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In quantitative pharmacology, multi-parameter receptor models are needed to account for the complex nonlinear relationship between fractional occupancy and response that can occur due to the intermixing of the effects of partial receptor activation and post-receptor signal amplification. Here, a general two-state receptor model and corresponding quantitative forms are proposed that unify three distinct processes, each characterized with its own parameter: 1) receptor binding, characterized by  K   d , the equilibrium dissociation constant used for binding affinity; 2) receptor activation, characterized by an (intrinsic) efficacy parameter  ε ; and 3) post-activation signal transduction (amplification), characterized by a gain parameter  γ . Constitutive activity is accommodated via an additional  ε   R0  parameter quantifying the activation of the ligand-free receptor. Receptors can be active or inactive in both their ligand-free and ligand-bound states (two-state receptor theory), but ligand binding alters the likelihood of activation (induced fit). Because structural data now confirm that for most receptors in their active conformation, the small-molecule ligand-binding site is buried inside, straightforward binding to the active form (direct conformational selection) is unlikely. The proposed general equation has parameters that are more intuitive and better suited for optimization by nonlinear regression than those of the operational (Black and Leff) or del Castillo–Katz model. The model provides a unified framework for fitting complex data including a) fractional responses that do not match independently measured fractional occupancies, b) responses measured after partial irreversible inactivation of the “receptor reserve” (Furchgott method), c) fractional responses that are different along distinct downstream pathways (biased agonism), and d) responses with constitutive receptor activity. Furthermore, unlike previous models, the present one can be reduced back for special cases of its parameters to consecutively nested simplified forms that can be used on their own when adequate (e.g.,  ε   R0  = 0, no constitutive activity;  γ  = 1:  E   max  model for partial agonism;  ε  = 1: Clark equation).

A Receptor Model With Binding Affinity, Activation Efficacy, and Signal Amplification Parameters for Complex Fractional Response Versus Occupancy Data