Predicting how lipid composition controls protein curvature sensing with a continuum bilayer membrane model

For a variety of biological processes including endocytosis and signaling, proteins must recruit from the cytoplasm to membranes. Several membrane-binding 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. One common mechanism of curvature sensing is through the insertion of an amphipathic helix into the outer membrane leaflet. Because lipid composition affects multiple material properties of the membrane including bending rigidity, thickness, lipid tilt, and compressibility, it has not been possible to predict how lipid composition controls protein curvature sensing by helix insertion. Here we develop and apply a two-leaflet continuum membrane model to quantify how such changes to the material properties can favor or disfavor protein curvature sensing by computing energetic and structural changes upon helix insertion, with corroboration against in vitro experiments. Our membrane model builds on previous work from our group to explicitly model both monolayers of the bilayer via representation by continuous triangular meshes. To the energy of each monolayer, we introduce a coupling energy that is derived from established energetics of lipid tilt but reformulated into a height term that is methodologically simpler to evaluate. In agreement with molecular dynamics simulations, our model produces a decrease in bilayer height around the site of insertion. We find that increasing membrane height increases curvature sensing. From the protein perspective, deeper or larger insertions also increase curvature sensing. Our experiments of helix insertion by the epsin N-terminal homology (ENTH) on vesicles with varying lipid tail groups show that lipids like DOPC drive stronger curvature sensing than DLPC, despite having the same head-group chemistry, confirming how the material properties of the membrane alter curvature sensing, in excellent agreement with the predictions of our bilayer membrane model. Our model thus quantitatively predicts how changes to membrane composition can alter membrane energetics driven by protein insertion, and can be more broadly extended to characterizing the structure and energetics of protein-driven membrane reshaping by protein assemblies. ### Competing Interest Statement The authors have declared no competing interest.