Clustering in Cell Cycle Dynamics with General Response/Signaling Feedback

TL;DR

This paper investigates how cell-cycle dependent feedback influences the collective dynamics of cell populations, revealing that negative feedback promotes stable clustering consistent with yeast experimental observations.

Contribution

It introduces a mathematical analysis of cell-cycle feedback models, demonstrating how negative feedback leads to stable cell clustering, a novel insight into cell cycle regulation.

Findings

Negative feedback promotes stable cell clustering.

Positive feedback stabilizes individual clusters.

Negative feedback aligns with yeast experimental data.

Abstract

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.