Determination of electron density profiles and area from simulations of undulating membranes

The traditional method for extracting electron density and other transmembrane profiles from molecular dynamics simulations of lipid bilayers fails for large bilayer systems, because it assumes a flat reference surface that does not take into account long wavelength undulations. We have developed what we believe to be a novel set of methods to characterize these undulations and extract the underlying profiles in the large systems. Our approach first obtains an undulation reference surface for each frame in the simulation and subsequently isolates the long-wavelength undulations by filtering out the intrinsic short wavelength modes. We then describe two methods to obtain the appropriate profiles from the undulating reference surface. Most combinations of methods give similar results for the electron density profiles of our simulations of 1024 DMPC lipids. From simulations of smaller systems, we also characterize the finite size effect related to the boundary conditions of the simulation box. In addition, we have developed a set of methods that use the undulation reference surface to determine the true area per lipid which, due to undulations, is larger than the projected area commonly reported from simulations.