ETHZ/Parameters

From 2007.igem.org

(Difference between revisions)
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=====.:: Introduction ::.=====
=====.:: Introduction ::.=====
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In this page, the equations that model our system are and explained. The values that were chosen for the system parameters are presented and the results of our simulations are analyzed. References are provided at the end of the page. For an introduction to system modeling in synthetic biology, please read our modeling tutorial [[ETHZ/Modeling_Basics|here]].</p><br>
In this page, the equations that model our system are and explained. The values that were chosen for the system parameters are presented and the results of our simulations are analyzed. References are provided at the end of the page. For an introduction to system modeling in synthetic biology, please read our modeling tutorial [[ETHZ/Modeling_Basics|here]].</p><br>
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=====.:: Table of Parameters ::.=====
+
=====.:: Model Parameters ::.=====
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+
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<p>
+
{| class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:left; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
{| class="wikitable" border="1" cellspacing="0" cellpadding="2" style="text-align:left; margin: 1em 1em 1em 0; background: #f9f9f9; border: 1px #aaa solid; border-collapse: collapse;"
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! Value
! Value
! Description
! Description
-
! References
+
! Comments
|-
|-
| c<sub>1</sub><sup>max</sup>
| c<sub>1</sub><sup>max</sup>
| 0.01 [mM/h]
| 0.01 [mM/h]
-
| max. transcription rate of<br> constitutive promoter <br>(per gene)
+
| max. transcription rate of constitutive promoter (per gene)
-
| Estimate
+
| promoter no. J23105; Reference: Estimate
|-
|-
| c<sub>2</sub><sup>max</sup>
| c<sub>2</sub><sup>max</sup>
| 0.01 [mM/h]
| 0.01 [mM/h]
-
| max. transcription rate of<br> luxR-activated promoter <br>(per gene)
+
| max. transcription rate of luxR-activated promoter (per gene)
-
| Estimate
+
| Reference: Estimate
|-
|-
| l<sup>hi</sup>
| l<sup>hi</sup>
| 25
| 25
| high-copy plasmid number
| high-copy plasmid number
-
| Estimate
+
| Reference: Estimate
|-
|-
| l<sup>lo</sup>
| l<sup>lo</sup>
| 5
| 5
| low-copy plasmid number
| low-copy plasmid number
-
| Estimate
+
| Reference: Estimate
|-
|-
-
| a<sub>p22cII,LacI</sub>
+
| a<sub>Q<sub>2</sub>,R</sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> p22cII/LacI-inhibited genes
+
| basic production of Q<sub>2</sub>/R-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| a<sub>p22cII</sub>
+
| a<sub>Q<sub>2</sub></sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> p22cII-inhibited genes
+
| basic production of Q<sub>2</sub>-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| a<sub>cI,TetR</sub>
+
| a<sub>Q<sub>1</sub>,S</sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> cI/TetR-inhibited genes
+
| basic production of Q<sub>1</sub>/S-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| a<sub>cI</sub>
+
| a<sub>Q<sub>1</sub></sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> cI-inhibited genes
+
| basic production of Q<sub>1</sub>-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| a<sub>p22cII,TetR</sub>
+
| a<sub>Q<sub>2</sub>,S</sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> p22cII/TetR-inhibited genes
+
| basic production of Q<sub>2</sub>/S-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| a<sub>cI,LacI</sub>
+
| a<sub>Q<sub>1</sub>,R</sub>
| 0.1 - 0.2
| 0.1 - 0.2
-
| basic production of<br> cI/TetR-inhibited genes
+
| basic production of Q<sub>1</sub>/R-inhibited genes
-
| Discussion
+
| Reference: Conclusions after discussion
|-
|-
-
| d<sub>LacI</sub>
+
| d<sub>R</sub>
-
| 2.31e-3 [pro sec]
+
| 2.31e-3 [per sec]
| degradation of lacI
| degradation of lacI
-
| [10]
+
| Ref. [10]
|-
|-
-
| d<sub>TetR</sub>
+
| d<sub>S</sub>
-
| 1e-5 [pro sec]/2.31e-3 [pro sec]
+
| 1e-5 [pro sec]/2.31e-3 [per sec]
-
| degradation of TetR
+
| degradation of tetR
-
| [9], [10]
+
| Ref. [9]/ Ref. [10]
|-
|-
-
| d<sub>LuxR</sub>
+
| d<sub>L</sub>
| 1e-3 - 1e-4 [per sec]
| 1e-3 - 1e-4 [per sec]
-
| degradation of LuxR
+
| degradation of luxR
-
| [6]
+
| Ref: [6]
|-
|-
-
| d<sub>cI</sub>
+
| d<sub>Q<sub>1</sub></sub>
| 7e-4 [per sec]
| 7e-4 [per sec]
| degradation of cI
| degradation of cI
-
| [7]
+
| Ref. [7]
|-
|-
-
| d<sub>p22cII</sub>
+
| d<sub>Q<sub>2</sub></sub>
|  
|  
| degradation of p22cII
| degradation of p22cII
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| 6.3e-3 [per min]
| 6.3e-3 [per min]
| degradation of YFP
| degradation of YFP
-
| suppl. mat. to Ref. [8]
+
| suppl. mat. to Ref. [8] corresponding to a half life of 110min
|-
|-
| d<sub>GFP</sub>
| d<sub>GFP</sub>
Line 110: Line 107:
| in analogy to YFP
| in analogy to YFP
|-
|-
-
| K<sub>LacI</sub>
+
| K<sub>R</sub>
-
| 1.3e-3 - 2e-3 [mM/h]
+
| 0.1 - 1 [pM]
-
| lacI repressor <br>dissociation constant
+
| lacI repressor dissociation constant
-
| [2], [5]
+
| Ref. [2]
|-
|-
-
| K<sub>IPTG</sub>
+
| K<sub>I<sub>R</sub></sub>
-
| 1.5e-10 [mM/h]
+
| 1.3 [&#181;M]
-
| IPTG-lacI repressor <br>dissociation constant
+
| IPTG-lacI repressor dissociation constant
-
| [5]
+
| Ref. [2]
|-
|-
-
| K<sub>TetR</sub>
+
| K<sub>S</sub>
-
| 5.6 (+-2) [nM-1]
+
| 179 [pM]
-
| tetR repressor <br>dissociation constant
+
| tetR repressor dissociation constant
-
| [1]
+
| Ref. [1]
|-
|-
-
| K<sub>aTc</sub>
+
| K<sub>I<sub>S</sub></sub>
-
| 1120 (+-400) [nM-1]
+
| 893 [pM]
-
| aTc-tetR repressor <br>dissociation constant
+
| aTc-tetR repressor dissociation constant
-
| [1], [3]
+
| Ref. [1]
|-
|-
-
| K<sub>LuxR</sub>
+
| K<sub>L</sub>
-
|  
+
| 55 - 520 [nM]
-
* 0.003 [mM/s]
+
| luxR activator dissociation constant
-
* 55 - 520 [nM]
+
| Ref: [6]
-
| luxR activator <br>dissociation constant
+
-
| [6]
+
|-
|-
-
| K<sub>AHL</sub>
+
| K<sub>I<sub>L</sub></sub>
-
|  
+
| 0.09 - 1 [&#181;M]
-
* 0.009 [mM/s] - 0.1 [mM/s]
+
| AHL-luxR activator dissociation constant
-
* 0.09 - 1 [&#181;M]
+
| Ref: [6]
-
| AHL-luxR activator <br>dissociation constant
+
-
| [6]
+
|-
|-
-
| K<sub>cI</sub>
+
| K<sub>Q<sub>1</sub></sub>
-
| 2e-3 [mM/h]
+
|
-
| cI repressor <br>dissociation constant
+
* 8 [pM]
-
| [5]
+
* 50 [nM]
 +
| cI repressor dissociation constant
 +
|
 +
* Ref. [12]
 +
* starting with values of Ref. [6] and using Ref. [3]
|-
|-
-
| K<sub>p22cII</sub>
+
| K<sub>Q<sub>2</sub></sub>
-
|  
+
| 0.577 [&#181;M]
-
| p22cII repressor <br>dissociation constant
+
| p22cII repressor dissociation constant
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
|-
|-
-
| n<sub>LacI</sub>
+
| n<sub>R</sub>
| 1
| 1
-
| lacI repressor <br>Hill cooperativity
+
| lacI repressor Hill cooperativity
-
| [5]
+
| Ref. [5]
|-
|-
-
| n<sub>IPTG</sub>
+
| n<sub>I<sub>R</sub></sub>
| 2
| 2
-
| IPTG-lacI repressor <br>Hill cooperativity
+
| IPTG-lacI repressor Hill cooperativity
-
| [5]
+
| Ref. [5]
|-
|-
-
| n<sub>TetR</sub>
+
| n<sub>S</sub>
| 3
| 3
-
| tetR repressor <br>Hill cooperativity
+
| tetR repressor Hill cooperativity
-
| [3]
+
| Ref. [3]
|-
|-
-
| n<sub>aTc</sub>
+
| n<sub>I<sub>S</sub></sub>
| 2 (1.5-2.5)
| 2 (1.5-2.5)
-
| aTc-tetR repressor <br>Hill cooperativity
+
| aTc-tetR repressor Hill cooperativity
-
| [3]
+
|Ref. [3]
|-
|-
-
| n<sub>LuxR</sub>
+
| n<sub>L</sub>
| 2
| 2
-
| luxR activator <br>Hill cooperativity
+
| luxR activator Hill cooperativity
-
| [6]
+
| Ref: [6]
|-
|-
-
| n<sub>AHL</sub>
+
| n<sub>I<sub>L</sub></sub>
| 1
| 1
-
| AHL-luxR activator <br>Hill cooperativity
+
| AHL-luxR activator Hill cooperativity
-
| [3]
+
| Ref. [3]
|-
|-
-
| n<sub>cI</sub>
+
| n<sub>Q<sub>1</sub></sub>
-
| 1.9
+
| 2
-
| cI repressor <br>Hill cooperativity
+
| cI repressor Hill cooperativity
-
| [5]
+
| Ref. [12]
|-
|-
-
| n<sub>p22cII</sub>
+
| n<sub>Q<sub>2</sub></sub>
-
|  
+
| 4
-
| p22cII repressor <br>Hill cooperativity
+
| p22cII repressor Hill cooperativity
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
|-
|-
|}
|}
-
 
-
 
-
 
-
</p><br>
 
=====.:: References ::.=====
=====.:: References ::.=====
<p>
<p>
-
[1] Weber W., Stelling J., Rimann M., Keller B., Daoud-El Baba M., Weber C.C., Aubel D., and Fussenegger M., <i>"A synthetic time-delay circuit in mammalian cells and mice"</i>, Proceedings of the National Academy of Sciences, vol. 104, no. 8, pp. 2643, 2007.<br>
 
-
[2] Setty Y., Mayo AE, Surette MG, and Alon U., <i>"Detailed map of a cis-regulatory input function"</i>, Proceeding of the National Academy of Sciences, vol. 100, no. 13, pp. 7702--7707, 2003.<br>
 
-
[3] Braun D., Basu S., and Weiss R., <i>"Parameter Estimation for Two Synthetic Gene Networks: A Case Study"</i>, IEEE Int'l Conf. Acoustics, Speech, and Signal Processing 2005, vol. 5, 2005.<br>
 
-
[4] Fung E., Wong W.W., Suen J.K., Bulter T., Lee S., and Liao J.C., <i>"A synthetic gene--metabolic oscillator"</i>, Nature, vol. 435, no. 7038, pp. 118--122, 2005, supplementary material.<br>
 
-
[5] Iadevaia S., and Mantzaris N.V., <i>"Genetic network driven control of PHBV copolymer composition"</i>, Journal of Biotechnology, vol. 122, no. 1, pp. 99--121, 2006.<br>
 
-
[6] Goryachev AB, Toh DJ, and Lee T., <i>"Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants"</i>, Biosystems, vol. 83, no. 2-3, pp. 178--187, 2006.<br>
 
-
[7] Arkin A., Ross J., and McAdams H.H., <i>"Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells"</i>, Genetics, vol. 149, no. 4, pp. 1633--1648, 1998.<br>
 
-
[8] Colman-Lerner A., Chin T.E., and Brent R., <i>"Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates"</i>, Cell, vol. 107, no. 6, pp. 739--750, 2001.<br>
 
-
[9] Becskei A., and Serrano L., <i>"Engineering stability in gene networks by autoregulation"</i>, Nature, vol. 405, no.6786, pp.590--593, 2000.<br>
 
-
[10] Tuttle L.M., Salis H., Tomshine J., and Kaznessis Y.N., <i>"Model-Driven Designs of an Oscillating Gene Network"</i>, Biophysical Journal, vol. 89, no. 6, pp. 3873--3883, 2005.<br>
 
-
 
-
</p><br>
 
[http://www.pnas.org/cgi/content/abstract/104/8/2643 &#91;1&#93; Weber W et al.] <i>"A synthetic time-delay circuit in mammalian cells and mice"</i>, P Natl Acad Sci USA 104(8):2643-2648, 2007<br />
[http://www.pnas.org/cgi/content/abstract/104/8/2643 &#91;1&#93; Weber W et al.] <i>"A synthetic time-delay circuit in mammalian cells and mice"</i>, P Natl Acad Sci USA 104(8):2643-2648, 2007<br />
[http://www.pnas.org/cgi/content/full/100/13/7702?ck=nck  &#91;2&#93; Setty Y et al.] <i>"Detailed map of a cis-regulatory input function"</i>, P Natl Acad Sci USA 100(13):7702-7707, 2003<br />
[http://www.pnas.org/cgi/content/full/100/13/7702?ck=nck  &#91;2&#93; Setty Y et al.] <i>"Detailed map of a cis-regulatory input function"</i>, P Natl Acad Sci USA 100(13):7702-7707, 2003<br />

Revision as of 10:05, 13 October 2007

.:: Introduction ::.

Having decided to work on an engineered biological system which exhibits learning, we elaborated on its design. Discussing with the biologists of the team, we realized that what we knew from the field of logic design as JK flip-flop with a latch may be implemented with biological parts using a modified toggle switch. Initial simulations showed us that it was possible to reach the desired behaviour. Therefore, a complete framework of differential equations describing the system was constructed and parameters were searched in the literature. Simulations performed with our new detailed model are very encouraging. In this page, the equations that model our system are and explained. The values that were chosen for the system parameters are presented and the results of our simulations are analyzed. References are provided at the end of the page. For an introduction to system modeling in synthetic biology, please read our modeling tutorial here.


.:: Model Parameters ::.
Parameter Value Description Comments
c1max 0.01 [mM/h] max. transcription rate of constitutive promoter (per gene) promoter no. J23105; Reference: Estimate
c2max 0.01 [mM/h] max. transcription rate of luxR-activated promoter (per gene) Reference: Estimate
lhi 25 high-copy plasmid number Reference: Estimate
llo 5 low-copy plasmid number Reference: Estimate
aQ2,R 0.1 - 0.2 basic production of Q2/R-inhibited genes Reference: Conclusions after discussion
aQ2 0.1 - 0.2 basic production of Q2-inhibited genes Reference: Conclusions after discussion
aQ1,S 0.1 - 0.2 basic production of Q1/S-inhibited genes Reference: Conclusions after discussion
aQ1 0.1 - 0.2 basic production of Q1-inhibited genes Reference: Conclusions after discussion
aQ2,S 0.1 - 0.2 basic production of Q2/S-inhibited genes Reference: Conclusions after discussion
aQ1,R 0.1 - 0.2 basic production of Q1/R-inhibited genes Reference: Conclusions after discussion
dR 2.31e-3 [per sec] degradation of lacI Ref. [10]
dS 1e-5 [pro sec]/2.31e-3 [per sec] degradation of tetR Ref. [9]/ Ref. [10]
dL 1e-3 - 1e-4 [per sec] degradation of luxR Ref: [6]
dQ1 7e-4 [per sec] degradation of cI Ref. [7]
dQ2 degradation of p22cII
dYFP 6.3e-3 [per min] degradation of YFP suppl. mat. to Ref. [8] corresponding to a half life of 110min
dGFP 6.3e-3 [per min] degradation of GFP in analogy to YFP
dRFP 6.3e-3 [per min] degradation of RFP in analogy to YFP
dCFP 6.3e-3 [per min] degradation of CFP in analogy to YFP
KR 0.1 - 1 [pM] lacI repressor dissociation constant Ref. [2]
KIR 1.3 [µM] IPTG-lacI repressor dissociation constant Ref. [2]
KS 179 [pM] tetR repressor dissociation constant Ref. [1]
KIS 893 [pM] aTc-tetR repressor dissociation constant Ref. [1]
KL 55 - 520 [nM] luxR activator dissociation constant Ref: [6]
KIL 0.09 - 1 [µM] AHL-luxR activator dissociation constant Ref: [6]
KQ1
  • 8 [pM]
  • 50 [nM]
cI repressor dissociation constant
  • Ref. [12]
  • starting with values of Ref. [6] and using Ref. [3]
KQ2 0.577 [µM] p22cII repressor dissociation constant Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
nR 1 lacI repressor Hill cooperativity Ref. [5]
nIR 2 IPTG-lacI repressor Hill cooperativity Ref. [5]
nS 3 tetR repressor Hill cooperativity Ref. [3]
nIS 2 (1.5-2.5) aTc-tetR repressor Hill cooperativity Ref. [3]
nL 2 luxR activator Hill cooperativity Ref: [6]
nIL 1 AHL-luxR activator Hill cooperativity Ref. [3]
nQ1 2 cI repressor Hill cooperativity Ref. [12]
nQ2 4 p22cII repressor Hill cooperativity Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?
.:: References ::.

[1] Weber W et al. "A synthetic time-delay circuit in mammalian cells and mice", P Natl Acad Sci USA 104(8):2643-2648, 2007
[2] Setty Y et al. "Detailed map of a cis-regulatory input function", P Natl Acad Sci USA 100(13):7702-7707, 2003
[3] Braun D et al. "Parameter Estimation for Two Synthetic Gene Networks: A Case Study", ICASSP 5:769-772, 2005
[4] Fung E et al. "A synthetic gene--metabolic oscillator", Nature 435:118-122, 2005 (supplementary material)
[5] Iadevaia S and Mantzais NV "Genetic network driven control of PHBV copolymer composition", J Biotechnol 122(1):99-121, 2006
[6] Goryachev AB et al. "Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants", Biosystems 83(2-3):178-187, 2004
[7] Arkin A et al. "Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells", Genetics 149: 1633-1648, 1998
[8] Colman-Lerner A et al. "Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates", Cell 107(6): 739-750, 2001 (supplementary material)
[9] Becskei A and Serrano L "Engineering stability in gene networks by autoregulation", Nature 405: 590-593, 2000
[10] Tuttle et al. "Model-Driven Designs of an Oscillating Gene Network", Biophys J 89(6):3873-3883, 2005
[11] McMillen LM et al. "Synchronizing genetic relaxation oscillators by intercell signaling", P Natl Acad Sci USA 99(2):679-684, 2002
[12] Basu S et al. "A synthetic multicellular system for programmed pattern formation", Nature 434:1130-1134, 2005