![Figure 4. Application of the n = 4 doubly coupled allosteric scheme (Eq. 20) to the G-V and Q-V curves predicted by the ILT model. Doubly coupled scheme parameters: ΔqL = 1.37 eo; VL = 73.0 mV; VJ = −86.6 mV; WC = −113 meV (2.61 kcal/mol); WD = −49.3 meV (1.14 kcal/mol). The VSD charge ΔqJ was derived from (Δqmax − ΔqL)/4 = 2.91 eo with Δqmax = 13 eo. (A) G-V curves; Po = ∂lnZ/∂lnL evaluated for the wild-type Shaker B channel (ShB, red trace) and ILT mutant (green trace, coupling parameters C and D set to zero). The open circles are Boltzmann fits to experimental G-Vs reported by Ledwell and Aldrich (1999). The five-particle ShB doubly coupled scheme and the reduced ILT scheme are shown next to their respective traces. (B) Q-V curves: 〈q〉 = (∂lnZ/∂lnJ)ΔqJ + (∂lnZ/∂lnL)ΔqL evaluated for ShB and ILT. Open circles are derived from the 2 + 1 Shaker kinetic model (notation from Schoppa and Sigworth, 1998b) with parameters obtained from Ledwell and Aldrich (1999). The shaded rectangle is the difference in global energy of activation, bounded left and right by the VM value for ILT and ShB, respectively. The leftward extension of the rectangle (dashed lines) denotes the apparent VM for the ILT mutant upon neglecting the right-shifted pore contribution to the Q-V curve. The pore charge is difficult to detect within the gating current because the rate of pore opening in ILT is slow (Ledwell and Aldrich, 1999), although independent verification of its existence comes from fluorescence experiments (Pathak et al., 2005). (C) Conductance Hill energy WH[g] = kTln[Po/(1 − Po)] for ShB and ILT predicted by the doubly coupled scheme. Cross-hairs indicate the locations of Po = 0.5, 10−7. The limiting slope = Δqmax of obligatory gating is denoted by the black line. (D) Activation charge displacement 〈qa〉 = kTd(lnPo)/dV for ShB and ILT predicted by the doubly coupled scheme. The dotted line is Δqmax − 〈q〉, which equals 〈qa〉 in the case of the obligatory coupled (strong allosteric) model (Sigg and Bezanilla, 1997).](https://cdn.rupress.org/rup/content_public/journal/jgp/144/1/10.1085_jgp.201311130/4/jgp_201311130_fig4.jpeg?Expires=1773542268&Signature=x1r~nrn2DV-lWhlCMTv9EkTn7TFN9WY-Xe1vDaxAHR3hz6iSLyiqz~vrSTnAdwfC3dfKV2nOePiyekEsTG0M9MTVmfvwT0SDGdqZYlBjHZAMB4iFFdEBeIRdAhldkU0972cHuXlcl3taCjVQ~h0Bj8gk11b66NS3RSXF~eT4w9hcYg1BCrzWRN1xn75MIIKjO2vWe8EKwMYFkWk8BuJmHaIHlge-Q-Izy6UvWaDXfroGiHSwJKkV9ztuXK-5ijlF4fCZ0V1Tsl8XMG6qnXEaXqrNSGMIPUVouw7rtBg8LJmxsLk9FMHBbstLgNaiJoGHdMEk0OwYIeyjH~4mc99aeA__&Key-Pair-Id=APKAIE5G5CRDK6RD3PGA)
Application of the n = 4 doubly coupled allosteric scheme (Eq. 20) to the G-V and Q-V curves predicted by the ILT model. Doubly coupled scheme parameters: ΔqL = 1.37 eo; VL = 73.0 mV; VJ = −86.6 mV; WC = −113 meV (2.61 kcal/mol); WD = −49.3 meV (1.14 kcal/mol). The VSD charge ΔqJ was derived from (Δqmax − ΔqL)/4 = 2.91 eo with Δqmax = 13 eo. (A) G-V curves; Po = ∂lnZ/∂lnL evaluated for the wild-type Shaker B channel (ShB, red trace) and ILT mutant (green trace, coupling parameters C and D set to zero). The open circles are Boltzmann fits to experimental G-Vs reported by Ledwell and Aldrich (1999). The five-particle ShB doubly coupled scheme and the reduced ILT scheme are shown next to their respective traces. (B) Q-V curves: 〈q〉 = (∂lnZ/∂lnJ)ΔqJ + (∂lnZ/∂lnL)ΔqL evaluated for ShB and ILT. Open circles are derived from the 2 + 1 Shaker kinetic model (notation from Schoppa and Sigworth, 1998b) with parameters obtained from Ledwell and Aldrich (1999). The shaded rectangle is the difference in global energy of activation, bounded left and right by the VM value for ILT and ShB, respectively. The leftward extension of the rectangle (dashed lines) denotes the apparent VM for the ILT mutant upon neglecting the right-shifted pore contribution to the Q-V curve. The pore charge is difficult to detect within the gating current because the rate of pore opening in ILT is slow (Ledwell and Aldrich, 1999), although independent verification of its existence comes from fluorescence experiments (Pathak et al., 2005). (C) Conductance Hill energy WH[g] = kTln[Po/(1 − Po)] for ShB and ILT predicted by the doubly coupled scheme. Cross-hairs indicate the locations of Po = 0.5, 10−7. The limiting slope = Δqmax of obligatory gating is denoted by the black line. (D) Activation charge displacement 〈qa〉 = kTd(lnPo)/dV for ShB and ILT predicted by the doubly coupled scheme. The dotted line is Δqmax − 〈q〉, which equals 〈qa〉 in the case of the obligatory coupled (strong allosteric) model (Sigg and Bezanilla, 1997).
