Membrane properties revealed by spatiotemporal response to a local inhomogeneity

We study theoretically the spatiotemporal response of a lipid membrane submitted to a local chemical change of its environment, taking into account the time-dependent profile of the reagent concentration due to diffusion in the solution above the membrane. We show that the effect of the evolution of the reagent concentration profile becomes negligible after some time. It then becomes possible to extract interesting properties of the membrane response to the chemical modification. We find that a local density asymmetry between the two monolayers relaxes by spreading diffusively in the whole membrane. This behavior is driven by intermonolayer friction. Moreover, we show how the ratio of the spontaneous curvature change to the equilibrium density change induced by the chemical modification can be extracted from the dynamics of the local membrane deformation. Such information cannot be obtained by analyzing the equilibrium vesicle shapes that exist in different membrane environments in light of the area-difference elasticity model.