Acurately Quantifying Correlation Times that Exceed the Timescale of Molecular Dynamics Simulations

Abstract

The biological and pharmaceutical importance of selective permeability across lipid membranes has motivated many attempts to characterize the molecular details underlying these processes using molecular dynamics (MD) simulations. However, it is generally difficult to prove that MD simulations have converged. This is because it is always possible that there exists a set of low-energy conformations that the simulations failed to visit. In this work, we circumvent this limitation for umbrella sampling (US) MD simulations by making use of information that is available in the random walks that are conducted by Hamiltonian-exchange simulations. Specifically, we introduce a new metric, the transmission factor, computed from 1-microsecond-long random walks of a side-chain analog and an antimicrobial peptide along the normal to a lipid bilayer. We show that the transmission factor detects free-energy barriers in degrees of freedom orthogonal to the US order parameter (hidden barriers). By quantifying the impact of hidden barriers on the random walks, we are able to identify solute insertion depths that are prone to systematic sampling errors. Furthermore, we use the transmission factor to quantitatively estimate the amount of additional simulation time required to attain convergence. We then conduct ten 5-microsecond simulations and show that the quantitative estimates of conformational correlation times computed via the transmission factor are accurate, even when the required time greatly exceeds the simulation timescale - something that, to our knowledge, has never before been achieved. Importantly, the approach of conducting Hamiltonian-exchange US simulations and then computing the transmission factor to estimate the amount of additional simulation time required to attain convergence is general and can be applied to other systems with different order parameters.