Mathematics – Dynamical Systems
Scientific paper
2011-11-29
J. Theor. Biology 292 (2012), 103-115
Mathematics
Dynamical Systems
To appear in J. Theoretical Biology 292 (2012), 103-115
Scientific paper
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 behaviour 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.
Boczko Erik
Buckalew Richard
Fernandez Bastien
Moses Gregory
Young Thomas
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