Membrane Permeability of Sucrose Calculated from Equilibrium Time-Correlation Functions Using Molecular Dynamics Simulations with Enhanced Sampling.

Abstract

A computational framework for rigorously computing the membrane permeability of small molecules from unbiased molecular dynamics simulations is presented. The method in its optimized form exploits the committor probability within the transition path theory framework and is applicable to molecules with free energy barriers for which a determination of the permeability coefficient from spontaneous crossings during equilibrium simulations would be unfeasible. A novel computational protocol is implemented through which the equilibrium time-correlation function is calculated from a combination of enhanced sampling to determine the equilibrium potential of mean force of the permeant molecule and a reweighted ensemble of short unbiased trajectories. By extracting the steady-state flux from committor-based equilibrium time-correlation functions of unbiased dynamics, the method provides a rigorous computational route to determine the permeability coefficient while going beyond the inhomogeneous solubility diffusion (ISD) model, which is built upon the assumption of overdamped dynamics. The highly polar, slowly permeating molecule sucrose is used here as an illustrative example of the committor-based permeability theory. For a full assessment of how the method compares to the ISD model, systems of DOPC and DLPC membranes are considered for both additive and polarizable force field models. Estimates based on the ISD permeability are systematically smaller than or equal to the values determined from the present method, indicating that non-Markovian memory effects that do not fully decay on the time scale of membrane crossing are potentially ignored.