Nonequilibrium dynamics of a fluid vesicle: Turing patterns and traveling waves

Abstract

In living cells, the shapes of biomembranes are dynamically regulated by proteins. We briefly review our recent studies on the membrane dynamics coupled with reaction-diffusion dynamics of curvature-inducing proteins. We simulated a vesicle in a fluid phase using a dynamically triangulated membrane model combined with a modified Brusselator model. The mechanochemical feedback of curvature-inducing proteins changes the condition of Turing patterns relative to those that occur on a non-deformable curved surface. Budding and multi-spindle shapes are also stabilized by Turing patterns. The speed of traveling waves increases or decreases with increasing local membrane curvature depending on the condition. Moreover, the reaction-diffusion waves can induce the self-oscillation of vesicle shapes.