Membrane Remodelling and Protein Interactions - A Free Energy Perspective

Abstract

We investigate the interplay between cell membrane curvature induced at the atomic scale, due to specialized peripheral membrane proteins, and the resulting membrane morphologies, of varying complexity, observed at the mesoscale. The biological membrane, in our approach, is represented by a dynamically triangulated surface while the proteins are modeled as curvature fields on the membrane, that are either isotropic or anisotropic. In order to compare with experiments, we have focused on the ENTH domain containing EPSIN whose curvature field is modeled as isotropic, and on the BAR, Exo70 and ESCRT family proteins whose curvature fields are determined to be anisotropic, both in experiments and in molecular simulations. Thermal undulations in the membrane and cooperativity in the curvature fields, due to the stabilization of a nematic phase, collectively drive the membrane into different morphological states (buds, tubules, etc.) that resemble those in cellular experiments in vivo and vesicle experiments in vitro. The relative stabilities of these self-organized shapes are examined by two approaches to compute the free energy of the system: (i) the Widom insertion technique to compute excess chemical potentials and (ii) thermodynamic integration using the Kirkwood coupling parameter to compute free energies. Building on these methods, we propose a hybrid scheme that couples both the approaches for computing free energies in membrane systems with heterogeneous and phase-segregated protein field - examples being the endoplasmic reticulum (ER) membrane discs with α- calreticulon protein confined to the rim and the vesicular bud formed due to the constriction by ESCRT proteins at its neck.