Mean and Gaussian Curvature of Lipid Mesophases measured using molecular dynamics

The ability to measure the mean and Gaussian curvature in lipid mesophases is important in our understanding of their formation and properties, and can be achieved both experimentally and computationally. Here we show that curvature can be measured using Molecular Dynamics simulations, however the reliability of the results is highly dependent on the choice of fitting algorithm, the atoms within the lipid membrane that are selected for fitting and the number of atoms that are included in the fit. We compare the results of our method to the L${\alpha}$ mesophase as previously studied, and subsequently extend the method to the Q$_{II}^{D}$ and H$_{II}$ mesophase, not previously studied in this way computationally, but whose curvatures are known both analytically and experimentally. By systematically comparing our results, we demonstrate a robust method which can be used in general to measure curvature.