From 2007.igem.org

.:: Introduction ::.

Having decided to work on an engineered biological system which exhibits learning, we elaborated on its design. Discussing with the biologists of the team, we realized that what we knew from the field of logic design as JK flip-flop with a latch may be implemented with biological parts using a modified toggle switch. Initial simulations showed us that it was possible to reach the desired behaviour. Therefore, a complete framework of differential equations describing the system was constructed and parameters were searched in the literature. Simulations performed with our new detailed model are very encouraging. In this page, the equations that model our system are and explained. The values that were chosen for the system parameters are presented and the results of our simulations are analyzed. References are provided at the end of the page. For an introduction to system modeling in synthetic biology, please read our modeling tutorial here.

.:: 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	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?

.:: 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