Shapes of biomembrane in living cells are regulated by curvature-inducing proteins. However, the effects of membrane deformation on signal transactions such as chemical waves have not been researched adequately. Here, we report that membrane deformation can alter the propagation of excitable reaction-diffusion waves using state-of-the-art simulations. Reaction waves can induce large shape transformations, such as membrane budding and necking, that erase or divide the wave, depending on the curvature generated by the waves, feedback to the wave propagation, and the ratio of the reaction and deformation times. Using genus-2 vesicles, we demonstrate that the occasional disappearance of the waves results in the reverse operation of the wave circuit. Our findings suggest that membrane deformation and reaction waves can together regulate signal transactions on biomembranes.

Biomembranes experience out-of-equilibrium conditions in living cells. Their undulation spectra are different from those in thermal equilibrium. Here, we report on the undulation of a fluid membrane pushed by the stepwise growth of filaments as in the leading edge of migrating cells, using three-dimensional Monte Carlo simulations. The undulations are largely modified from equilibrium behavior. When the tension is constrained, the low-wave-number modes are suppressed or enhanced at small or large growth step sizes, respectively, for high membrane surface tensions. In contrast, they are always suppressed for the tensionless membrane , wherein the wave-number range of the suppression depends on the step size. When the membrane area is constrained, in addition to these features, a specific mode is excited for zero and low surface tensions. The reduction of the undulation first induces membrane buckling at the lowest wave-number, and subsequently, other modes are excited, leading to a steady state.

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