Gaussian curvature elasticity determined from global shape transformations and local stress distributions: a comparative study using the MARTINI model

We calculate the Gaussian curvature modulus &z.kgrm; of a systematically coarse-grained (CG) one-component lipid membrane by applying the method recently proposed by Hu et al. [ Biophys. J. , 2012, 102 , 1403] to the MARTINI representation of 1,2-dimyristoyl- sn -glycero-3-phosphocholine (DMPC). We find the value &z.kgrm; / κ = −1.04 ± 0.03 for the elastic ratio between the Gaussian and the mean curvature modulus and deduce &z.kgrm; m / κ m −0.98 ± 0.09 for the monolayer elastic ratio, where the latter is based on plausible assumptions for the distance z 0 of the monolayer neutral surface from the bilayer midplane and the spontaneous lipid curvature K 0m . By also analyzing the lateral stress profile σ 0 ( z ) of our system, two other lipid types and pertinent data from the literature, we show that determining K 0m and &z.kgrm; through the first and second moment of σ 0 ( z ) gives rise to physically implausible values for these observables. This discrepancy, which we previously observed for a much simpler CG model, suggests that the moment conditions derived from simple continuum assumptions miss the effect of physically important correlations in the lipid bilayer.