Parameters

PDF file (detailed explanation on parameters and how we deduced them) for Toggle Switch

kplac	pLac production rate	600 proteins/min	[1]
kpTet	pTet production rate	600 proteins/min	[1]
kpMer	pMer production rate	600 proteins/min	[1]
δLacI	LacI degradation rate	4.6E-2 min−1	PDF file
δTetR	TetR degradation rate	4.6E-2 min−1	PDF file
δMerR	MerR degradation rate	4.6E-2 min−1	PDF file
KpLac - LacI	plac - LacI dissociation constant	5.45E-7 M	Kyoto 10
KpMer - MerR	pMer - MerR dissociation constant	1.00E-8 M	[2]
KpTet - TerR	pTet - TetR dissociation constant	5.00E-8 M	[3]
KLacI - IPTG	LacI - IPTG dissociation constant	2.96E-5 M	[4]
KTetR - aTc	aTc - TetR dissociation constant	1.5E-8 M	[5]
KHg2+ - MerR	Hg2+ - MerR dissociation constant	1E-7 M	[2]
nplac	plac cooperativity number	2,3	[4]
npMer	pMer cooperativity number	2,5	[6]
npTet	pTet cooperativity number	3	[7]

References

[1] Nature. 2000 Jan 20;403(6767):335-8. A synthetic oscillatory network of transcriptional regulators. Elowitz MB, Leibler S.

[2] Mol Gen Genet. 1999 Aug;262(1):154-62. Purification and characterization of MerR, the regulator of the broad-spectrum mercury resistance genes in Streptomyces lividans 1326. Rother D, Mattes R, Altenbuchner J.

[3] David Braun et al. Parameter estimation for two synthetic gene networks: A case study. IEEE 2005.

[4] Nature 403, 339-342 (20 January 2000) Construction of a genetic toggle switch in Escherichia coli. Timothy S. Gardner Charles R. Cantor & James J. Collins

[5] O. Scholz, P. Schubert, M. Kintrup and W. Hillen, Tet repressor induction without Mg2+, Biochemistry 39 (2000), pp. 10914–10920

[6] Ultrasensitivity and heavy-metal selectivity of the allosterically modulated MerR transcription complex. D M Ralston and T V O'Halloran

[7] Systems analysis of a quorum sensing network: design constraints imposed by the functional requirements, network topology and kinetic constants. Goryachev AB, Toh DJ, Lee T.

Parameters sensitivity

In order to know if an error on the parameters would induce a completely different behaviour of our system, we studied the sensitivity of our system to a change on the parameters.

This study was performed by increasing or decreasing our parameters values by a range of percentages (from -66% to +300% for each parameter). Then we studied the change on the output of our system, the ratio of IPTG over aTc that induces the coloration.

On the following figure one can see the influence on the output of our system (the ratio of IPTG over aTc on the interface) for several different aTc concentrations. For these concentrations the switch is still efficient, even though the resulting variation on the output will induce an error on our measure.

Figure 1: Parameters sensitivity for 2.8e-07 M of aTc

Note: On the next two figures the parameters are the following 1 kplac 2 Vcell 3 kpTet 4 KpLac - LacI 5 KpTet - TerR 6 KLacI - IPTG 7 KTetR - aTc 8 nplac 9 npTet 10 δTetR 11 δLacI

Figure 2: Parameters sensitivity for 6.3e-06 M of aTc

Variations from 1 to 13 : 1 -66% 2 -50% 3 -20% 4 -10% 5 -5% 6 +0% 7 +5% 8 +10% 9 +20% 10 +50% 11 +100% 11 +200% 11 +300%

For low values of aTc concentration the error is too minor to perturb the mechanism of our system. If the error is superior to -50% or +100% for parameters such as K_{pLac - LacI} or K_{pTet - TetR} however, it will be impossible to predict the output. In such a case a characterization of the responsible parameter would be necessary.

For higher values of aTc concentration however, the value of IPTG necessary for a switch is very high and errors on the parameters can cause the system not to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary value for quantification would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.

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