Oscillations and Bifurcation Structure of Reaction-Diffusion Model for Cell Polarity Formation

TL;DR

This paper analyzes a reaction-diffusion model for cell polarity, revealing four spatiotemporal patterns including oscillations, driven by diffusion instability, and explores how external signals influence these polarity oscillations.

Contribution

It provides a detailed bifurcation analysis of a reaction-diffusion system modeling cell polarity, identifying oscillatory behaviors and the impact of external signals.

Findings

Identification of four distinct spatiotemporal patterns including oscillations.

Demonstration that diffusion-driven instability triggers polarity oscillations.

Analysis of external signals' effects on cell polarity dynamics.

Abstract

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful model for understanding cell polarity formation. We show that this model exhibits four different spatiotemporal patterns including two types of oscillatory patterns, which can be regarded as cell polarity oscillations with the reversal and non-reversal of polarity, respectively. The trigger causing these patterns is a diffusion-driven (Turing-like) instability. Moreover, we investigate the effects of extracellular signals on the cell polarity oscillations.