Biomolecular Simulations under Realistic Macroscopic Salt Conditions

Biomolecular simulations are typically performed in an aqueous environment where the number of ions remains fixed for the duration of the simulation, generally with either a minimally neutralizing ion environment or a number of salt pairs intended to match the macroscopic salt concentration. In contrast, real biomolecules experience local ion environments where the salt concentration is dynamic and may differ from bulk. The degree of salt concentration variability and average deviation from the macroscopic concentration remains, as yet, unknown. Here, we describe the theory and implementation of a Monte Carlo osmostat that can be added to explicit solvent molecular dynamics or Monte Carlo simulations to sample from a semigrand canonical ensemble in which the number of salt pairs fluctuates dynamically during the simulation. The osmostat reproduce the correct equilibrium statistics for a simulation volume that can exchange ions with a large reservoir at a defined macroscopic salt concentration. To achieve useful Monte Carlo acceptance rates, the method makes use of nonequilibrium candidate Monte Carlo (NCMC) moves in which monovalent ions and water molecules are alchemically transmuted using short nonequilibrium trajectories, with a modified Metropolis-Hastings criterion ensuring correct equilibrium statistics for an (Δµ, N, p, T) ensemble. We demonstrate how typical protein (DHFR and the tyrosine kinase Src) and nucleic acid (Drew-Dickerson B-DNA dodecamer) systems exhibit salt concentration distributions that significantly differ from fixed-salt bulk simulations and display fluctuations that are on the same order of magnitude as the average.