Jumping frequencies in membrane channels. Comparison between stochastic molecular dynamics simulation and rate theory

Permeation of molecules through membrane channels involves local interactions with a limited number of ligand groups. A method for the molecular dynamics simulation of particle movement in small ligand systems is described. It is assumed that the ligand groups carry out thermal vibrations, whereas the rest of the channel molecule and the surroundings act as a heat bath which is coupled via random forces to the motions of the ligands. The simulation technique is applied to a simple system which contains some of the essential features influencing jumping rates in membrane channels, such as flexibility of ligand configuration or inertial effects in the motion of the ligands. Since the simulation is based on strictly microscopic parameters of the particle-ligand system, a rigorous test of the predictions of rate theory is possible. It is found that rate theory describes the general dependence of jumping frequency k' on temperature and on ligand binding strength rather well, although the values of k' obtained by computer simulation are 2-3 times smaller than those predicted by rate theory.