Nonaxisymmetric vesicle shapes in a generalized bilayer-couple model and the transition between oblate and prolate axisymmetric shapes

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Abstract
A theoretical approach to calculate shapes of phospholipid vesicles is developed. It is general in the sense that it is not restricted to shapes with special symmetry properties, and it includes a stability analysis of the shapes. In keeping with recent experimental findings, the description of the vesicle membrane is based on the generalized bilayer-couple model. According to this concept, the bilayer structure of the membrane is modeled by representing its two monolayers as closed neutral surfaces with a constant separation distance. Equilibrium shapes are assumed to correspond to the minimum of the membrane elastic energy at constant values of the membrane area and the vesicle volume. The elastic energy is composed of the local and nonlocal bending energies of the membrane. The latter term represents the energy contribution of the relative area changes of monolayers. The variational problem to calculate equilibrium shapes is solved by applying a Ritz method based on an expansion in spherical harmonics. The numerical computations concentrate on the range of model parameters for which nonaxisymmetric shapes are obtained. In addition, axisymmetric shapes which are obtained in the same range of model parameters are examined. It is shown that small differences of the ratio between the nonlocal and local bending moduli (q) may cause significant changes in the nature of shape transformations. For high q values, nonaxisymmetric shapes are stable, and they represent the intermediate states in the continuous transformation between oblate and prolate axisymmetric shapes. At low q values characteristic for phospholipid bilayers, the nonaxisymmetric shapes are unstable. In this case, the transition between oblate and prolate axisymmetric shapes is discontinuous.