Free Energy Calculation of Membrane Permeation - Simulation Results Suggest Relaxation of Headgroup-Solute Interactions is the Slowest Degree of Freedom

Abstract

Molecular Dynamics (MD) simulations have been extensively used to investigate membrane-solute interactions. Understanding the interactions associated with solute translocation across lipid bilayers facilitates prediction of passive permeation rates of cell membranes, which is a very important property in the field of drug design and pharmacology. In this work, we use accelerated MD techniques to calculate the free energy of translocation of several small molecules across 1,2-dioleoyl-sn-glycero-3-phosphatidylcholine (DOPC) lipid bilayers as a first step toward understanding the translocation mechanism. We compare the results for the translocation of arginine, a sodium ion, alanine and water as obtained from Metadynamics, Umbrella Sampling and Replica Exchange Umbrella Sampling. Within the fixed length of our simulation, we find that all methods produce comparable results for neutral permeants, but the results differ for polar and positively charged molecules. Using replica exchange umbrella sampling, we identify the difficulty in relaxation of strong electrostatic interactions between lipid headgroups and the solute to be the cause of this difference. Only after extensive equilibration, the artifacts from electrostatic interactions decay, allowing us to calculate the correct free energy profiles of all studied permeants. We show that the true transition state is sampled using replica exchange umbrella sampling. Most importantly, we highlight the large extent to which the results of free energy calculations depend on initial system configurations. Based on our results, we provide some guidance to evaluate the accuracy of free energy profiles that will be helpful to elucidate the mechanism of membrane permeation.