Analytical estimation of state-to-state rate constants is carried out for a recently developed discrete state model of chloride ion motion in a CLC chloride channel (Coalson and Cheng, J. Phys. Chem. B 2010, 114, 1424). In the original presentation of this model, the same rate constants were evaluated via three-dimensional Brownian dynamics simulations. multiparticle three-dimensional Smoluchowski equation. Taking The underlying dynamical theory is an appropriate single- or advantage of approximate geometric symmetries (based on the details of the model channel geometry), well-known formulas for state-to-state transition rates are appealed to herein and adapted as necessary to the problem at hand. Rates of ionic influx from a bulk electrolyte reservoir to the nearest binding site within the channel pore are particularly challenging to compute analytically because they reflect multi ion interactions (as opposed to single ion dynamics). A simple empirical correction factor is added to the single ion rate constant formula in this case to account for the saturation of influx rate constants with increasing bulk Cl- concentration. Overall, the agreement between all analytically estimated rate constants is within a factor of 2 of those computed via three-dimensional Brownian dynamics simulations, and often better than this Current-concentration curves obtained using rate constants derived from these two different computational approaches agree to within 25%.
