Team:Paris/Network analysis and design/Core system/Model construction/Detailed justification
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= Normalization = | = Normalization = | ||
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+ | We 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: | ||
+ | [[Image:Beta_Resize.jpg|center]] | ||
+ | <br> | ||
+ | [[Image:Beta_p_Resize.jpg|center]] | ||
+ | <br> | ||
+ | * In fact, if we take CFP for example: | ||
+ | [[Image:CFP.jpg|center]] | ||
+ | The maximum of [CFP] is reached when [fliA] = 1 and [flhDC] = 1 ; when we solve with these condidtions, we obtain : | ||
+ | [[Image:CFP_Solve.jpg|center]] | ||
+ | Then setting the equilibrium value of [CFP] to 1 corresponds to setting | ||
+ | [[Image:Beta_Gamma_resize.jpg|center]] | ||
+ | * The analysis of fliA is different, but not the result: | ||
+ | [[Image:FliA_Analysis.jpg|center]] | ||
+ | With an input of flhDC equal to 1, the solution of the differential equation is: | ||
+ | [[Image:FliA_Solve.jpg|center]] | ||
+ | And the condition on the equilibrium imposes | ||
+ | [[Image:Beta_Gamma_Resize_FliA.jpg|center]] | ||
+ | * To conclude, we see that we always get the same condition: | ||
+ | [[Image:Final_Resize.jpg|center]] | ||
+ | * Finally, since we had imposed γ=1 we resulted with β+β'=1. | ||
= Parameters table = | = Parameters table = | ||
= Bibliography = | = Bibliography = |
Revision as of 16:01, 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 pasNormalizationWe 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
Parameters tableBibliography |