Determination of mean and Gaussian curvatures of highly curved asymmetric lipid bilayers: the case study of the influence of cholesterol on the membrane shape

Although molecular dynamics simulations of highly curved lipid bilayers have become increasingly popular in recent years, there is no simple and general method of computing the shape and curvature of the bilayer, which is bent arbitrarily in three dimensions. In this work we propose a method, which allows computing local normal, mean and Gaussian curvatures at any point of an arbitrarily curved lipid membrane using molecular dynamics trajectories. The method is based on the analysis of local membrane patches and is applicable to the membranes of any shape and topology - bilayers, vesicles, micelles, bicelles, etc. The method is applied to a highly curved asymmetric DOPC/DOPS lipid bilayer simulated by means of extended coarse-grained molecular dynamics simulations. It is shown that addition of cholesterol makes the membrane more topologically heterogeneous by increasing the content of highly curved regions with either saddle-like or sphere-like topology. The topology of the DOPS lipid domains is more sensitive to the addition of cholesterol than DOPC domains.