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 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_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	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 [pro 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]	lacI repressor dissociation constant	Ref. [2]
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]	luxR activator dissociation constant	Ref: [6]
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?
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: [6]
nIL	1	AHL-luxR activator Hill cooperativity	Ref. [3]
nQ1	1.9	cI repressor Hill cooperativity	Ref. [5]
nQ2	4	p22cII repressor Hill cooperativity	Ref. [11]. Note that they use a protein cII and we have p22cII. Does that match?

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://dx.doi.org/10.1016/j.jbiotec.2005.08.030)
6. Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants (http://dx.doi.org/10.1016/j.biosystems.2005.04.006)
7. Stochastic Kinetic Analysis of Developmental Pathway Bifurcation in Phage λ-Infected E. coli Cells
8. Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates
9. Engineering stability in gene networks by autoregulation
10. Model-Driven Designs of an Oscillating Gene Network
11. Synchronizing genetic relaxation oscillators by intercell signaling (http://www.pnas.org/cgi/reprint/99/2/679)

Variable Mapping

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