Figure 2.

Schematic illustration of the voltage effects on the thermodynamics (i.e., described by voltage-dependent equilibrium free energy change) and kinetics (i.e., described by voltage-dependent rate constants) of VSMP activation (gating). Two hypothetical (red and blue) free energy profiles are obtained by using the empirical valence bond (EVB) approach^71,84 with Gaussian couplings. (Red) Free energy profile at “zero” (depolarization) membrane potential along a collective reaction coordinate of the charge movements in VSD. (Blue) Voltage-dependent free energy profile (i.e., voltage effects on the free energy profile of zero membrane potential). An application of positive voltage (membrane potential) stabilizes VSMP activation (stabilization of the activated state), whose quantitative relation is given by ΔΔg(V) ≡ Δg(V)−Δg(0) = −Q_gV, as in eq 26. The corresponding stabilization of the transition state is expressed by the linear-free energy relationship, given by ΔΔg^†(V) ≃ zΔΔ(V) = −zQ_gV, as in eq 55, where analytic expression for the fraction of charge (z) is given by $z=\frac{1}{2}\left(1-\frac{\mathrm{\Delta }g(V)}{\mathrm{\Lambda }}\right)=\frac{1}{2}+\frac{C_{L,Eq}}{Q_g}(V-V_{1/2})$, as in eq 56. α(V) and β(V) are, respectively, the corresponding forward and backward voltage dependent rate constants eqs 61 and 62, related to each other via the fundamental free energy relation of first kind of eq 13 or the work-fluctuation theorem of eq 19). ΔG_rx = Δg(0) and ΔG^† = Δg^†(0) represents, respectively, the free energy difference and the free energy barrier at “zero” depolarization membrane potential, given by eqs 25 and 26, and 55, respectively.