Modeling membrane deformations and lipid demixing upon protein-membrane interaction: the BAR dimer adsorption.

We use a self-consistent mean-field theory, designed to investigate membrane reshaping and lipid demixing upon interaction with proteins, to explore BAR domains interacting with large patches of lipid membranes of heterogeneous compositions. The computational model includes contributions to the system free energy from electrostatic interactions and elastic energies of the membrane, as well as salt and lipid mixing entropies. The results from our simulation of a single adsorbing Amphiphysin BAR dimer indicate that it is capable of stabilizing a significantly curved membrane. However, we predict that such deformations will occur only for membrane patches that have the inherent propensity for high curvature, reflected in the tendency to create local distortions that closely match the curvature of the BAR dimer itself. Such favorable preconditioning for BAR-membrane interaction may be the result of perturbations such as local lipid demixing induced by the interaction, or of a prior insertion of the BAR domain's amphiphatic N-helix. From our simulations it appears that local segregation of charged lipids under the influence of the BAR dimer cannot produce high enough asymmetry between bilayer leaflets to induce significant bending. In the absence of additional energy contributions that favor membrane asymmetry, the membrane will remain nearly flat upon single BAR dimer adsorption, relative to the undulation expected from thermal fluctuations. Thus, we conclude that the N-helix insertions have a critical mechanistic role in the local perturbation and curving of the membrane, which is then stabilized by the electrostatic interaction with the BAR dimer. We discuss how these results can be used to estimate the tendency of BARs to bend membranes in terms of a spatially nonisotropic spontaneous curvature.