ETHZ/Simulations

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Contents

Basic Model

Constitutively produced proteins

Model01b.png

Learning system

Model02b.png

Reporter system

Model03b.png

System Equations

Constitutively produced proteins

Eq01.png

Learning system

Eq02.png

Reporter system

Eq03.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: Svens estimate ;-)
c2max 0.01 [mM/h] max. transcription rate of luxR-activated promoter (per gene) Reference: Svens estimate ;-)
lhi 25 high-copy plasmid number Reference: Svens estimate ;-)
llo 5 low-copy plasmid number Reference: Svens estimate ;-)
aQ2,R 0.1 - 0.2 basic production of Q2/R-inhibited genes Reference: discussion with Jörg and Sven
aQ2 0.1 - 0.2 basic production of Q2-inhibited genes Reference: discussion with Jörg and Sven
aQ1,S 0.1 - 0.2 basic production of Q1/S-inhibited genes Reference: discussion with Jörg and Sven
aQ1 0.1 - 0.2 basic production of Q1-inhibited genes Reference: discussion with Jörg and Sven
aQ2,S 0.1 - 0.2 basic production of Q2/S-inhibited genes Reference: discussion with Jörg and Sven
aQ1,R 0.1 - 0.2 basic production of Q1/R-inhibited genes Reference: discussion with Jörg and Sven
dR 2.31e-3 [pro sec] degradation of lacI Tuttle et al. (2005) Biophys J 89(6):3873
dS 1e-5 [pro sec]/2.31e-3 [pro sec] degradation of tetR Ref bs2000 Nature 405:590-593/Tuttle et al. (2005) Biophys J 89(6):3873
dL 1e-3 - 1e-4 [per sec] degradation of luxR Ref: A.B. Goryachev et al. (2006) BioSystems 83:178-187
dQ1 7e-4 [per sec] degradation of cI Ref arm1998 Genetics 149:1633-1648
dQ2 degradation of p22cII
dYFP 6.3e-3 [per min] degradation of YFP suppl. mat. to Colman-Lerner et al. (2001) Cell 107:739-759 cooresponding 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 1.3e-3 - 2e-3 [mM/h] lacI repressor dissociation constant lower value is from Ref. [2], higher value is from Ref. [5]
KIR 1.5e-10 [mM/h] IPTG-lacI repressor dissociation constant Ref. [5]
KS 5.6 (+-2) [nM-1] tetR repressor dissociation constant Ref. [1] Note: This is for heptameric operator. Check if this is what we have.
KIS 1120 (+-400) [nM-1] aTc-tetR repressor dissociation constant Ref. [1] and Ref. [3]. According to Ref. [3], ratio between tetR repressor dissociation constant and aTc-tetR repressor dissociation constant is 0.4/80.
KL 0.003 [mM/s] luxR activator dissociation constant Ref: A.B. Goryachev et al. (2006) BioSystems 83:178-187 (Ratio of association/dissociation)
KIL 0.009 [mM/s] - 0.1 [mM/s] AHL-luxR activator dissociation constant Ref: A.B. Goryachev et al. (2006) BioSystems 83:178-187 (Ratio of association/dissociation)
KQ1 2e-3 [mM/h] cI repressor dissociation constant Ref. [5]
KQ2 p22cII repressor dissociation constant
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: A.B. Goryachev et al. (2006) BioSystems 83:178-187
nIL 1 AHL-luxR activator Hill cooperativity Ref. [3]
nQ1 1.9 cI repressor Hill cooperativity Ref. [5]
nQ2 p22cII repressor Hill cooperativity

References

  1. A synthetic time-delay circuit in mammalian cells and mice (http://www.pnas.org/cgi/content/abstract/104/8/2643)
  2. Detailed map of a cis-regulatory input function (http://www.pnas.org/cgi/content/full/100/13/7702?ck=nck)
  3. Parameter Estimation for two synthetic gene networks (http://ieeexplore.ieee.org/iel5/9711/30654/01416417.pdf)
  4. Supplementary on-line information for "A Synthetic gene-metabolic oscillator" (no link)
  5. Genetic network driven control of PHBV copolymer composition (http://doi:10.1016/j.jbiotec.2005.08.030)

Variable Mapping

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