A computational approach to curvature sensing in lipid bilayers

Abstract: Local curvature is a key driving force for spatial organization of cellular membranes, via a phenomenon known as membrane curvature sensing, where the binding energy of membrane associated macromolecules depends on the local membrane shape. However, the microscopic mechanisms of curvature sensing are not well understood. Molecular dynamics simulations offer a powerful complement to biochemical experiments, yet their contribution to the study of curvature sensing has been limited, due in part to the lack of efficient methods, not least because of methodological difficulties in dealing with curved membranes. We develop a method based on simulated buckling, which has been previously employed to study mechanical properties of membranes. Here, we describe, validate and evaluate this method. We then apply to study curvature sensing properties of three model systems, using coarse-grained simulations. On the first system, we study lipid sorting in a three-component lipid mixture with emphasis on cardiolipin. We find that if curvature is high, curvature sensing is strong enough to drive cardiolipin molecules to negative curvature regions, outcompeting other lipids, without the need of external interactions or cooperative effects. We then simulated three systems consisting of a short amphipathic peptide attached to the surface of a buckled membrane. All three peptides localize to positive curvature, in agreement with the so-called cylindrical hydrophobic insertion mechanism. Their orientational preferences, however, defy the prediction of alignment perpendicular to the direction of maximum curvature. They also fail to show expected symmetries, indicating there is more to the picture than purely shape-based effects. The curvature sensing probe of the next system is a transmembrane trimeric protein, which shows preference to intermediate curvature, in agreement with theoretical predictions. But the lack of an expected 2-fold rotation symmetry indicates that the trimer senses the local curvature gradient, and not just the point-wise local curvature. Finally, dispensing with the buckling methodology, we simulated a series of symmetric transmembrane multimers embedded in cylindrical bilayers. Based on the results of these simulations and theoretical arguments, we discuss the relationship between structural symmetry and curvature sensitivity. We conclude that anisotropic (i.e. orientation-dependent) curvature sensing is strongly limited by odd and high order rotational symmetries. However, measurements of in-plane orientation on peptides and asymmetric proteins, as well as dimers and tetramers, should yield valuable information. Our method, along with our initial conclusions, provides an useful tool for the understanding of the relationship between membrane shape and membrane protein function, and should prove useful to biophysicists in the design and interpretation of experimental curvature sensing assays.