Reaction-Diffusion Waves Coupled with Membrane Curvature

TL;DR

This study investigates how reaction-diffusion waves of proteins interact with membrane curvature, revealing that mechanochemical feedback can alter wave patterns, speed, and induce vesicle shape oscillations, highlighting the significance of such coupling in cellular processes.

Contribution

The paper introduces a simulation framework combining membrane mechanics with reaction-diffusion dynamics to explore mechanochemical feedback effects on wave patterns.

Findings

Wave patterns change from propagating to nonpropagating and spiral due to mechanochemical effects.

Wave speed varies with local membrane curvature depending on membrane properties.

Vesicle shape self-oscillates in response to reaction-diffusion waves, aligning with experimental observations.

Abstract

The reaction-diffusion waves of proteins are known to be involved in fundamental cellular functions, such as cell migration, cell division, and vesicular transportation. In some of these phenomena, pattern formation on the membranes is induced by the coupling between membrane deformation and the reaction-diffusion system through curvature-inducing proteins that bend the biological membranes. Although the membrane shape and the dynamics of the curvature-inducing proteins affect each other in these systems, the effect of such mechanochemical feedback loops on the waves has not been studied in detail. In this study, reaction-diffusion waves coupled with membrane deformation are investigated using simulations combining a dynamically triangulated membrane model with the Brusselator model extended to include the effect of membrane curvature. It is found that the propagating wave patterns change into nonpropageting patterns and spiral wave patterns due to the mechanochemical effects. Moreover, the wave speed is positively or negatively correlated with the local membrane curvature depending on the spontaneous curvature and bending rigidity. In addition, self-oscillation of the vesicle shape occurs, associated with the reaction-diffusion waves of curvature-inducing proteins. This agrees with the experimental observation of liposomes with a reconstituted Min system, which plays a key role in the cell division of Escherichia coli. The findings of this study demonstrate the importance of mechanochemical coupling in biological phenomena.