Generalized Langevin models of molecular dynamics simulations with applications to ion channels

We present a new methodology, which combines molecular dynamics and stochastic dynamics, for modeling the permeation of ions across biological ion channels. Using molecular dynamics, a free energy profile is determined for the ion(s) in the channel, and the distribution of random and frictional forces is measured over discrete segments of the ion channel. The parameters thus determined are used in stochastic dynamics simulations based on the nonlinear generalized Langevin equation. We first provide the theoretical basis of this procedure, which we refer to as "distributional molecular dynamics," and detail the methods for estimating the parameters from molecular dynamics to be used in stochastic dynamics. We test the technique by applying it to study the dynamics of ion permeation across the gramicidin pore. Given the known difficulty in modeling the conduction of ions in gramicidin using classical molecular dynamics, there is a degree of uncertainty regarding the validity of the MD-derived potential of mean force (PMF) for gramicidin. Using our techniques and systematically changing the PMF, we are able to reverse engineer a modified PMF which gives a current-voltage curve closely matching experimental results.This work was supported by grants from the National Health and Medical Research Council of Australia. The calculations upon which this work is based were carried out using the SGI Altix cluster of the Australian National University Supercomputer Facility. NAMD was developed by the Theoretical and Computational Biophysics Group in the Beckman Institute for Advanced Science and Technology at the University of Illinois at Urbana-Champaign