Assessment of Membrane Deformation Continuum Elastic Models Based on Molecular Simulations of Gramicidin A

Abstract

We have assessed the continuum elastic model (CEM) for membrane deformations by comparison with all-atom molecular dynamics (MD) simulation results of gramicidin A (gA) dimers inserted into four different lipid bilayers formed by DLPC, DMPC, DOPC, and POPC. The CEM based on the smectic liquid crystal assumption for lipid membrane has been reported to efficiently model the protein-induced membrane deformation. In this description, the hydrophobic mismatch is assumed to be the dominant non-specific physical interaction between protein and lipid bilayer, and the deformation energy is modeled by compression-expansion, splay-distortion, and surface tension contributions. Using various boundary conditions (constrained, relaxed, and MD-based) and elastic modulus profiles (uniform and space-dependent), the deformation profile and the resulting energy were calculated and compared with the MD simulation results. Good agreement of the CEM and MD results is obtained for bilayer thickness profiles beyond the first lipid shell region from the gA channel when the MD-based boundary condition is used at lipid-protein contact. However, the continuum membrane representation near the protein contact, in the first shell, does not capture the atomic-level protein-lipid interactions. Thus careful/separate treatment of the first lipid shell region is required for the CEM to fully represent the realistic lipid bilayer deformation, as deduced from MD simulations. Introducing a space-dependent modulus profile has little effect on the deformation profile, but the calculated deformation energy depends strongly on the modulus profile.