(A) The allosteric two-state model of receptor activation (adapted from Hall, 2000). Eight receptor species, two free (R, inactive and R*, active), four singly ligand-bound (AR and BR, inactive and AR* and BR*, active) and two doubly bound (ARB, inactive and AR*B, active), with A and B being the agonist and the modulator, respectively. Because of the thermodynamic cycles, there are 12 equilibrium constants but only seven independent parameters, L, K, M, γ, α, β and δ. L measures the propensity of the free receptor to form active states; K and M the affinities of A and B for the inactive free receptor, respectively; α and β, the intrinsic efficacies of A and B, respectively; γ, the binding co-operativity between A and B; and δ, the activation co-operativity between A and B. The functional response, f, is defined as the fraction of active receptors, [R]Active/[R]T. (B) Simulation with the allosteric two-state model of receptor activation (Equation 5). A basal response, which depends on L-value, is inherent to the model and ligands A and B are agonists, neutral antagonists or inverse agonists if they increase, not change or decrease the basal response (α or β greater, equal or lower than 1, respectively). Agonist concentration-effect curves in the absence and presence of an AM, B, with intrinsic negative efficacy. All the parameters are fixed except the activation co-operativity parameter δ, which varies among the curves. Fixed parameters: [B] = 10−4 except for the black curve for which [B] = 0, K = 10−6, M = 10−6, L = 0.5, α = 10, β = 10−1, γ = 1. Variable parameter: δ = 1, δ = 102, δ = 10−1, δ = 10−3.