Working hypothesis of Ca²⁺ activation and proton-sensitive gating of MthK. (A) Abbreviated model describing Ca²⁺ activation and proton-sensitive gating of MthK (Scheme II; see Results and Discussion for explanation of the model). (B) Po versus [Ca²⁺] relations predicted by Scheme II with the parameters: K_H = 2.78 × 10⁻⁹ M H⁺; K_C = 7.71 mM Ca²⁺; L = 3.2 × 10⁻⁴; C = 50.6; D = 1.0; E = 0.00930 (Scheme IIA, black dashed lines); and K_H = 4.53 × 10⁻⁹ M H⁺; K_C = 19.1 mM Ca²⁺; L = 3.2 × 10⁻⁴; C = 132; D = 0.0381; E = 1.0 (Scheme IIB, red dashed lines). Symbols correspond to mean Po at each [Ca²⁺] at pH 9.0, 8.5, 8.1, 7.7, 7.3, 6.9, and 6.5 (as described in previous figures). (C) Log(EC₅₀) versus pH relation predicted by Schemes IIA and IIB (black and red dashed lines, respectively), estimated from analysis of the predicted curves using the Hill equation. Experimental data (filled circles) are superimposed. (D) Hill coefficient versus pH as predicted by Schemes IIA and IIB (black and red dashed lines, respectively), also estimated from analysis of the predicted curves using the Hill equation, with experimental data (filled circles) superimposed. The higher Hill coefficients observed in the experimental data imply strong positive cooperativity or additional Ca²⁺-binding sites not included in Scheme II.