Nearly spherical vesicle shapes calculated by use of spherical harmonics : axisymmetric and nonaxisymmetric shapes and their stability

Abstract

A theoretical approach to determine nearly spherical shapes of phospholipid vesicles is developed. The method is general in the sense that it does not depend on any symmetry restrictions. Equilibrium shapes are assumed to correspond to the minimum of the membrane bending elastic energy at constant values of the membrane area, the vesicle volume and the difference of areas of the two leaflets of the phospholipid bilayer. The bending energy and the constraints are expanded up to fourth order terms in the deviation from a sphere, and in the subsequent calculations all terms up to the third order are included. The deviation is expressed as a series of spherical harmonics. It sis shown that the stability of the solutions can be tested by inspecting the eigenvalues of the matrix of second derivatives of the bending energy with respect to independent amplitudes of spherical harmonics expansion. The method is applied to the calculation of axisymmetric and nonaxisymmetric shapes, and the influences of different approximations are discussed. It is shown that at variations of the leaflet area difference stable oblate and stable prolate shapes are transformed into each other in a continuous manner.