Clustering in cell cycle dynamics with general response/signaling feedback

• Published in: Journal of theoretical biology 2012-01, Vol.292 (7), p.103-115
• Main Authors: Young, Todd R., Fernandez, Bastien, Buckalew, Richard, Moses, Gregory, Boczko, Erik M.
• Format: Article
• Language: English
• Subjects: Animals; Autonomous oscillations in yeast; Biological Clocks - physiology; Cell cycle; Cell Cycle - physiology; Cluster Analysis; Dynamical Systems; equations; Feedback, Physiological - physiology; Inhomogeneous feedback; Mathematics; Models, Biological; Nonlinear Sciences; Pattern Formation and Solitons; Signal Transduction - physiology; yeasts; Yeasts - cytology
• ISSN: 0022-5193; 1095-8541
• DOI: 10.1016/j.jtbi.2011.10.002

Motivated by experimental and theoretical work on autonomous oscillations in yeast, we analyze ordinary differential equations models of large populations of cells with cell-cycle dependent feedback. We assume a particular type of feedback that we call responsive/signaling (RS), but do not specify a functional form of the feedback. We study the dynamics and emergent behavior of solutions, particularly temporal clustering and stability of clustered solutions. We establish the existence of certain periodic clustered solutions as well as “uniform” solutions and add to the evidence that cell-cycle dependent feedback robustly leads to cell-cycle clustering. We highlight the fundamental differences in dynamics between systems with negative and positive feedback. For positive feedback systems the most important mechanism seems to be the stability of individual isolated clusters. On the other hand we find that in negative feedback systems, clusters must interact with each other to reinforce coherence. We conclude from various details of the mathematical analysis that negative feedback is most consistent with observations in yeast experiments. ► We analyze the dynamics of a broad class of cell cycle feedback mechanisms. ► For positive feedback isolated clusters are stable, but unstable for negative. ► Non-isolated clusters are unstable for positive feedback, stable for negative. ► The case of k=2 clusters is studied completely. ► Positive feedback generally leads to synchronization, negative to clustering.