Abstract
Like thin elastic sheets, lipid bilayers can bend and stretch, and are characterized by mechanical constants such as bending rigidity (Kc) and area compressibility (Ka), which define the free energy of bilayer deformation and thus have direct implications in quantifying the energetics of protein-membrane interactions. Limited experimental data for Kc and Ka of different lipid mixtures makes such calculations challenging. Existing computational methods for calculating Ka from MD simulations exhibit strong dependence on bilayer size, or require multiple simulations with constraints on the area, or tension. We present a novel computational framework that is independent of system size and requires analysis only of a single sufficiently converged simulation trajectory. The method is based on Helfrich's theory of elasticity by relating relative changes in area to relative changes in thickness. The distribution of local fluctuations in the thickness of each bilayer leaflet is used to construct a potential of mean force and recover the bilayer Ka from a quadratic fit. The rapid calculation utilizes freely available software packages. We present results for a variety of single and multicomponent bilayers of phosphatidylcholine, phosphatidylethanolamine and sphingomyelin, utilizing simulation results at different temperatures and bilayer sizes. The calculated compressibility moduli range from 170 to 320 mN/m and agree for the majority of tested cases with values reported from experiments and other computational methods. We further validate our method in a comparison with an existing polymer brush model and confirm the linear relationship between thickness and (Kc/Ka) ˆ (1/2), all calculated from the simulation trajectories.
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