Team:Paris/Modeling/hill approach


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Hill functions approach


As a first approach, we had decided to take into account the binding to the promoters steps. Moreover, the transcription rates were expected to be Hill functions. Obvisouly, this modeling requires a huge number of parameters. To obtain them, we had planed to devise specific experiments (described below).

First Approach

As a first approximation, we have proposed a set of 5 ordinary differential equations, without taking into account the translation step. Besides, we have had not introduced yet a synchronizaton module. Therefore, the repression of FlhDC is directly modeled by the presence of the 'Z3' gene (that is the last that is turned on).

In this framework, we have found parameters that have provided oscillations as well as a function that automatically detects whether the output of the ode system is oscillating. This has allowed to screen a little the parameters used, in order to evaluate the robustness of the system.

The methods employed are described there : First Approach.

More precise Bio-Mathematical Description

After trying to obtain oscillations from a simple model, we have tried to described more precisely the studied system. Therefore, we have obtained the following formalism : Bio-Mathematical Description.