Mean Curvature Dictates the Diffusion of Lipids Along Curved Membranes

Curved cellular membranes are both abundant and functionally relevant. While novel tomography approaches reveal the structural details of curved membranes, their dynamics pose an experimental challenge. Curvature especially affects the diffusion of lipids and macromolecules, yet neither experiments nor continuum models distinguish geometric effects from those caused by curvature-induced changes in membrane properties. Molecular simulations could excel here, yet despite community interest towards curved membranes, tools for their analysis are still lacking. Here, we quantify curvature effects on lipid motion along membranes with mean and/or Gaussian curvature using an approach based on Vertex-oriented Triangle Propagation algorithm applied to coarse- grained simulations. This approach computes geodesic distances significantly faster than conventional implementations of path-finding algorithms. We find that Gaussian curvature plays a surprisingly small role, whereas mean curvature, i.e. the packing of lipid headgroups largely dictates their mobility. Our implementation, coined CurD, is fast, easy to use, and freely available.