Quantitative Assessment of Methods Used To Obtain Rate Constants from Molecular Dynamics Simulations-Translocation of Cholesterol across Lipid Bilayers

Accurately calculating rate constants of macroscopic chemical processes from molecular dynamics simulations is a long-sought but elusive goal. The problem is particularly relevant for processes occurring in biological systems, as is the case for ligand-protein and ligand-membrane interactions. Several formalisms to determine rate constants from easily accessible free-energy profiles [Δ Go( z)] of a molecule along a coordinate of interest have been proposed. However, their applicability for molecular interactions in condensed media has not been critically evaluated or validated. This work presents such evaluation and validation and introduces improved methodology. As a case study, we have characterized quantitatively the rate of translocation of cholesterol across 1-palmitoyl-2-oleoyl- sn-glycero-3-phosphocholine bilayers. Translocation across lipid bilayers is the rate-limiting step in the permeation of most drugs through biomembranes. We use coarse-grained molecular dynamics simulations and different kinetic formalisms to calculate this rate constant. A self-consistent test of the applicability of various available formalisms is provided by comparing their predictions with the translocation rates obtained from actual events observed in long unrestrained simulations. To this effect, a novel procedure was used to obtain the effective rate constant, based on an analysis of time intervals between transitions among different states along the reaction coordinate. While most tested formalisms lead to results in reasonable agreement (within a factor of 5) with this effective rate constant, the most adequate one is based on the explicit relaxation frequencies from the transition state in the forward and backward directions along the reaction coordinate.