Team:Paris/Network analysis and design/Core system/Model construction/Detailed justification
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Revision as of 16:59, 28 October 2008
We shall present here a more detailed presentation of the choice we made as far as our model is concerned
Sum effect and linear modelling
Hill functionWhen we had no relevant information, we decided to model the promoter activity by a Hill function. This was the case for the effect of envZ over FlhDC : Thus the dynamic equation for [FlhDC] : As for the parameters, we decided to chose coherent values, that is nEnvZ=4 and θEnvZ=0.5. NormalizationFliA, CFP, YFP, EnvZ-RFPWe kept the β and β’ values found by S. Kalir and U. Alon, since they showed the relative influence of flhDC and fliA. To have the same order of magnitude between each specie, we normalized those parameters between 0 and 1 as following. We reasoned independently for each equation, wishing to set the equilibrium values of the concentration to 1 given input values of 1. This gave:
The maximum of [CFP] is reached when [fliA] = 1 and [flhDC] = 1 ; when we solve with these condidtions, we obtain : Then setting the equilibrium value of [CFP] to 1 corresponds to setting
With an input of flhDC equal to 1, the solution of the differential equation is: And the condition on the equilibrium imposes
FlhDC
hence the need to set
Determining the degradation rateWe evaluated in the wet lab the half life time for our cells, and then calculated the degradation constants using : The value for half-life time we found and used is 35min. Parameters table
c.u. being an arbitrary concentration unit. |