M2 Project: Mathematical modeling of the cell cycle

In this report we describe the work we have done for our M2 project in the Erasmus Mundus Masters in Complex Systems Science. We have studied a model of the cell cycle. The model was conceived to explain experimental observations of respiratory oscillations in yeast cultures. An essential feature of the model is that a negative feedback mechanism robustly produces clustering. We explain the model and give a brief overview of previously obtained results. Then we discuss the case of two unequal clusters, and elaborate on why a method based on reduction does not provide accurate results. We then describe a phenomenon which we call decoupling and can be observed for certain parameter values. We offer some perspectives on our results and outline directions for further investigation. Throughout we illustrate with results obtained from numerical simulations. The appendix contains some unfinished work and supplementary material.