Team:Paris/Network analysis and design/Core system/Model construction/Detailed justification
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hence the need to set | hence the need to set | ||
[[Image:Beta_flhDC.jpg|center]] | [[Image:Beta_flhDC.jpg|center]] | ||
+ | * This is highly interesting since we do not need to find a value for β<sub>FlhDC</sub> | ||
* Furthermore, since [EnvZ] has been normalized, we have to do so for θ<sub>EnvZ</sub> as well, since its role is to stand as a reference concentration for EnvZ. Therefore, we have to normalize it in the same way we did for [EnvZ]: | * Furthermore, since [EnvZ] has been normalized, we have to do so for θ<sub>EnvZ</sub> as well, since its role is to stand as a reference concentration for EnvZ. Therefore, we have to normalize it in the same way we did for [EnvZ]: | ||
we had [[Image:norm_envZ.jpg|center]] | we had [[Image:norm_envZ.jpg|center]] |
Revision as of 16:40, 26 October 2008
Detailed justification
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 protein concentration evolution 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
Parameters table
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