Bending stiffness of lipid bilayers. III. Gaussian curvature

The Gaussian curvature term in the expression for the energy density in bending of a lipid bilayer can be decomposed in two terms one symmetric and the other one antisymmetric in the principal curvatures. The symmetric term is proportional to the square of the mean local curvature. A similar term has exclusively been used to calculate the equilibrium shape of bilayer structures the topology of which does not change. It is suggested that the antisymmetric term which is proportional to the square of the deviator of the local curvature should not be neglected in such calculations.