Free Energy Calculations of Membrane Permeation: Challenges due to Strong Headgroup-Solute Interactions

TL;DR

This study compares free energy calculation methods for membrane permeation, highlighting challenges with charged molecules due to slow electrostatic relaxation, and offers guidance for accurate simulation practices.

Contribution

It systematically evaluates different biased MD techniques for membrane permeation, revealing the impact of electrostatic relaxation times on free energy profiles.

Findings

All methods agree for neutral permeants

Charged molecules show discrepancies across methods

Replica exchange improves transition state sampling

Abstract

Understanding how different classes of molecules move across biological membranes is a prerequisite to predicting a solute's permeation rate, which is a critical factor in the fields of drug design and pharmacology. We use biased Molecular Dynamics computer simulations to calculate and compare the free energy profiles of translocation of several small molecules across 1,2-dioleoyl-sn-glycero-3-phosphocholine (DOPC) lipid bilayers as a first step towards determining the most efficient method for free energy calculations. We study the translocation of arginine, a sodium ion, alanine, and a single water molecule using the Metadynamics, Umbrella Sampling, and Replica Exchange Umbrella Sampling techniques. Within the fixed lengths of our simulations, we find that all methods produce similar results for charge-neutral permeants, but not for polar or positively charged molecules. We identify the long relaxation timescale of electrostatic interactions between lipid headgroups and the solute to be the principal cause of this difference, and show that this slow process can lead to an erroneous dependence of computed free energy profiles on the initial system configuration. We demonstrate the use of committor analysis to validate the proper sampling of the presumed transition state, which in our simulations is achieved only in replica exchange calculations. Based on these results we provide some useful guidance to perform and evaluate free energy calculations of membrane permeation.