Accelerating the Rate of Convergence of Umbrella Sampling Simulations in Lipid Bilayers

Abstract

All molecular dynamics simulations are susceptible to sampling errors, which degrade the accuracy and precision of observed values. Systems containing atomistic lipid bilayers are particularly susceptible to sampling errors because bilayer conformational autocorrelation times can exceed hundreds of nanoseconds. To identify optimal methods for enhancing sampling efficiency, we quantitatively evaluate convergence rates using generalized ensemble sampling algorithms in calculations of the potential of mean force for the insertion of a side chain analog of arginine in a lipid bilayer. Umbrella sampling (US) is used to restrain solute insertion depth along the bilayer normal, the order parameter commonly used in simulations of molecular solutes in lipid bilayers. The rate of statistical convergence of the standard free energy of binding of the solute to the lipid bilayer is increased three-fold when US simulations are modified to conduct random walks along the bilayer normal using Hamiltonian exchange algorithms. We introduce a new metric, computed from simulations conducting random walks along the bilayer normal, to detect sampling barriers in degrees of freedom orthogonal to the US order parameter, which often result in systematic sampling errors but usually remain hidden. This new metric is used to evaluate the height of hidden free energy barriers in order to identify solute insertion depths which are prone to systematic sampling errors. Accordingly, we demonstrate that applying random walks in temperature at these selected insertion depths leads to further increases in the rate of convergence of the binding free energy. Finally, we apply an enhanced US protocol combining random walks in insertion depth and in temperature to quantify the influence of embedded arginine on lipid flip-flop and on the formation of transient water pores, effects that are likely to contribute to the activity of arginine-rich antimicrobial peptides.