Colloquium: ODE Models of Cell Cycle Dynamics and Clustering, Todd Young

Abstract: Biologists have long observed periodic-like oxygen consumption oscillations in yeast populations under certain conditions and several unsatisfactory explanations for this phenomenon have been proposed.

We hypothesize that these oscillations could be caused by cell cycle weak synchronization or clustering. We develop some novel ODE models of the cell cycle. We give proofs and simulations showing that both positive and negative feedback are possible agents that can cause clustering of populations within the cell cycle for these models. Furthermore, this clustering phenomenon is seen to be robust; it occurs for a variety of models, a broad selection of parameter values in those models and even for random perturbations of the models. Since there are necessarily an integer number of clusters, clustering can lead to periodic-like behavior with periods that are nearly integer divisors of the period  of the cell cycle.

Related experiments have shown conclusively that cell cycle clustering occurs in oscillating cultures.