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 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

Note :On the above figures the parameters are from 1 to 11 :
k_plac- V_cell (volume of cell) - k_{pTet
KpLac - LacI - KpTet - TerR KLacI - IPTG
KTetR - aTc - nplac -npTet
δTetRδLacI}

Variations from 1 to 13 : -66% -50% -20% -10% -5% 0% +5% +10% +20% 50% 100% 200% 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.

Applicable to mercury