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.

.:: Table of Parameters ::.

Parameter	Value	Description	References
c1max	0.01 [mM/h]	max. transcription rate of constitutive promoter (per gene)	Estimate
c2max	0.01 [mM/h]	max. transcription rate of luxR-activated promoter (per gene)	Estimate
lhi	25	high-copy plasmid number	Estimate
llo	5	low-copy plasmid number	Estimate
ap22cII,LacI	0.1 - 0.2	basic production of p22cII/LacI-inhibited genes	Discussion
ap22cII	0.1 - 0.2	basic production of p22cII-inhibited genes	Discussion
acI,TetR	0.1 - 0.2	basic production of cI/TetR-inhibited genes	Discussion
acI	0.1 - 0.2	basic production of cI-inhibited genes	Discussion
ap22cII,TetR	0.1 - 0.2	basic production of p22cII/TetR-inhibited genes	Discussion
acI,LacI	0.1 - 0.2	basic production of cI/TetR-inhibited genes	Discussion
dLacI	2.31e-3 [pro sec]	degradation of lacI	[10]
dTetR	1e-5 [pro sec]/2.31e-3 [pro sec]	degradation of TetR	[9], [10]
dLuxR	1e-3 - 1e-4 [per sec]	degradation of LuxR	[6]
dcI	7e-4 [per sec]	degradation of cI	[7]
dp22cII		degradation of p22cII
dYFP	6.3e-3 [per min]	degradation of YFP	suppl. mat. to Ref. [8]
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
KLacI	1.3e-3 - 2e-3 [mM/h]	lacI repressor dissociation constant	[2], [5]
KIPTG	1.5e-10 [mM/h]	IPTG-lacI repressor dissociation constant	[5]
KTetR	5.6 (+-2) [nM-1]	tetR repressor dissociation constant	[1]
KaTc	1120 (+-400) [nM-1]	aTc-tetR repressor dissociation constant	[1], [3]
KLuxR	0.003 [mM/s] 55 - 520 [nM]	luxR activator dissociation constant	[6]
KAHL	0.009 [mM/s] - 0.1 [mM/s] 0.09 - 1 [µM]	AHL-luxR activator dissociation constant	[6]
KcI	2e-3 [mM/h]	cI repressor dissociation constant	[5]
Kp22cII		p22cII repressor dissociation constant
nLacI	1	lacI repressor Hill cooperativity	[5]
nIPTG	2	IPTG-lacI repressor Hill cooperativity	[5]
nTetR	3	tetR repressor Hill cooperativity	[3]
naTc	2 (1.5-2.5)	aTc-tetR repressor Hill cooperativity	[3]
nLuxR	2	luxR activator Hill cooperativity	[6]
nAHL	1	AHL-luxR activator Hill cooperativity	[3]
ncI	1.9	cI repressor Hill cooperativity	[5]
np22cII		p22cII repressor Hill cooperativity

.:: References ::.

[1] Weber W., Stelling J., Rimann M., Keller B., Daoud-El Baba M., Weber C.C., Aubel D., and Fussenegger M., "A synthetic time-delay circuit in mammalian cells and mice", Proceedings of the National Academy of Sciences, vol. 104, no. 8, pp. 2643, 2007.
[2] Setty Y., Mayo AE, Surette MG, and Alon U., "Detailed map of a cis-regulatory input function", Proceeding of the National Academy of Sciences, vol. 100, no. 13, pp. 7702--7707, 2003.
[3] Braun D., Basu S., and Weiss R., "Parameter Estimation for Two Synthetic Gene Networks: A Case Study", IEEE Int'l Conf. Acoustics, Speech, and Signal Processing 2005, vol. 5, 2005.
[4] Fung E., Wong W.W., Suen J.K., Bulter T., Lee S., and Liao J.C., "A synthetic gene--metabolic oscillator", Nature, vol. 435, no. 7038, pp. 118--122, 2005, supplementary material.
[5] Iadevaia S., and Mantzaris N.V., "Genetic network driven control of PHBV copolymer composition", Journal of Biotechnology, vol. 122, no. 1, pp. 99--121, 2006.
[6] Goryachev AB, Toh DJ, and Lee T., "Systems analysis of a quorum sensing network: Design constraints imposed by the functional requirements, network topology and kinetic constants", Biosystems, vol. 83, no. 2-3, pp. 178--187, 2006.
[7] Arkin A., Ross J., and McAdams H.H., "Stochastic kinetic analysis of developmental pathway bifurcation in phage λ-Infected Escherichia coli cells", Genetics, vol. 149, no. 4, pp. 1633--1648, 1998.
[8] Colman-Lerner A., Chin T.E., and Brent R., "Yeast Cbk1 and Mob2 Activate Daughter-Specific Genetic Programs to Induce Asymmetric Cell Fates", Cell, vol. 107, no. 6, pp. 739--750, 2001.
[9] Becskei A., and Serrano L., "Engineering stability in gene networks by autoregulation", Nature, vol. 405, no.6786, pp.590--593, 2000.
[10] Tuttle L.M., Salis H., Tomshine J., and Kaznessis Y.N., "Model-Driven Designs of an Oscillating Gene Network", Biophysical Journal, vol. 89, no. 6, pp. 3873--3883, 2005.

[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