Team:Paris/Network analysis and design/Core system/Model construction/Detailed justification
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* Finally, since we had imposed γ=1 we resulted with β+β'=1. | * Finally, since we had imposed γ=1 we resulted with β+β'=1. | ||
- | == | + | == FlhDC == |
* Likewise the previous analysis, we set γ<sub>FlhDC</sub> to 1. Then, since FlhDC is fully expressed when envZ is not, we see that when solving under this conditions, we get | * Likewise the previous analysis, we set γ<sub>FlhDC</sub> to 1. Then, since FlhDC is fully expressed when envZ is not, we see that when solving under this conditions, we get | ||
[[Image:flhDC_norm.jpg|center]] | [[Image:flhDC_norm.jpg|center]] |
Revision as of 16:07, 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
Use hill quand on ne sait pasNormalizationpour les betaWe 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 tableBibliography |