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.

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 l^lo/l^hi in the model equations.

Model Parameters

Parameter	Value	Description	Comments
c1max		max. transcription rate of constitutive promoter (per gene)	promoter no. J23105
c2max		max. transcription rate of luxR-activated promoter (per gene)
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	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