Energetics of lipid bilayers with applications to deformations induced by inclusions

A new energy for the description of large deformations of lipid bilayers is formulated with mathematical rigor. This energy is derived by considering the smectic A liquid crystalline nature of lipid bilayers and the coupling between the deformations of the layers and their constituent lipid molecules. Analogies between smectic A liquid crystals, with an infinite number of layers, and lipid bilayers, with a finite number of layers, are further discussed. The novelty of the energy density is demonstrated by studying the large deformations of planar lipid bilayers induced by cylindrical inclusions. The results of this study are directly compared with the results obtained using May's theoretical framework [May, Eur. Biophys. J., 2000, 29, 17–28] in which small deformations are assumed. As expected, the proposed energy density predicts larger distortions of the lipid molecules and deformations of the lipid bilayers close to an inclusion.