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.
Eventually our modellisation would just help us to find which ones of the sets of "biologicaly available parameters"/"logical circuit" are the bests, but it may help further simulations on similar protocols, too.
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
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