Figure 3.

Energetic linkage between the voltage-dependent and ligand-dependent pathways. (A) An allosteric model of a hypothetical ion channel with a single voltage-sensing and ligand binding domain. The voltage sensor exists in two states (V_R and V_A) and its activation energetics are governed by its intrinsic equilibrium constant, $K_V^0$, and its voltage dependence, z_V. The pore unit has an intrinsic activation constant and intrinsic voltage dependence given by $K_P^0$ and z_P, respectively. The ligand binding domain has an intrinsic binding affinity of $K_B^0$. All the three “structural units” are allosterically coupled to each other via interactions represented by the terms θ_VP, θ_LV, and θ_LP. The model parameters are $K_V^0$ = 0.1, $K_P^0$ = 0.01, $K_B^0$ = 100 M⁻¹, θ_VP = 100, θ_LV = 1, θ_LP = 1,000, z_V = 2.5, and z_P = 1.5. (B) Simulated fractional gating charge displacement (Q_f vs. V) curves for this system at saturating (closed circles) and zero (open circles) ligand concentrations. The red vertical line is the V_M axis for each of the curves and the shaded area is equal to the area of the rectangle bound the two V_M axes. This area, when scaled by Q_max of the system (z_P + z_V), gives the net energetic facilitation of the voltage-dependent pathway by the ligand and is equal to −k_BTln(θ_LVθ_LP). (C) The fractional ligand binding curves (X_f vs. ln x) at very low (open circles) and very high voltages (closed circles) are shown, and the red vertical lines are the corresponding ln x_m axes. The area of the shaded region is equal to area of the rectangle bound the two ln x_m axes, which when scaled by N_max of the system (equal to 1 in this case) and k_BT, gives the net energetic facilitation of the ligand-dependent pathway by voltage and is equal to −k_BTln(θ_LVθ_LP). Note that the two shaded in areas in B and C after appropriate scaling will be equal.