Median ligand activity of an arbitrary three-step ligand binding process. (A) A three-step sequential ligand binding process (N_max = 3) where B_i represents the state of the protein with “i” ligands bound (i = 0, 1, 2, and 3) and K_j is the equilibrium constant for the j^th step of the process (j = 1, 2, or 3). In each step, a single molecule of the ligand binds to the protein, B. (B) The ligand binding curve for Scheme I generated using arbitrary values of K_j (K₁ = 0.01 M⁻¹, K₂ = 0.1 M⁻¹, K₃ = 10 M⁻¹). Demarcated by horizontal broken lines is the area between the binding curve and the ln x = 0 axis (solid black vertical line), which represents the integral $∫0NmaxlnxdX−$⁠. By virtue of the integration, the area on the right of the ln x = 0 axis is negative and that on its right is positive. The sum of these areas (taking their signs into consideration) is a measure of total free energy associated with saturating the protein with the ligands (⁠$ΔG−C/RT$⁠, where $ΔG−C=−RT ln(K1 K2 K3)$⁠). The vertical red dashed line is the median ligand activity axis. By its definition, the two shaded regions on either side of the ln x_m axis are equal in area. Eq. 11 implies that the region demarcated by the horizontal dashed lines and the rectangle defined by the ln x = 0, ln x_m, $X−$ = 0, and $X−$ = N_max lines are equal in area and that both give a measure of $ΔG−C$⁠.