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.
Bibliographical noteFunding Information:
B.F. thanks the Courant Institute (NYU) for hospitality. He was supported by CNRS and by the EU Marie Curie fellowship PIOF-GA-2009-235741. E.B., T.Y. and this work were supported by the NIH-NIGMS grant R01GM090207. The authors thank the referees for invaluable corrections and comments that greatly improved the manuscript.
- Autonomous oscillations in yeast
- Cell cycle
- Inhomogeneous feedback