For a pore with two distinct ion binding sites, in the presence of both Cl

^{−} and gluconate, there exist nine distinct equilibrium states and 28 transition rates (see

scheme ), where Cl represents a site occupied by a Cl

^{−} ion, G represents a site occupied by a gluconate ion, and 0 represents a vacant site. With three binding sites, this increases to 27 distinct equilibrium states and 92 rate constants. The complexity of such models necessitates simplifying assumptions, such as fixing the locations of ion binding sites. Although Eyring Transition State Theory () does not apply to condensed phases, it can be useful when thinking about ion permeation and is practical for fitting data because it reduces hundreds of free parameters to a manageable kinetic scheme. In the present study, we modeled a range of experimental data using the AJUSTE program described by . This program uses energy barriers rather than kinetic constants as fitting parameters so that microscopic reversibility would not have to be imposed as a constraint. To reduce the dependence on Eyring assumptions, more general rate constants were then calculated for all the allowable transitions between occupancy states in two- and three-site models with the membrane potential set at 0 mV. Rate constants for transitions between any two states

*i* and

*j* in a two- (9 occupancy states) and three- (28 occupancy states) site model were calculated as 4

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