Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation

Masataka Kuwamura; Hirofumi Izuhara; Shin-Ichiro Ei

doi:10.1007/s00285-022-01723-5

Oscillations and bifurcation structure of reaction-diffusion model for cell polarity formation

J Math Biol. 2022 Feb 25;84(4):22. doi: 10.1007/s00285-022-01723-5.

Authors

Masataka Kuwamura¹, Hirofumi Izuhara², Shin-Ichiro Ei³

Affiliations

¹ Graduate School of Human Development and Environment, Kobe University, Kobe, 657-8501, Japan. kuwamura@main.h.kobe-u.ac.jp.
² Faculty of Engineering, University of Miyazaki, 1-1 Gakuen Kibanadai-nishi, Miyazaki, 889-2192, Japan.
³ Department of Mathematics, Hokkaido University, Sapporo, 060-0810, Japan.

PMID: 35212844
DOI: 10.1007/s00285-022-01723-5

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:e108, 2007). 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.

Keywords: Bistable nonlinearity; Cell polarity oscillations; Reaction–diffusion system.

Publication types

Research Support, Non-U.S. Gov't

MeSH terms

Cell Polarity*
Diffusion