ODE, RDE and SDE Models of Cell Cycle Dynamics and Clustering in Yeast
  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. These "autonomous oscillations" have often appeared with periods that are nearly integer divisors of the calculated doubling time of the culture.   We hypothesize that these oscillations could be caused by a weak form of cell cycle synchronization that we call clustering. We develop some novel ordinary differential equation models of the cell cycle. For these models, and for random and stochastic perturbations, we give both rigorous proofs and simulations showing that both positive and negative growth rate feedback within the cell cycle are possible agents that can cause clustering of populations within the cell cycle. It occurs for a variety of models and for a broad selection of parameter values. These results suggest that the clustering phenomenon is robust and is likely to be observed in nature. Since there are necessarily an integer number of clusters, clustering would lead to periodic-like behavior with periods that are nearly integer divisors of the period of the cell cycle. 
Erik M. Boczko, Tomas Gedeon, Chris C. Stowers and Todd Young