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. Author manuscript; available in PMC: 2017 Jan 28.
Published in final edited form as: J Phys Chem B. 2016 Jan 14;120(3):418–432. doi: 10.1021/acs.jpcb.5b10956

Figure 5.

Figure 5

(A) Voltage dependency of Ci-VSD activation (Q–V curve) obtained directly from the CG voltage dependent energetics. The least-square fit to the voltage dependent open (activated) probability (ref.20) yields a half voltage of 52.2 mV and a gating charge of ~0.85e. This value of half voltage is a good agreement with an observed half voltage of 58 mV26 and is consistent with that obtained from the intersection of two probability densities using the fundamental free energy relation of first kind of eq 13 (i.e., the work-fluctuation theorem of eq 19) (see Figure 3A). A gating charge of ~0.85e is also in a good agreement with an observed value of ~1e and is consistent with those estimated from the equilibrium free energy difference (~1.2e) using eq 29 and several different approaches examined in section V. (B) Nonlinear voltage dependent capacitance (CNL,Neq), associated with structural changes of electrolytes, reflecting the conformational changes of Ci-VSD. The nonlinear voltage dependent capacitance is obtained from the “un-normalized” Q–V curve from part A. The nonlinear voltage dependent capacitance is shifted upward by the linear voltage independent capacitance (CL,Eq) of 0.64 μF, yielding the “total” capacitance of the system, as shown in the figure. The area, formed by a curve of the nonlinear voltage dependent capacitance and a line of the linear voltage independent capacitance of CL,Eq = 0.64 μF, is equal to the gating charge (Qg) of ~0.85e. An equilibrium measurement of the linear component of capacitance (CL,Eq) is related to a nonequilibrium measurement of the nonlinear component of voltage dependent capacitance (CNL,Neq), via the mean value theorem in Calculus eq 39), as dictated by the fluctuation–dissipation theorem for the gating charge (eq 36).