Hybrid continuum-particle method for fluctuating lipid bilayer membranes with diffusing protein inclusions

Biological membranes contain many types of embedded proteins whose collective organization and functions depend importantly on the mechanical interplay with the lipid bilayer. We introduce new methods at the level of individual proteins embedded within the bilayer in a manner closely related to the Immersed Boundary Method (Atzberger et al., 2007, [1], Peskin, 2002, [31]). Our approach accounts for the bidirectional coupling between the membranes and proteins, the elastic mechanics of the bilayer, the hydrodynamic interactions, and the thermal fluctuations. For proteins that induce curvature, we show that the bidirectional membrane-protein coupled dynamics has important consequences for the effective diffusivities of embedded proteins. We further show that collective effects arising from different area fractions and curvatures of the embedded proteins impact significantly membrane mechanics. The proposed modeling approach and computational methods are quite general and could be useful in the investigation of a wide variety of phenomena involving membrane-protein interactions.