Figure 5.
Figure 5. Fits of blocker-free gating models to the Hill plot. Experiment R2. The experimental Hill plot is in gray, whereas fitted lines are solid red. Linear asymptotic regions are designated by black (shallow outer segments) or green (steeper intermediate region) dashed lines, accompanied by the model-specific formula that describes them. (A) The COSB model. The value of φ was set to 0.2 as previously established (Liu et al., 2012). Fitted parameters were: ΔqL = 0.16 eo; VL = −41 mV; ΔqK1 = 3.49 eo; VK1 = 1.58 mV; ΔqK2 = 1.28 eo; VK2 = 20.3 mV; b = 0.0074. The COSB model predicts that the blocking transition S→B should be represented by a steep positive asymptote with limiting slope ΔqK2 (dashed green line). However, to more closely fit the data, the positive-voltage asymptote was clipped at the value of kTlnb (lower dashed black line). (B) Allosteric scheme (n = 1). The shallow upper and lower extreme asymptotes are functions of the pore sensor L and the strength of its interaction with J, whereas the steeper intermediate slope (Hill coefficient) is a lower limit for the total gating charge dominated by the J particle. The very small difference in slope between the shallow asymptotes reflects a tiny coupling charge (ΔqD = 0.003 eo). ΔqL = 0.16 eo; VL = −39 mV; ΔqJ = 1.65 eo; VJ = 60 mV; WD = −91 meV (−2.1 kcal/mol). (C) The two-population model. The common slope of the two shallow asymptotes reflects gating in the channel with the smaller gating charge (channel 1). The steeper intermediate slope is the weighted mean of particle potentials from both channels. ΔqL1 = 0.33 eo, VL1 = −205 mV, ΔqL2 = 1.81 eo, VL2 = 4 mV; f1 = 0.50. (D–F) Residuals from least-squares fit. Linear regression lines for the residuals at the outer asymptotic regions are in red. Residuals points were normally distributed around their regression line (P value range: 0.49–0.99, Shapiro–Wilk test). The slopes of the outer residuals in the allosteric model, and in the Neg residual of the COSB model, are statistically equal to zero (P = 0.99, F test). However, nonzero slopes in the residuals are found in the Pos asymptotes of the COSB and two-populations model (P < 0.001) and in the Neg asymptote of the two-populations model (P = 0.02). (G–I) χ2 values used in the fit statistic, with inverse weights 0.148 meV2 (Neg) and 2.12 meV2 (Pos), equal to the variances calculated from residuals in the nondecimated data.

Fits of blocker-free gating models to the Hill plot. Experiment R2. The experimental Hill plot is in gray, whereas fitted lines are solid red. Linear asymptotic regions are designated by black (shallow outer segments) or green (steeper intermediate region) dashed lines, accompanied by the model-specific formula that describes them. (A) The COSB model. The value of φ was set to 0.2 as previously established (Liu et al., 2012). Fitted parameters were: ΔqL = 0.16 eo; VL = −41 mV; ΔqK1 = 3.49 eo; VK1 = 1.58 mV; ΔqK2 = 1.28 eo; VK2 = 20.3 mV; b = 0.0074. The COSB model predicts that the blocking transition S→B should be represented by a steep positive asymptote with limiting slope ΔqK2 (dashed green line). However, to more closely fit the data, the positive-voltage asymptote was clipped at the value of kTlnb (lower dashed black line). (B) Allosteric scheme (n = 1). The shallow upper and lower extreme asymptotes are functions of the pore sensor L and the strength of its interaction with J, whereas the steeper intermediate slope (Hill coefficient) is a lower limit for the total gating charge dominated by the J particle. The very small difference in slope between the shallow asymptotes reflects a tiny coupling charge (ΔqD = 0.003 eo). ΔqL = 0.16 eo; VL = −39 mV; ΔqJ = 1.65 eo; VJ = 60 mV; WD = −91 meV (−2.1 kcal/mol). (C) The two-population model. The common slope of the two shallow asymptotes reflects gating in the channel with the smaller gating charge (channel 1). The steeper intermediate slope is the weighted mean of particle potentials from both channels. ΔqL1 = 0.33 eo, VL1 = −205 mV, ΔqL2 = 1.81 eo, VL2 = 4 mV; f1 = 0.50. (D–F) Residuals from least-squares fit. Linear regression lines for the residuals at the outer asymptotic regions are in red. Residuals points were normally distributed around their regression line (P value range: 0.49–0.99, Shapiro–Wilk test). The slopes of the outer residuals in the allosteric model, and in the Neg residual of the COSB model, are statistically equal to zero (P = 0.99, F test). However, nonzero slopes in the residuals are found in the Pos asymptotes of the COSB and two-populations model (P < 0.001) and in the Neg asymptote of the two-populations model (P = 0.02). (G–I) χ2 values used in the fit statistic, with inverse weights 0.148 meV2 (Neg) and 2.12 meV2 (Pos), equal to the variances calculated from residuals in the nondecimated data.

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