Adaptive Brownian dynamics simulation for estimating potential mean force in ion channel permeation

Ion channels are biological nanotubes formed by large protein molecules in the cell membrane. This paper presents a novel multiparticle simulation methodology, which we call adaptive controlled Brownian dynamics, for estimating the force experienced by a permeating ion at each discrete position along the ion-conducting pathway. The profile of this force, commonly known as the potential of mean force, results from the electrostatic interactions between the ions in the conduit and all the charges carried by atoms forming the channel the protein, as well as the induced charges on the protein wall. The current across the channel is solely determined by the potential of mean force encountered by the permeant ions. The simulation algorithm yields consistent estimates of this profile. The algorithm operates on an angstrom unit spatial scale and femtosecond time scale. Numerical simulations on the gramicidin ion channel show that the algorithm yields the potential of mean force profile that accurately reproduces experimental observations.