Inferring protein-induced spontaneous curvature of lipid bilayers from molecular simulation

Proteins and lipids of a biological cell work together to reshape the membranes in which they reside. Membrane reshaping is necessary for vesicular traffic and maintenance of organelle shape and structure. Curvature is the fundamental mathematical description of the local shape of a surface. Through the well-established Helfrich/Canham/Evans model of bilayer shape, curvature sensing and induction are both consequences of a protein's spontaneous curvature, the local curvature at which the Helfrich model energy is a minimum. This paper describes a straightforward approach for estimating the strength and sign of a bilayer-associated molecule's curvature induction from molecular simulation: Correlating the molecule's lateral position with curvature on thermally-fluctuating bilayer modes. Example demonstrations range from a large multi-pass coarse-grained transmembrane protein to an all-atom amphipathic helical segment. Quantification of these systems is placed in the context of experiments seeking the same strength and sign of curvature induction.