Lipid Bilayer Fluctuations in silico: Statistical Improvements and Systematic Corrections

The energetics of lipid bilayer deformations can be described by continuum theories in which each type of deformation is weighted by an elastic modulus. In computer simulations, these moduli can be determined by fitting power spectra of fluctuating fields (e.g. surface height) to the predictions of those continuum theories. This data analysis involves numerous choices, such as how to define a membrane surface or how to determine the fitting range, which significantly affect the observables of interest. Here, we examine in detail the systematic trends resulting from these choices, on the basis of atomistic simulation trajectories of 13 different lipid model membranes, as well as coarse-grained MARTINI simulations of much larger systems, both created by Venable et al. We in particular discuss systematic effects connected with: (1) interpolation of height and directional fields; (2) normalization and averaging of lipid directors; (3) determining small-scale cutoffs. Additionally, we discuss statistical aspects such as correcting for time correlations in the power spectra, bootstrapping for uncertainties on the parameters, and simultaneously fitting different spectra. Overall, ever-improving computational abilities have lead to statistical uncertainties in the elastic moduli that are often smaller than systematic shifts arising from equally plausible choices, rendering the latter the more important concern.