Figure 4.

(A) The operational model of allosterism. Four receptor species, one free (R), two singly bound (AR and RB) and one doubly bound (ARB). Because of the thermodynamic cycle, there are four equilibrium constants but only three independent parameters, K, M and α. K and M measure the affinities of the agonist and the modulator for the free receptor, respectively, and α, the binding co-operativity between A and B. Stimulus is defined including only the occupied receptors (S = ε_A[AR] + ε_B[RB] + ε_AB[ARB]). A rectangular hyperbolic function f = E/E_m transduces stimulus into response, with K_E defined as in Figure 2B. (B) The operational model of allosterism including constitutive receptor activity. Constitutive receptor activity is incorporated in the model by including the concentration of free receptors within the definition of stimulus (S = [R] + ε_A[AR] + ε_B[RB] + ε_AB[ARB]). A rectangular hyperbolic function f = E/E_m transduces stimulus into response, with K_E defined as in Figure 2B. (C,D) Simulation with the operational model of allosterism, including constitutive receptor activity (Equation 8). Fixed parameters: receptor system, χ = 0.5; partial agonist A, K = 10⁻⁶, ε_A = 5; AM B, M = 10⁻⁶, ε_B = 1; agonist-modulator co-operativity parameters, α = 10, δ = 5. (C) Agonist concentration-effect curves in the absence and presence of increasing concentrations of AM B. (D) Modulator concentration-effect curves in the absence and presence of increasing concentrations of the agonist A, with the same pharmacological parameters for the system and the ligands as in Figure 4C.