Determining the Gaussian Curvature Modulus of Lipid Membranes in Simulations: A Comparative Study via Global Shape Transformations and Local Stress Distributions

The Gaussian curvature modulus κ-bar matters for many important biological processes that involve topological and/or boundary changes of cell membrane, e.g. endo- and exo-cytosis. However, only sparse experimental measurements of have been reported, and even fewer accurate results obtained via computer simulations exist. Here, we propose a novel approach to determine κ-bar in silico by monitoring patch-closure processes of pre-curved circular bilayers. Applying this method to two different coarse-grained (CG) membrane models, namely the generic Cooke model [1] and the more finely-resolved and systematically parameterized MARTINI model [2], we find elastic ratios between the two curvature moduli, κ-bar/κ, in the range between −0.85 and −1.05, in line with previous estimates in literature. Yet, for the same systems studied, another well known method, which derives the material parameters from moments of the lateral stress profile, produces results that are neither in accordance with the patch-closure method nor, in fact, physically plausible. One potential reason of the failure lies in the mean field essence of this second method, which does not consider lipid-lipid correlations. Our study hence raises concerns about attempts to derive curvature-elastic properties using the stress profile method.[1] I. Cooke et al, Phys Rev E, 72, 011506 (2005)[2] S. J. Marrink et al, J Phys Chem B, 111, 7812 (2007)