Direct Derivation of Free Energies of Membrane Deformation and Other Solvent Density Variations From Enhanced Sampling Molecular Dynamics

Abstract

We report a methodology to calculate the free energy of a shape transformation in a lipid membrane directly from a molecular dynamics simulation. The bilayer need not be homogeneous or symmetric and can be atomically detailed or coarse grained. The method is based on a collective variable that quantifies the similarity between the membrane and a set of predefined density distributions. Enhanced sampling of this "Multi-Map" variable re-shapes the bilayer and permits the derivation of the corresponding potential of mean force. Calculated energies thus reflect the dynamic interplay of atoms and molecules, rather than postulated effects. Evaluation of deformations of different shape, amplitude, and range demonstrates that the macroscopic bending modulus assumed by the Helfrich-Canham model is increasingly unsuitable below the 100-Å scale. In this range of major biological significance, direct free-energy calculations reveal a much greater plasticity. We also quantify the stiffening effect of cholesterol on bilayers of different composition and compare with experiments. Lastly, we illustrate how this approach facilitates analysis of other solvent reorganization processes, such as hydrophobic hydration. Published 2019. This article is a U.S. Government work and is in the public domain in the USA.