Determining Structural and Mechanical Properties from Molecular Dynamics Simulations of Lipid Vesicles

We have developed an algorithm to determine membrane structure, area per lipid, and bending rigidity from molecular dynamics simulations of lipid vesicles. Current methods to extract structure from vesicle simulations define densities relative to the global center of mass of the vesicle. This approach ignores the long-wavelength fluctuations (undulations) that develop across the sphere and broaden the underlying structure. Our method establishes a local reference frame by defining a radially undulating reference surface (URS) and thereby removes the broadening effect of the undulations. Using an arc-length low-pass filter, we render the URS by defining the bilayer midplane on an equi-angular θ, ϕ-grid (colatitude, longitude). This surface is then expanded onto a truncated series of spherical harmonics. The spherical harmonic coefficients characterize the long-wavelength fluctuations that define both the local reference frame-used to determine the bilayer's structure-and the area per lipid (A_L) along the undulating surface. Additionally, the resulting power spectrum of spherical harmonic coefficients can be fit to a Helfrich continuum model for membrane bending in spherical geometry to extract bending rigidity (k_c). k_c values determined for both DMPC and DMPC + cholesterol (30 mol %) vesicles are consistent with values from corresponding flat-patch systems determined using an independent, previously published spectral method. These new tools to accurately extract structure, A_L, and k_c should prove invaluable in evaluating the construction and equilibration of lipid vesicle simulations.