the value of [CRP], [(CRP-cAMP)] wouldn’t exceed this threshold.
- Activation by AraC*:
Explanation 4
Inspired from AraC. By discussing with the biologists we concluded that Ca is also a stable protein.Explanation 5
By discussing with the biologists, we assumed that there is around 10 times more cAMP out of the cell than inside the cell.Explanation 6
In the reference [6], we have kcat=100 min-1 in vitro. However, by discussing with the biologists, we assumed that in vivo this value was higher.
Quorum sensing parameters
| Parameter Name | Value | Unit | Source |
|---|---|---|---|
| cAMP diffusion coefficient Ddiff | 2.66 10-4 | cm2.min-1 | Yes, [8] |
| E. coli volume vc | 10-12 | cm3 | Yes, [9] |
| E. coli number by cm3 ρ | 0.5 10-12 | cm-3 | No, explanation 1 |
| lenght and width lx = ly | 2 | cm | chosen |
| Number of points Nx = Ny | 20 | / | chosen |
| Time Δt | 1000 | min | chosen |
| Number of time Nt | 1000 | / | chosen |
| Initial concentration of cAMP N | 10-4 | mol.L-1 | chosen, explanation 2 |
Explanation 1
We assumed that they would not be glued together, but not too far at the same time.Explanation 2
We work above the threshold, because we want to know the speed of the diffusion when we have a detection.References
- [1] Bionumbers. http://bionumbers.hms.harvard.edu/search.aspx?log=y&task=searchbytrmorg&trm=arac&org=
- [2] Purification of and properties of the cyclic adenosine 2' ,5'-monophosphate receptor which mediates cyclic adenosine 3',5'-monophosphate dependent gene transcription in E. Coli. W.B. Aderson, A. B. Schneider, M. Emmer, R.L. Perlman, and I. Pasta
- [3] AraC protein, regulation of the L-arabinose operon inEscherichiacoli, and the light switch mechanism of AraC action. Robert Schleif Biology Department, Johns Hopkins University, Baltimore, MD, USA.
- [4] Epstein et Hesse 1975.
- [5] Transcriptional regulation shapes the organization of genes on bacterial chromosomes.Sarath Chandra Janga, Heladia Salgado, Augustino Martinez. http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2699516/
- [6] Regulation of adenylate cyclase in E. coli. Edith Gstrein-Reider and Manfred Schweiger, Institut fur Biochemie (nat. Fak.), UniversitAt Innsbruck, A-6020 Innsbruck, Austria.
- [7] Purification and characterization of adenylate cyclase from E. coli K12. Yang and Epstein 1983.
- [8] Solubility and diffusion coefficient of adenosine 3’ :5’ – monophosphate. Martin Dworkin and Kenneth H. Keller, 1976.
