ETHZ/Simulations

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==== Constitutively produced proteins ====
==== Constitutively produced proteins ====
-
[[Image:Model01.png]]
+
[[Image:Model01b.png]]
==== Learning system ====
==== Learning system ====
-
[[Image:Model02.png]]
+
[[Image:Model02b.png]]
==== Reporter system ====
==== Reporter system ====
-
[[Image:Model03.png]]
+
[[Image:Model03b.png]]
== System Equations ==
== System Equations ==
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==== Constitutively produced proteins ====
==== Constitutively produced proteins ====
-
[[Image:Eq01.png|171px]]
+
[[Image:Constitutive_braced.png|330px]]
==== Learning system ====
==== Learning system ====
-
[[Image:Eq02.png|475px]]
+
[[Image:Toggle_braced.png|770px]]
==== Reporter system ====
==== Reporter system ====
-
[[Image:Eq03.png|586px]]
+
[[Image:Reporter_braced.png|778px]]
==== Allosteric regulation ====
==== Allosteric regulation ====
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==== Comments ====
==== Comments ====
-
Note that the three constitutively produced proteins R, S and L exist in two different forms: as free proteins and in complexes they build with I<sub>R</sub>, I<sub>S</sub> and I<sub>L</sub>, respectively. The total amount of protein is denoted with a subscript <i>t</i> (e.g. R<sub>t</sub>) in the above formulas. The amount of protein existing as complex is denoted with a superscript * (e.g. R*). The difference is the amount of free protein (e.g. R<sub>t</sub> - R*).
+
Note that the three constitutively produced proteins lacI, tetR and luxR exist in two different forms: as free proteins and in complexes they build with IPTG, aTc and AHL, respectively.
In this new formulation of the model equations, the characterization is more amenable to human interpretation (although equivalent to  the previous formuation). The promoters are now characterized by their ''maximum transcription rate'' (c<sub>i</sub><sup>max</sup>) and the ''basic production'' (a<sub>X</sub>), which gives the 'leakage' if the gene is fully inhibited. Note that in the given mathematical formulation the ''basic production'' is specified as a percentage of the ''max. transcription rate'' and is therefore unitless.
In this new formulation of the model equations, the characterization is more amenable to human interpretation (although equivalent to  the previous formuation). The promoters are now characterized by their ''maximum transcription rate'' (c<sub>i</sub><sup>max</sup>) and the ''basic production'' (a<sub>X</sub>), which gives the 'leakage' if the gene is fully inhibited. Note that in the given mathematical formulation the ''basic production'' is specified as a percentage of the ''max. transcription rate'' and is therefore unitless.
Line 49: Line 49:
|-
|-
| c<sub>1</sub><sup>max</sup>
| c<sub>1</sub><sup>max</sup>
-
|  
+
| 0.01 [mM/h]
| max. transcription rate of constitutive promoter (per gene)
| max. transcription rate of constitutive promoter (per gene)
-
| promoter no. J23105
+
| promoter no. J23105; Reference: Estimate
|-
|-
| c<sub>2</sub><sup>max</sup>
| c<sub>2</sub><sup>max</sup>
-
|  
+
| 0.01 [mM/h]
| max. transcription rate of luxR-activated promoter (per gene)
| max. transcription rate of luxR-activated promoter (per gene)
-
|  
+
| Reference: Estimate
|-
|-
| l<sup>hi</sup>
| l<sup>hi</sup>
| 25
| 25
| high-copy plasmid number
| high-copy plasmid number
-
| Reference: Svens estimate ;-)
+
| Reference: Estimate
|-
|-
| l<sup>lo</sup>
| l<sup>lo</sup>
| 5
| 5
| low-copy plasmid number
| low-copy plasmid number
-
| Reference: Svens estimate ;-)
+
| Reference: Estimate
|-
|-
| a<sub>Q<sub>2</sub>,R</sub>
| a<sub>Q<sub>2</sub>,R</sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>2</sub>/R-inhibited genes
| basic production of Q<sub>2</sub>/R-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| a<sub>Q<sub>2</sub></sub>
| a<sub>Q<sub>2</sub></sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>2</sub>-inhibited genes
| basic production of Q<sub>2</sub>-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| a<sub>Q<sub>1</sub>,S</sub>
| a<sub>Q<sub>1</sub>,S</sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>1</sub>/S-inhibited genes
| basic production of Q<sub>1</sub>/S-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| a<sub>Q<sub>1</sub></sub>
| a<sub>Q<sub>1</sub></sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>1</sub>-inhibited genes
| basic production of Q<sub>1</sub>-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| a<sub>Q<sub>2</sub>,S</sub>
| a<sub>Q<sub>2</sub>,S</sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>2</sub>/S-inhibited genes
| basic production of Q<sub>2</sub>/S-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| a<sub>Q<sub>1</sub>,R</sub>
| a<sub>Q<sub>1</sub>,R</sub>
| 0.1 - 0.2
| 0.1 - 0.2
| basic production of Q<sub>1</sub>/R-inhibited genes
| basic production of Q<sub>1</sub>/R-inhibited genes
-
| Reference: discussion with Jörg and Sven
+
| Reference: Conclusions after discussion
|-
|-
| d<sub>R</sub>
| d<sub>R</sub>
-
| 2.31e-3 [pro sec]
+
| 2.31e-3 [per sec]
| degradation of lacI
| degradation of lacI
-
| Tuttle et al. (2005) Biophys J 89(6):3873
+
| Ref. [10]
|-
|-
| d<sub>S</sub>
| d<sub>S</sub>
-
| 1e-5 [pro sec]/2.31e-3 [pro sec]
+
|  
 +
* 1e-5 [per sec]
 +
* 2.31e-3 [per sec]
| degradation of tetR
| degradation of tetR
-
| Ref bs2000 Nature 405:590-593/Tuttle et al. (2005) Biophys J 89(6):3873
+
|  
 +
* Ref. [9]
 +
* Ref. [10]
|-
|-
| d<sub>L</sub>
| d<sub>L</sub>
-
|  
+
| 1e-3 - 1e-4 [per sec]
| degradation of luxR
| degradation of luxR
 +
| Ref: [6]
|-
|-
| d<sub>Q<sub>1</sub></sub>
| d<sub>Q<sub>1</sub></sub>
-
| 7e-4 [pro sec]
+
| 7e-4 [per sec]
| degradation of cI
| degradation of cI
-
| Ref arm1998 Genetics 149:1633-1648
+
| Ref. [7]
|-
|-
| d<sub>Q<sub>2</sub></sub>
| d<sub>Q<sub>2</sub></sub>
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| 6.3e-3 [per min]
| 6.3e-3 [per min]
| degradation of YFP
| degradation of YFP
-
| suppl. mat. to Colman-Lerner et al. (2001) Cell 107:739-759 cooresponding to a half life of 110min
+
| suppl. mat. to Ref. [8] corresponding to a half life of 110min
|-
|-
| d<sub>GFP</sub>
| d<sub>GFP</sub>
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|-
|-
| K<sub>R</sub>
| K<sub>R</sub>
-
| 1.3e-3 - 2e-3 [mM/h]
+
|
 +
* 0.1 - 1 [pM]
 +
* 800 [nM]
| lacI repressor dissociation constant
| lacI repressor dissociation constant
-
| lower value is from Ref. [2], higher value is from Ref. [5]
+
|
 +
* Ref. [2]
 +
* Ref. [12]
|-
|-
| K<sub>I<sub>R</sub></sub>
| K<sub>I<sub>R</sub></sub>
-
| 1.5e-10 [mM/h]
+
| 1.3 [&#181;M]
| IPTG-lacI repressor dissociation constant
| IPTG-lacI repressor dissociation constant
-
| Ref. [5]
+
| Ref. [2]
|-
|-
| K<sub>S</sub>
| K<sub>S</sub>
-
|  
+
| 179 [pM]
| tetR repressor dissociation constant
| tetR repressor dissociation constant
 +
| Ref. [1]
|-
|-
| K<sub>I<sub>S</sub></sub>
| K<sub>I<sub>S</sub></sub>
-
|  
+
| 893 [pM]
| aTc-tetR repressor dissociation constant
| aTc-tetR repressor dissociation constant
 +
| Ref. [1]
|-
|-
| K<sub>L</sub>
| K<sub>L</sub>
-
|  
+
|
 +
* 55 - 520 [nM]
 +
* 10 [nM]
| luxR activator dissociation constant
| luxR activator dissociation constant
 +
|
 +
* Ref: [6]
 +
* Ref: [12]
|-
|-
| K<sub>I<sub>L</sub></sub>
| K<sub>I<sub>L</sub></sub>
-
|  
+
| 0.09 - 1 [&#181;M]
| AHL-luxR activator dissociation constant
| AHL-luxR activator dissociation constant
 +
| Ref: [6]
|-
|-
| K<sub>Q<sub>1</sub></sub>
| K<sub>Q<sub>1</sub></sub>
-
| 2e-3 [mM/h]
+
|
 +
* 8 [pM]
 +
* 50 [nM]
| cI repressor dissociation constant
| cI repressor dissociation constant
-
| Ref. [5]
+
|
 +
* Ref. [12]
 +
* starting with values of Ref. [6] and using Ref. [3]
|-
|-
| K<sub>Q<sub>2</sub></sub>
| K<sub>Q<sub>2</sub></sub>
-
|  
+
| 0.577 [&#181;M]
| p22cII repressor dissociation constant
| p22cII repressor dissociation constant
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match? It matches. p22 cII just means its cII derived frome a p22 vector ;-)
|-
|-
| n<sub>R</sub>
| n<sub>R</sub>
-
| 1
+
|
 +
* 1
 +
* 2
| lacI repressor Hill cooperativity
| lacI repressor Hill cooperativity
-
| Ref. [5]
+
|
 +
* Ref. [5]
 +
* Ref. [12]
|-
|-
| n<sub>I<sub>R</sub></sub>
| n<sub>I<sub>R</sub></sub>
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|-
|-
| n<sub>I<sub>S</sub></sub>
| n<sub>I<sub>S</sub></sub>
-
|  
+
| 2 (1.5-2.5)
| aTc-tetR repressor Hill cooperativity
| aTc-tetR repressor Hill cooperativity
 +
|Ref. [3]
|-
|-
| n<sub>L</sub>
| n<sub>L</sub>
-
| 1
+
| 2
| luxR activator Hill cooperativity
| luxR activator Hill cooperativity
-
| Ref. [3]
+
| Ref: [6]
|-
|-
| n<sub>I<sub>L</sub></sub>
| n<sub>I<sub>L</sub></sub>
Line 206: Line 233:
|-
|-
| n<sub>Q<sub>1</sub></sub>
| n<sub>Q<sub>1</sub></sub>
-
| 1.9
+
| 2
| cI repressor Hill cooperativity
| cI repressor Hill cooperativity
-
| Ref. [5]
+
| Ref. [12]
|-
|-
| n<sub>Q<sub>2</sub></sub>
| n<sub>Q<sub>2</sub></sub>
-
|  
+
| 4
| p22cII repressor Hill cooperativity
| p22cII repressor Hill cooperativity
 +
| Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match? It matches. p22 cII just means its cII derived frome a p22 vector ;-)
|-
|-
|}
|}
== References ==
== References ==
-
 
+
[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 />
-
# A synthetic time-delay circuit in mammalian cells and mice (http://www.pnas.org/cgi/content/abstract/104/8/2643)
+
[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 />
-
# Detailed map of a cis-regulatory input function (http://www.pnas.org/cgi/content/full/100/13/7702?ck=nck)
+
[http://ieeexplore.ieee.org/iel5/9711/30654/01416417.pdf &#91;3&#93; Braun D et al.] <i>"Parameter Estimation for Two Synthetic Gene Networks: A Case Study"</i>, ICASSP 5:769-772, 2005<br />
-
# Parameter Estimation for two synthetic gene networks (http://ieeexplore.ieee.org/iel5/9711/30654/01416417.pdf)
+
[http://www.nature.com/nature/journal/v435/n7038/suppinfo/nature03508.html &#91;4&#93; Fung E et al.] <i>"A synthetic gene--metabolic oscillator"</i>, Nature 435:118-122, 2005 (supplementary material)<br />
-
# Supplementary on-line information for "A Synthetic gene-metabolic oscillator" (no link)
+
[http://dx.doi.org/10.1016/j.jbiotec.2005.08.030  &#91;5&#93; Iadevaia S and  Mantzais NV] <i>"Genetic network driven control of PHBV copolymer composition"</i>, J Biotechnol 122(1):99-121, 2006<br />
-
# Genetic network driven control of PHBV copolymer composition (http://doi:10.1016/j.jbiotec.2005.08.030)
+
[http://dx.doi.org/10.1016/j.biosystems.2005.04.006  &#91;6&#93; Goryachev AB et al.] <i>"Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants"</i>, Biosystems 83(2-3):178-187, 2004<br />
 +
[http://www.genetics.org/cgi/content/abstract/149/4/1633  &#91;7&#93; Arkin A et al.] <i>"Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells"</i>, Genetics 149: 1633-1648, 1998<br />
 +
[http://download.cell.com/supplementarydata/cell/107/6/739/DC1/index.htm &#91;8&#93; Colman-Lerner A et al.] <i>"Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates"</i>, Cell 107(6): 739-750, 2001 (supplementary material)<br />
 +
[http://www.nature.com/nature/journal/v405/n6786/abs/405590a0.html  &#91;9&#93; Becskei A and Serrano L] <i>"Engineering stability in gene networks by autoregulation"</i>, Nature 405: 590-593, 2000<br />
 +
[http://www.biophysj.org/cgi/content/full/89/6/3873?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&searchid=1&FIRSTINDEX=0&volume=89&firstpage=3873&resourcetype=HWCIT  &#91;10&#93; Tuttle et al.] <i>"Model-Driven Designs of an Oscillating Gene Network"</i>, Biophys J 89(6):3873-3883, 2005<br />
 +
[http://www.pnas.org/cgi/reprint/99/2/679  &#91;11&#93; McMillen LM et al.] <i>"Synchronizing genetic relaxation oscillators by intercell signaling"</i>, P Natl Acad Sci USA 99(2):679-684, 2002<br />
 +
[http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html  &#91;12&#93; Basu S et al.] <i>"A synthetic multicellular system for programmed pattern formation"</i>, Nature 434:1130-1134, 2005<br />
== Variable Mapping ==
== Variable Mapping ==

Latest revision as of 12:55, 18 October 2007

Contents

Basic Model

Constitutively produced proteins

Model01b.png

Learning system

Model02b.png

Reporter system

Model03b.png

System Equations

Constitutively produced proteins

Constitutive braced.png

Learning system

Toggle braced.png

Reporter system

Reporter braced.png

Allosteric regulation

Eq04.png


Comments

Note that the three constitutively produced proteins lacI, tetR and luxR exist in two different forms: as free proteins and in complexes they build with IPTG, aTc and AHL, respectively.

In this new formulation of the model equations, the characterization is more amenable to human interpretation (although equivalent to the previous formuation). The promoters are now characterized by their maximum transcription rate (cimax) and the basic production (aX), which gives the 'leakage' if the gene is fully inhibited. Note that in the given mathematical formulation the basic production is specified as a percentage of the max. transcription rate and is therefore unitless.

The max. transcription rate is given per gene (as agreed with Sven during the meeting at Sep 20.). This means that to get the total transcription rate we need to multiply with the number of gene copies per cell which is represented as llo/lhi in the model equations.

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 [per 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]
  • 800 [nM]
lacI repressor dissociation constant
  • Ref. [2]
  • Ref. [12]
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]
  • 10 [nM]
luxR activator dissociation constant
  • Ref: [6]
  • Ref: [12]
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? It matches. p22 cII just means its cII derived frome a p22 vector ;-)
nR
  • 1
  • 2
lacI repressor Hill cooperativity
  • Ref. [5]
  • Ref. [12]
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? It matches. p22 cII just means its cII derived frome a p22 vector ;-)

References

[http://www.pnas.org/cgi/content/abstract/104/8/2643 [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
[http://www.pnas.org/cgi/content/full/100/13/7702?ck=nck [2] Setty Y et al.] "Detailed map of a cis-regulatory input function", P Natl Acad Sci USA 100(13):7702-7707, 2003
[http://ieeexplore.ieee.org/iel5/9711/30654/01416417.pdf [3] Braun D et al.] "Parameter Estimation for Two Synthetic Gene Networks: A Case Study", ICASSP 5:769-772, 2005
[http://www.nature.com/nature/journal/v435/n7038/suppinfo/nature03508.html [4] Fung E et al.] "A synthetic gene--metabolic oscillator", Nature 435:118-122, 2005 (supplementary material)
[http://dx.doi.org/10.1016/j.jbiotec.2005.08.030 [5] Iadevaia S and Mantzais NV] "Genetic network driven control of PHBV copolymer composition", J Biotechnol 122(1):99-121, 2006
[http://dx.doi.org/10.1016/j.biosystems.2005.04.006 [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
[http://www.genetics.org/cgi/content/abstract/149/4/1633 [7] Arkin A et al.] "Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells", Genetics 149: 1633-1648, 1998
[http://download.cell.com/supplementarydata/cell/107/6/739/DC1/index.htm [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)
[http://www.nature.com/nature/journal/v405/n6786/abs/405590a0.html [9] Becskei A and Serrano L] "Engineering stability in gene networks by autoregulation", Nature 405: 590-593, 2000
[http://www.biophysj.org/cgi/content/full/89/6/3873?maxtoshow=&HITS=10&hits=10&RESULTFORMAT=&searchid=1&FIRSTINDEX=0&volume=89&firstpage=3873&resourcetype=HWCIT [10] Tuttle et al.] "Model-Driven Designs of an Oscillating Gene Network", Biophys J 89(6):3873-3883, 2005
[http://www.pnas.org/cgi/reprint/99/2/679 [11] McMillen LM et al.] "Synchronizing genetic relaxation oscillators by intercell signaling", P Natl Acad Sci USA 99(2):679-684, 2002
[http://www.nature.com/nature/journal/v434/n7037/full/nature03461.html [12] Basu S et al.] "A synthetic multicellular system for programmed pattern formation", Nature 434:1130-1134, 2005

Variable Mapping

Variable Compound
R lacI
IR IPTG
S tetR
IS aTc
L luxR
IL AHL
Q1 cI
Q2 p22cII
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