Observation of stable shapes and conformal diffusion in genus 2 vesicles

The observed equilibrium shapes of phospholipid vesicles of topological genus 2 (shapes with two holes) are found to be in agreement with theoretical predictions on the basis of a minimization of the elastic curvature energy for fluid membranes under the constraints of constant area, volume, and area difference (between the inner and outer layers of the membrane). For some particular geometrical characteristics, the shapes of the vesicles change continuously and randomly on a slow time scale (tens of seconds) and thus exhibit conformal diffusion. This phenomenon is a reflection of the conformal degeneracy of the elastic curvature energy. Its observation sets a limit (three constraints) on the number of physical constraints relevant to the determination of the shapes of vesicles.