Team:Paris/Modeling/FromMolReactToNLOde

Idea and Assumptions
We will here propose a Mathematical Modeling of the elementary molecular reactions. The idea of the Characterization Approach is that this modelization must both accounts for every small steps of the system and allow the experimental characterizations.

Therefore, 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 (n) in its complexation caracterization probably around 2*4 = 8 (but perhaps completly different ! ; the estimation of the error by the Parameters Finder Programs would tell us if it stays consistent).

Mathematical Interpretation and Simulation of the Molecular Reactions
First, we consider the complexation phenomenon. We show, under the quasi steady-state hypothesis, how it leads to Non-Linear interactions like "Hill functions".

Then, we apply these results to the Molecular Reactions of our system. That gives all the theoretical calculation of the complexations, and finally, with the previous assumptions, we get the equations of the full system of ODEs.

For complete PDF with all Reactions and Numbered References : complete list of reactions and equations