ETHZ/Parameters

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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.
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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>
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=====.:: Table of Parameters ::.=====
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= Parameters for the educatETH <i>E.coli</i> system =
<p>
<p>
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In order to ensure that our simulation results match the biology as close as possible, we tried to find good estimates for the biological system parameters. To this end, we performed an extensive literature review. However, not all parameters were found in the literature, especially those which do not refer to vastly used proteins. Whenever this was the case, logical estimates were provided by our biologists based on empirical values.
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</p><br>
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{| 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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== Model Parameters ==
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! Parameter                         
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! Value
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=== General parameters ===
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! Description
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{| class="wikitable" width="100%" 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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! References
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!width="10%"| Parameter                         
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!width="10%"| Value
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!width="20%"| Description
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!width="60%"| 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)
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| max. transcription rate of constitutive promoter (per gene)
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| Estimate
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| promoter no. J23105; 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)
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| max. transcription rate of LuxR-activated promoter (per gene)
| Estimate
| Estimate
|-
|-
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| Estimate
| Estimate
|-
|-
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| a<sub>p22cII,LacI</sub>
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| a
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| 0.1 - 0.2
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| 1%
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| basic production of<br> p22cII/LacI-inhibited genes
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| basic production levels
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| Discussion
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| Estimate
|-
|-
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| a<sub>p22cII</sub>
+
|}
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| 0.1 - 0.2
+
 
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| basic production of<br> p22cII-inhibited genes
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=== Degradation constants ===
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| Discussion
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{| class="wikitable" width="100%" 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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|-
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!width="10%"| Parameter                       
-
| a<sub>cI,TetR</sub>
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!width="10%"| Value
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| 0.1 - 0.2
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!width="20%"| Description
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| basic production of<br> cI/TetR-inhibited genes
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!width="60%"| Comments
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| Discussion
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-
|-
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| a<sub>cI</sub>
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| 0.1 - 0.2
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| basic production of<br> cI-inhibited genes
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| Discussion
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-
|-
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| a<sub>p22cII,TetR</sub>
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-
| 0.1 - 0.2
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| basic production of<br> p22cII/TetR-inhibited genes
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-
| Discussion
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-
|-
+
-
| a<sub>cI,LacI</sub>
+
-
| 0.1 - 0.2
+
-
| basic production of<br> cI/TetR-inhibited genes
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-
| Discussion
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|-
|-
| d<sub>LacI</sub>
| d<sub>LacI</sub>
-
| 2.31e-3 [pro sec]
+
| 2.31e-3 [1/s]
-
| degradation of lacI
+
| degradation of LacI
-
| [10]
+
| Ref. [10]
|-
|-
| d<sub>TetR</sub>
| d<sub>TetR</sub>
-
| 1e-5 [pro sec]/2.31e-3 [pro sec]
+
|  
 +
*1e-5 [1/s]
 +
*2.31e-3 [1/s]
| degradation of TetR
| degradation of TetR
-
| [9], [10]
+
|  
 +
*Ref. [9]
 +
*Ref. [10]
|-
|-
| d<sub>LuxR</sub>
| d<sub>LuxR</sub>
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| 1e-3 - 1e-4 [per sec]
+
| 1e-3 - 1e-4 [1/s]
| degradation of LuxR
| degradation of LuxR
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| [6]
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| Ref: [6]
|-
|-
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| d<sub>cI</sub>
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| d<sub>CI</sub>
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| 7e-4 [per sec]
+
| 7e-4 [1/s]
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| degradation of cI
+
| degradation of CI
-
| [7]
+
| Ref. [7]
|-
|-
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| d<sub>p22cII</sub>
+
| d<sub>P22CII</sub>
 +
|
 +
| degradation of P22CII
|  
|  
-
| degradation of p22cII
 
|-
|-
| d<sub>YFP</sub>
| d<sub>YFP</sub>
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| 6.3e-3 [per min]
+
| 6.3e-3 [1/min]
| degradation of YFP
| degradation of YFP
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| suppl. mat. to Ref. [8]
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| suppl. mat. to Ref. [8] corresponding to a half life of 110min
|-
|-
| d<sub>GFP</sub>
| d<sub>GFP</sub>
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| 6.3e-3 [per min]
+
| 6.3e-3 [1/min]
| degradation of GFP
| degradation of GFP
| in analogy to YFP
| in analogy to YFP
|-
|-
| d<sub>RFP</sub>
| d<sub>RFP</sub>
-
| 6.3e-3 [per min]
+
| 6.3e-3 [1/min]
| degradation of RFP
| degradation of RFP
| in analogy to YFP
| in analogy to YFP
|-
|-
| d<sub>CFP</sub>
| d<sub>CFP</sub>
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| 6.3e-3 [per min]
+
| 6.3e-3 [1/min]
| degradation of CFP
| degradation of CFP
| in analogy to YFP
| in analogy to YFP
 +
|-
 +
|}
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=== Dissociation constants ===
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{| class="wikitable" width="100%" 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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!width="10%"| Parameter                       
 +
!width="10%"| Value
 +
!width="20%"| Description
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!width="60%"| Comments
|-
|-
| K<sub>LacI</sub>
| K<sub>LacI</sub>
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| 1.3e-3 - 2e-3 [mM/h]
+
|  
-
| lacI repressor <br>dissociation constant
+
* 0.1 - 1 [pM]
-
| [2], [5]
+
* 800 [nM]
 +
| LacI repressor dissociation constant
 +
|  
 +
* Ref. [2]
 +
* Ref. [12]
|-
|-
| K<sub>IPTG</sub>
| K<sub>IPTG</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>TetR</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>ATC</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>LuxR</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>AHL</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>CI</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>P22CII</sub>
-
|  
+
| 0.577 [&#181;M]
-
| p22cII repressor <br>dissociation constant
+
| P22CII repressor dissociation constant
 +
| Ref. [11]
 +
|-
 +
|}
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=== Hill cooperativity ===
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{| class="wikitable" width="100%" 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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!width="10%"| Parameter                       
 +
!width="10%"| Value
 +
!width="20%"| Description
 +
!width="60%"| Comments
|-
|-
| n<sub>LacI</sub>
| n<sub>LacI</sub>
-
| 1
+
|  
-
| lacI repressor <br>Hill cooperativity
+
* 1
-
| [5]
+
* 2
 +
| LacI repressor Hill cooperativity
 +
|  
 +
* Ref. [5]
 +
* Ref. [12]
|-
|-
| n<sub>IPTG</sub>
| n<sub>IPTG</sub>
| 2
| 2
-
| IPTG-lacI repressor <br>Hill cooperativity
+
| IPTG-LacI repressor Hill cooperativity
-
| [5]
+
| Ref. [5]
|-
|-
| n<sub>TetR</sub>
| n<sub>TetR</sub>
| 3
| 3
-
| tetR repressor <br>Hill cooperativity
+
| TetR repressor Hill cooperativity
-
| [3]
+
| Ref. [3]
|-
|-
-
| n<sub>aTc</sub>
+
| n<sub>ATC</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>LuxR</sub>
| 2
| 2
-
| luxR activator <br>Hill cooperativity
+
| LuxR activator Hill cooperativity
-
| [6]
+
| Ref: [6]
|-
|-
| n<sub>AHL</sub>
| n<sub>AHL</sub>
| 1
| 1
-
| AHL-luxR activator <br>Hill cooperativity
+
| AHL-LuxR activator Hill cooperativity
-
| [3]
+
| Ref. [3]
|-
|-
-
| n<sub>cI</sub>
+
| n<sub>CI</sub>
-
| 1.9
+
| 2
-
| cI repressor <br>Hill cooperativity
+
| CI repressor Hill cooperativity
-
| [5]
+
| Ref. [12]
|-
|-
-
| n<sub>p22cII</sub>
+
| n<sub>P22CII</sub>
-
|  
+
| 4
-
| p22cII repressor <br>Hill cooperativity
+
| P22CII repressor Hill cooperativity
 +
| Ref. [11]
|-
|-
|}
|}
 +
<br>
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+
== References ==
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</p><br>
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=====.:: References ::.=====
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<p>
<p>
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[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>
 
-
 
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</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 />

Latest revision as of 14:27, 26 October 2007

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Parameters for the educatETH E.coli system

In order to ensure that our simulation results match the biology as close as possible, we tried to find good estimates for the biological system parameters. To this end, we performed an extensive literature review. However, not all parameters were found in the literature, especially those which do not refer to vastly used proteins. Whenever this was the case, logical estimates were provided by our biologists based on empirical values.


Model Parameters

General parameters

Parameter Value Description Comments
c1max 0.01 [mM/h] max. transcription rate of constitutive promoter (per gene) promoter no. J23105; Estimate
c2max 0.01 [mM/h] max. transcription rate of LuxR-activated promoter (per gene) Estimate
lhi 25 high-copy plasmid number Estimate
llo 5 low-copy plasmid number Estimate
a 1% basic production levels Estimate

Degradation constants

Parameter Value Description Comments
dLacI 2.31e-3 [1/s] degradation of LacI Ref. [10]
dTetR
  • 1e-5 [1/s]
  • 2.31e-3 [1/s]
degradation of TetR
  • Ref. [9]
  • Ref. [10]
dLuxR 1e-3 - 1e-4 [1/s] degradation of LuxR Ref: [6]
dCI 7e-4 [1/s] degradation of CI Ref. [7]
dP22CII degradation of P22CII
dYFP 6.3e-3 [1/min] degradation of YFP suppl. mat. to Ref. [8] corresponding to a half life of 110min
dGFP 6.3e-3 [1/min] degradation of GFP in analogy to YFP
dRFP 6.3e-3 [1/min] degradation of RFP in analogy to YFP
dCFP 6.3e-3 [1/min] degradation of CFP in analogy to YFP

Dissociation constants

Parameter Value Description Comments
KLacI
  • 0.1 - 1 [pM]
  • 800 [nM]
LacI repressor dissociation constant
  • Ref. [2]
  • Ref. [12]
KIPTG 1.3 [µM] IPTG-LacI repressor dissociation constant Ref. [2]
KTetR 179 [pM] TetR repressor dissociation constant Ref. [1]
KATC 893 [pM] ATC-TetR repressor dissociation constant Ref. [1]
KLuxR 55 - 520 [nM] LuxR activator dissociation constant Ref: [6]
KAHL 0.09 - 1 [µM] AHL-LuxR activator dissociation constant Ref: [6]
KCI
  • 8 [pM]
  • 50 [nM]
CI repressor dissociation constant
  • Ref. [12]
  • starting with values of Ref. [6] and using Ref. [3]
KP22CII 0.577 [µM] P22CII repressor dissociation constant Ref. [11]

Hill cooperativity

Parameter Value Description Comments
nLacI
  • 1
  • 2
LacI repressor Hill cooperativity
  • Ref. [5]
  • Ref. [12]
nIPTG 2 IPTG-LacI repressor Hill cooperativity Ref. [5]
nTetR 3 TetR repressor Hill cooperativity Ref. [3]
nATC 2 (1.5-2.5) ATC-TetR repressor Hill cooperativity Ref. [3]
nLuxR 2 LuxR activator Hill cooperativity Ref: [6]
nAHL 1 AHL-LuxR activator Hill cooperativity Ref. [3]
nCI 2 CI repressor Hill cooperativity Ref. [12]
nP22CII 4 P22CII repressor Hill cooperativity Ref. [11]


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

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