Symmetry breaking in a bulk-surface reaction-diffusion model for signaling networks

TL;DR

This paper explores how symmetry breaking and diffusive instabilities in a coupled bulk-surface reaction-diffusion model can lead to cell polarization, identifying a realistic mechanism driven by differences in cytosolic and membrane diffusion.

Contribution

It introduces a new stability mechanism for cell polarization based on realistic diffusion differences, supported by theoretical analysis and numerical simulations.

Findings

Identified two mechanisms for symmetry breaking: classical Turing and a more realistic diffusion-driven instability.

The realistic mechanism involves differences between cytosolic and membrane diffusion.

Numerical simulations confirm the theoretical predictions beyond linear stability analysis.

Abstract

Signaling molecules play an important role for many cellular functions. We investigate here a general system of two membrane reaction-diffusion equations coupled to a diffusion equation inside the cell by a Robin-type boundary condition and a flux term in the membrane equations. A specific model of this form was recently proposed by the authors for the GTPase cycle in cells. We investigate here a putative role of diffusive instabilities in cell polarization. By a linearized stability analysis we identify two different mechanisms. The first resembles a classical Turing instability for the membrane subsystem and requires (unrealistically) large differences in the lateral diffusion of activator and substrate. The second possibility on the other hand is induced by the difference in cytosolic and lateral diffusion and appears much more realistic. We complement our theoretical analysis by numerical simulations that confirm the new stability mechanism and allow to investigate the evolution beyond the regime where the linearization applies.