Predicting protein curvature sensing across membrane compositions with a bilayer continuum model.

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 sensing'. Curvature sensing 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 sensing 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 sensing. We evaluate both energetic and structural changes to vesicles upon helix insertion, with strong agreement to new experiments and all-atom MD 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 the established energetics of lipid tilt. In agreement with experiment, our model predicts stronger curvature sensing in membranes with distinct tail groups (POPC vs DOPC vs DLPC), despite having identical head-group chemistry; the model shows that the primary driving force for weaker curvature sensing 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 multi-scale 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.