CurD: A Tool for Diffusion Analyses on Curved Membranes

Curved membranes are abundant and functionally relevant in living matter, yet they have eluded computational studies due to methodological limitations. With multiple approaches available for setting up simulations on such curved membranes, there is a growing need for efficient and versatile tools to analyze their outcomes. Here, we present CurD, a freely available tool for analyzing the diffusion of membrane constituents along curved surfaces. The tool efficiently uses the Vertex-oriented Triangle Propagation algorithm to compute geodesic distances significantly faster than conventional implementations of path-finding algorithms, while providing a friendly command-line interface. With CurD, we resolve the effects of curvature and lipid packing densities on the diffusion of lipids on two curved membranes---one with only mean curvature and another with both Mean and Gaussian curvature. We find that Gaussian curvature plays a surprisingly small role, whereas mean curvature or packing of lipid headgroups largely dictates their mobility.