Team:Paris/Modeling/hill approach


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(More precise Bio-Mathematical Description)
(First Approach)
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The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]].
The methods employed are described there : [[Team:Paris/Modeling/first approach| First Approach]].
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==More precise Bio-Mathematical Description==
==More precise Bio-Mathematical Description==

Revision as of 14:38, 12 August 2008


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

What kind of Mathematical Simulation ?

We decided to use mostly Ordinary Differential Equation approach, at least for the study of the Oscillations and of the FIFO. For the Synchronisation module, we will probably use Probabilistic Differential Equations, in order to introduce the differences between the cells.

Bio-Chemical General Assumptions

We know that the following equations do not describe properly what really happens in the cells. For exemple, we know that the transcription factor flhD-flhC is actually an hexamere flhD4C2. But, as we will surely not get access to the dissociation constant of the hexamerisation, we just treat it as an abstract inducer protein flhDC, with an order in its Hill function probably between 3 and 6 (but perhaps completly different; the estimation of the error by the 'findparam' program will tell us if we are right to do so).

For the moment, at each part of our modelisation, we reduce the expression of a gene at its transcription. The translation process is not taken into acount.

To see more details about the modelisation and the values of the involved constants, see the bibliography.

Separated and detailed Parts of our Project