  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.
