Ion permeation through the gramicidin channel: Atomically detailed modeling by the stochastic difference equation

Abstract

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.

Membrane Permeation of a Peptide: It Is Better to be Positive

“…Weaker binding of anions compared to cations has been observed before in constrained simulations. An example is binding to the surface of the membrane by sodium and chloride ions 37 or the permeation of these ions through the membrane. 38–40 Recent experiments and simulations suggest a similar membrane binding for both atomic ions.…”

Structure prediction of small transmembrane helix bundles

“…Molecular dynamic studies with and without membrane have furthermore explored the different structural possibilities as well as ion permeation capabilities of pore forming peptides like alamethicin or gramicidin [39][40][41][42][43].…”

Calculation of the dielectric permittivity profile for a nonuniform system: Application to a lipid bilayer simulation

“…In simulations of a complex system such as a protein in aqueous solution, 1 a membrane channel, [30][31][32] peptide, 18,33 or small-molecule permeants 11,34 -39 embedded in a lipid bilayer, the behavior of neither the solvent nor the bilayer itself is of primary interest, while the explicit representation of water or lipid molecules greatly increases the computational expense of a simulation. Accordingly there has been much interest in implicit models for the aqueous solvent or bilayer.…”