From 2007.igem.org

Contents 1 Basic Model 1.1 Constitutively produced proteins 1.2 Learning system 1.3 Reporter system 2 System Equations 2.1 Constitutively produced proteins 2.2 Learning system 2.3 Reporter system 2.4 Allosteric regulation 2.5 Comments 3 Model Parameters 4 References 5 Variable Mapping

Basic Model

Constitutively produced proteins

Learning system

Reporter system

System Equations

Constitutively produced proteins

Learning system

Reporter system

Allosteric regulation

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_R, I_S and I_L, respectively. The total amount of protein is denoted with a subscript t (e.g. R_t) 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_t - R*).

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_i^max) and the basic production (a_X), 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.

Model Parameters

Parameter	Value	Description	Comments
c1max		max. transcription rate of constitutive promoter
c2max		max. transcription rate of luxR-activated promoter
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	0.06	degradation of lacI	Ref. [4] --please only add parameter values with proper dimensions, a number like this is useless (Uhrm 04:43, 13 September 2007 (EDT))--
dS	1e-5 [pro sec]	degradation of tetR	Ref bs2000 Nature 405:590-593
dL		degradation of luxR
dQ1	7e-4 [pro sec]	degradation of cI	Ref arm1998 Genetics 149:1633-1648
dQ2		degradation of p22cII
dYFP		degradation of YFP
dGFP		degradation of GFP
dRFP		degradation of RFP
dCFP		degradation of CFP
dIL		degradation of AHL-luxR activator
dIR		degradation of IPTG-lacI repressor
dIS		degradation of aTc-tetR repressor
cQ1,1		promoter strength (R/Q2 inhibited)	maybe Ref. [5] can be of help here (for inhibition of R)
cQ1,2		promoter strength (L activated/Q2 inhibited)
cQ2,1		promoter strength (S/Q1 inhibited)	maybe Ref. [5] can be of help here (for inhibition of Q1)
cQ2,2		promoter strength (L activated/Q1 inhibited)	maybe Ref. [5] can be of help here (for inhibition of Q1)
cYFP		promoter strength (S/Q1 inhibited)	see also cQ2,1
cGFP		promoter strength (R/Q2 inhibited)	see also cQ1,1
cRFP		promoter strength (S/Q2 inhibited)
cCFP		promoter strength (R/Q1 inhibited)
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		tetR repressor dissociation constant
KIS		aTc-tetR repressor dissociation constant
KL		luxR activator dissociation constant
KIL		AHL-luxR activator dissociation constant
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		aTc-tetR repressor Hill cooperativity
nL	1	luxR activator Hill cooperativity	Ref. [3]
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