Figure 8.

A simple single-site Eyring barrier model can be used to demonstrate voltage-dependent changes in P _K/P _Na ratio. Parameters of the model used here can be described in relation to a simple kinetic scheme (A) in which N₀, N₁, and N₂ represent the external, intramembrane, and internal energy wells, respectively; where k ₀₁ and k ₁₀ are the forward and backward rate constants between N₀ and N₁, and k ₁₂ and k ₂₁ are the equivalent rate constants between N₁ and N₂. Values for these rate constants are shown given for both Na⁺ and K⁺ ions at 0 mV and the solutions used for the data in Fig. 7 A. Rate constants (s⁻¹): (Na⁺) k ₀₁, 2.77 × 10⁺⁸; k ₁₀, 1.13 × 10⁺⁵; k ₁₂, 2.05 × 10⁺⁸; k ₂₁, 5.01 × 10⁺¹¹; (K⁺) k ₀₁, 1.84 × 10⁺¹¹; k ₁₀, 4.57 × 10⁺⁸; k ₁₂, 6.18 × 10⁺⁷; k ₂₁, 2.49 × 10⁺¹¹. To calculate the rate constants at other potentials, it is necessary to define the placements of the barriers and wells within the transmembrane field. For the model used here, N₀ and N₂ were presumed to be at 0 and 100% of the electrical distance from the external side of the membrane, while N₁ was set at 45% of this distance. Internal and external energy barriers were placed at 10 and 90% of the transmembrane field, respectively. (B) Simulations of changes in internal K⁺ concentrations approximate the data shown in Fig. 7 A, when the same internal and external solutions are used. For this simulation, the patch was presumed to contain 1,500 channels. (C) Predicted single-channel Na⁺ and K⁺ fluxes were generated by this model for the 10-mM internal K⁺ condition, suggesting voltage-dependent changes in relative permeabilities. (D) P _K/P _Na ratios obtained from predicted reversal potentials for this model under different ionic conditions. (○) Simulations with 115 Na_o//115 Na_i and differing internally, (□) variable external [K⁺]. ▵ were obtained from simulations using internal 11.5 mM Na⁺, external 115 mM Na⁺, and variable K⁺. Experimental values obtained in this study are shown as filled symbols (mean ± SD): •, Na⁺ _o//Na⁺ _i + variable K⁺; ▪, Na⁺ _o + 2.5–10 mM K⁺ _o//Na⁺ _i.