Predicting protein curvature sorting across membrane compositions

Cytoplasmic proteins must recruit to membranes to function in processes such as endocytosis and cell division. Many of these proteins recognize not only the chemical structure of the membrane lipids, but the curvature of the surface, binding more strongly to more highly curved surfaces, or curvature sorting. Curvature sorting by amphipathic helices is known to vary with membrane bending rigidity, but changes to lipid composition can simultaneously alter membrane thickness, spontaneous curvature, and leaflet symmetry, thus far preventing a systematic characterization of lipid composition on such curvature preferences through either experiment or simulation. Here, we develop and apply a bilayer continuum membrane model that can tractably address this gap, quantifying how controlled changes to each material property can favor or disfavor protein curvature sorting. We evaluate both energetic and structural changes to vesicles upon helix insertion, with strong agreement to new in vitro experiments and all-atom molecular dynamics simulations, respectively. Our membrane model builds on previous work to include both monolayers of the bilayer via representation by continuous triangular meshes. We introduce a coupling energy that captures the incompressibility of the membrane and approximates the established energetics of lipid tilt without using an explicit tilt field. In agreement with experiment, our model predicts stronger curvature sorting in membranes with distinct tail groups (POPC vs. DOPC vs. DLPC), despite having identical headgroup chemistry; the model shows that the primary driving force for weaker curvature sorting in DLPC is that it is thinner and more wedge shaped. Somewhat surprisingly, asymmetry in lipid shape composition between the two leaflets has a negligible contribution to membrane mechanics following insertion. Our multiscale approach can be used to quantitatively and efficiently predict how changes to membrane composition in flat to highly curved surfaces alter membrane energetics driven by proteins, a mechanism that helps proteins target membranes at the correct time and place.