The existence of non-axisymmetric bilayer vesicle shapes predicted by the bilayer couple model

Abstract

The existence of non-axisymmetric shapes with minimal bending energy is proved by means of a mathematical model. A parametric model is used; the shapes considered have an elliptical top view whilst their front view contour is described using Cassini ovals. Taking into account the bilayer couple model, the minimization of the membrane bending energy is performed at a constant membrane area A, a constant enclosed volume V and a constant difference between the two membrane leaflet areas delta A. It is shown that for certain sets of A, V and delta A the non-axisymmetric shapes calculated with the use of the parametric model have lower energy than the corresponding axisymmetric shapes obtained by the exact solution of the general variational problem. As an exact solution of the general variational problem for non-axisymmetric shapes would yield even lower energy, this indicates the existence of non-axisymmetric shapes with minimal bending energy in a region of the V/delta A phase diagram.