Lateral Interaction of Cylindrical Transmembrane Peptides in a One-Dimensional Approximation

Abstract—

Various membrane inclusions can induce deformations of lipid bilayer membranes. The characteristic length of deformation propagation along the membrane is about several nanometers. Overlapping of deformations induced by different membrane inclusions leads to their effective lateral interaction. The interaction energy can be calculated within the framework of an adequate theory of elasticity. However, in practice, such a calculation can be carried out in an analytical form only for effectively one-dimensional systems, for example, those with translational or rotational symmetry. In the general case of systems with low symmetry, the problem cannot be solved analytically. We theoretically considered the interaction of two cylindrical transmembrane peptides mediated by membrane deformations. The interaction energies were obtained by numerical minimization of the elastic energy functional. In addition, we calculated the interaction energies in a one-dimensional approximation, assuming that the system possesses the translational symmetry. It was shown that the one-dimensional approximation quite well reproduces the results of exact numerical calculations in lipid bilayers of various thicknesses and rigidities.