title: Discrete-state representation of ion permeation coupled to fast gating in a model of CLC-chloride channels: analytic estimation of the state-to-state rate constants.
abstract: 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. The underlying dynamical theory is an appropriate single- or multiparticle three-dimensional Smoluchowski equation. Taking 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%.
authors.affiliation: Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA. coalson@pitt.edu
authors.forename: Rob D
authors.initials: RD
authors.lastname: Coalson
authors.forename: Mary Hongying
authors.initials: MH
authors.lastname: Cheng
mesh_terms: D001665:Binding Sites; D018118:Chloride Channels / Q000737:chemistry / Q000378:metabolism; D002712:Chlorides / Q000378:metabolism*; D015640:Ion Channel Gating; D017136:Ion Transport; D007700:Kinetics; D008564:Membrane Potentials; D008956:Models, Chemical; D056004:Molecular Dynamics Simulation; D012044:Regression Analysis
chemical_list: D018118:Chloride Channels; D002712:Chlorides