FMC versus GIA in voltage-gated ion channels. (A) Principle of the mutant cycle analysis, wherein two sites (X,Y) are mutated individually or jointly. By measuring the free energies of perturbation along each path, the interaction energy between the two sites can be assessed as ΔΔG_nonadd = ΔG_p4 − ΔG_p1 = ΔG_p2 − ΔG_p3. (B) The relative open probability versus voltage curve showing the half-maximal voltage of activation, V_1/2. The red dashed line is the tangent to the sigmoid curve at V_1/2, and the slope of this tangent is linearly related to the Boltzmann slope (z_app). In FMC, the free energy of perturbation along each path of the thermodynamic cycle in A is computed as Δ(z_appV_1/2)F. (C) The Q-V curve with the median voltage for activation, V_M, is depicted by the red vertical line. By definition, the two dashed areas on either side of the median voltage axis are equal. In GIA, the free energy of perturbation along each path of the thermodynamic cycle in A is computed as Δ(Q_maxV_M)F.