Modélisation et analyse d'un simple système moléculaire et le problème de l'hérédité

Abstract

This work is in the discipline of mathematical biology and aims to study the cell divisions taking to account the problem of heredity. First, we establish the biological basis for a proper understanding of this work. Next we investigate of the origin of heredity in a cell, by noting that molecules carrying heredity must be preserved well and control the behavior of the cell. Subsequently, we give a model of cell reproduction, which will give us the opportunity to verigy if the assumptions hold for the molecules carrying heredity are actually observed in this model. Initially, a deterministic model of cell reproduction apply to large number of molecules is studied. Then, this model is slightly modified to incorporate the possible changes within the cell, which will also be studied. In a second step, the model established is reconsidered as stochastic, and the integrate and analyzed. This model will be valid for small numbers of molecules.

Date of Award	24 Jun 2011
Original language	French
Supervisor	Timoteo Carletti (Supervisor), Eric Depiereux (Jury), Joseph Winkin (Jury) & Anne Lemaitre (Jury)