An electrochemical gating model is presented to account for the effects described in the companion paper by M. R. Silver, M. S. Shapiro, and T. E. DeCoursey (1994. Journal of General Physiology, 103:519-548) of Rb+ and Rb+/K+ mixtures on the kinetics and voltage dependence of an inwardly rectifying (IR) K+ channel. The model proposes that both Rb+ and K+ act as allosteric modulators of an intrinsically voltage dependent isomerization between open and closed states. Occupancy of binding sites on the outside of the channel promotes channel opening and stabilizes the open state. Rb+ binds to separate sites within the pore and plugs IR channels. Occupancy of the pore by Rb+ can modify the rates of isomerization and the affinity of the allosteric sites for activator ions. The model also incorporates the proposed triple-barreled nature of the IR channel (Matsuda, H., 1988. Journal of Physiology. 397:237-258.) by proposing that plugging of the channel is a cooperative process involving a single site in each of the three bores, 80% of the way through the membrane field. Interaction between bores during plugging and permeation is consistent with correlated flux models of the properties of the IR channel. Parallel bores multiply the number allosteric sites associated with the macromolecular channel and allow for steep voltage dependence without compromising the parallel shift of the half-activation potential with reversal potential. Our model proposes at least six and possibly 12 such allosteric binding sites for activator ions. We derive algebraic relations that permit derivation of parameters that define simple versions of our model from the data of Silver et al. (1994). Numerical simulations based on those parameters closely reproduce that data. The model reproduces the RS+ induced slowing of IR kinetics and the negative shift of the relation between the half-activation voltage (V1/2) and reversal potential when channel plugging is associated with (a) a slowing of the isomerization rates; (b) an increase in the affinity of allosteric sites on closed channels that promote opening; and (c) a decrease in the affinity of sites on open channels that slow closing. Rb+ also slows closing at positive potentials where open channel blockade is unlikely. Allowing Rb+ to be 1.5 times more potent than K+ as an activator in the model can account for this effect and improves the match between the predicted and observed relation between the Rb+ to K+ mole fraction and the opening rate at V1/2.(ABSTRACT TRUNCATED AT 400 WORDS)

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