Modélisation multi-échelle de la régulation du cycle cellulaire par l'horloge circadienne : applications pour la chronothérapie

Cette thèse est dédiée au développement d’un modèle mathématique multi-échelle pour la régulation du cycle cellulaire par l’horloge circadienne. Ceci est motivé par le fait que plusieurs études ont montré un lien direct entre certains cancers et un dysfonctionnement du mécanisme de l’horloge circadienne. Le but est de comprendre l’effet des rythmes circadiens et leur perturbation sur la prolifération d’une population de cellulesThis thesis is dedicated to the development of a multiscale mathematical model that describes the regulation of the cell cycle by the circadian clock. What motivated this work is the fact that several tumorigenic diseases are linked to circadian rhythms disruption. We would like to understand the effect of circadian rhythms on the proliferation of a cell population and hence give plausible explanation for diseases that arise form circadian clock disruption. The mammalian cell cycle and the circadian clock are two molecular processes that operate in a rhythmic manner and exquisite precision. On one hand, the cell cycle is driven by the rhythmic activity of cyclin dependent kinases which dictate the time a cell must engage mitosis and the time it must divide giving birth to two daughter cells. On the other hand, the circadian clock is a system of transcriptional and translational feedback-loops that generates sustained oscillations of different mRNAs and proteins with a period of approximately 24 h. It turns out that several components of the circadian clock regulates various cyclin-dependent kinases at different stages of the cell cycle. This makes the circadian clock a key player of the temporal organization of the cell cycle and makes these two biological processes act as two tightly coupled oscillators. Our modeling approach consists of using a molecular-structured partial differential equation that describes the proliferation of a cell population. Proliferation depends on the coupled cell cycle-circadian clock molecular state of cells. Due to the large number of molecular components involved in the cell cycle-circadian clock system, the problem becomes of high-dimensionality and specific numerical techniques are needed to solve the equatio