Pattern Formation in Reaction-Diffusion System on Membrane with Mechanochemical Feedback

TL;DR

This study explores how mechanochemical feedback influences pattern formation on deforming biological membranes, revealing new pattern types and transitions driven by membrane shape changes.

Contribution

It introduces a combined simulation and analytical approach to understand nonequilibrium pattern formation on deformable membranes, highlighting the impact of mechanochemical feedback.

Findings

Membrane deformation alters stable reaction-diffusion patterns.

Budding and multi-spindle shapes are induced by Turing patterns.

Transition from oscillation to stable spot patterns observed.

Abstract

Shapes of biological membranes are dynamically regulated in living cells. Although membrane shape deformation by proteins at thermal equilibrium has been extensively studied, nonequilibrium dynamics have been much less explored. Recently, chemical reaction propagation has been experimentally observed in plasma membranes. Thus, it is important to understand how the reaction-diffusion dynamics are modified on deformable curved membranes. Here, we investigated nonequilibrium pattern formation on vesicles induced by mechanochemical feedback between membrane deformation and chemical reactions, using dynamically triangulated membrane simulations combined with the Brusselator model. We found that membrane deformation changes stable patterns relative to those that occur on a non-deformable curved surface, as determined by linear stability analysis. We further found that budding and multi-spindle shapes are induced by Turing patterns, and we also observed the transition from oscillation patterns to stable spot patterns. Our results demonstrate the importance of mechanochemical feedback in pattern formation on deforming membranes.