Sensitivity to parameters study

Robustness of our system

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 changes in the parameter values.

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 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% 12 +200% 13 +300%

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

For higher aTc concentrations however, the level of IPTG at which the switch occurs is very high. Errors on the parameters prevents the system to switch for the chosen IPTG gradient. In this case, the IPTG maximal necessary valuefor quantification would be too high for a living cell. The only problem being a decrease of the maximum value we can quantify.

Figure 2: Parameters sensitivity for 6.2e-04 M of aTc

Applicable to mercury

According to the previous study, the following parameters are determinant for system's robustness:

• $k_{plac}$
• $k_{ptet}$
• $K_{pLac-LacI}$
• $K_{pTet-TetR}$
• $K_{lacI-IPTG}$
• $K_{tetR-aTc}$
• $n_{plac}$
• $n_{ptet}$

By comparing to the set of parameters for mercury, we can observed that the variation of parameters always stay in the stability area:

• $k_{pmerT}$: the same as pTet
• $K_{pmerT-merR}$: 20% of $K_{pTet_TetR}$
• $K_{merR-Hg{2+}}$: 1000% of $K_{tetR_aTc}$
• $n_{pmerT}$: $\approx$ 15% of $n_{pTet}$

Variations of these parameters will have an influence on the results but value are still reasonnable (variation $\approx$ 200% of the final results).

With this set of parameters for mercury, the system should work as well as for aTc.