Permeation and gating in proteins: kinetic Monte Carlo reaction path following

We present a new Monte Carlo technique, kinetic Monte Carlo reaction path following (kMCRPF), for the computer simulation of permeation and large-scale gating transitions in protein channels. It combines ideas from Metropolis Monte Carlo (MMC) and kinetic Monte Carlo (kMC) algorithms, and is particularly suitable when a reaction coordinate is well defined. Evolution of transition proceeds on the reaction coordinate by small jumps (kMC technique) toward the nearest lowest-energy uphill or downhill states, with the jumps thermally activated (constrained MMC). This approach permits navigation among potential minima on an energy surface, finding the minimum-energy paths and determining their associated free-energy profiles. The methodological and algorithmic strategies underlying the kMCRPF method are described. We have tested it using an analytical model and applied it to study permeation through the curvilinear ClC chloride and aquaporin pores and to gating in the gramicidin A channel. These studies of permeation and gating in real proteins provide extensive procedural tests of the method.