Ion permeation through the gramicidin channel: atomically detailed modeling by the Stochastic Difference Equation

Atomically detailed descriptions of ionic solution, membrane, and the gramicidin channel are used to compute molecular dynamics trajectories of ion permeation. The microsecond trajectories are calculated with the Stochastic Difference Equation (SDE), which provides approximate solutions to the equations of motions (with filtered high-frequency modes) of extended timescales. The relative permeations of lithium, sodium, and potassium are estimated by using a novel, kinetic cycle protocol and are compared with experiment. The transport through native gramicidin and one fluoro-valine variant is considered as well. Qualitative agreement between theory and experiment is obtained. The faster permeation rate of sodium compared to lithium is reproduced in the calculations. The calculations also reproduce the slower diffusion through a gramicidin with fluorinated valine compared to native gramicidin. The calculations are inconclusive about the relative rates of potassium and sodium. The experiment suggests that potassium permeates more quickly. We directly probe the kinetics of a biophysical process at a relevant time window without reducing the atomically detailed description of the system. The calculations were able to capture subtle balances between binding and diffusion that determine permeation rates. The same model gave the correct ordering of diffusion rates for cases in which electrostatic binding has opposite effects and must be supplemented by dynamic factors. Diffusion rates are faster when favorable electrostatic interactions of ions in the channel (compared to the solvent) are observed. Studies of a gramicidin variant suggest an opposite effect, in which permeation is faster for the less polar channel, indicating dynamic effects. Although both trends can be explained qualitatively, it is not possible to predict (before doing the SDE calculations) which factor is more important.