Nonlinear Deformations of Bilayer Lipid Membranes

Abstract

Novel continuum models that describe the equilibrium configurations of planar lipid bilayers will be presented. The models are derived within the nonlinear theory for smectic A liquid crystals proposed by Stewart (IW Stewart 2007 Contin. Mech. Thermodyn. 18:343) in which the usual director and unit layer normal do not always necessarily coincide. The total energy of lipid bilayers consists of an elastic splay term, smectic layer bending and compression terms, a coupling term between the director and layer normal, a surface tension term, and a surface anchoring term. Nonlinear equilibrium equations are obtained by using variational methods and are then solved by analytical and numerical methods. The solutions illustrate the nonlinear deformations of lipid bilayers including the misalignment of lipid molecules at their interface with other media such as, for example, proteins and surface substrates.