Analysis of agonism and inverse agonism in functional assays with constitutive activity: estimation of orthosteric ligand affinity constants for active and inactive receptor states.

We describe a modification of receptor theory for the estimation of observed affinities (K(obs)) and relative efficacies of orthosteric ligands in functional assays that exhibit constitutive activity. Our theory includes parameters for the fractions of the occupied receptor population in the active (intrinsic efficacy, ε) and inactive (ε(i)) states and analogous parameters for the fractions of the free receptor population in the active (ε(sys)) and inactive (ε(i-sys)) states. The total stimulus represents the summation of the active states of the free and occupied receptor populations. A modified operational model is developed that expresses the response as a logistic function of the total stimulus. This function includes the standard parameters related to affinity and efficacy (K(obs) and τ) as well as a parameter proportional to the activity of the free receptor complex, τ(sys). Two related parameters are proportional to the fraction of the free (τ(i-sys)) and occupied (τ(i)) receptor populations in the inactive state. We show that the estimates of the affinity constants of orthosteric ligands for the active (K(b)) and inactive (K(a)) states of the receptor are equivalent to τK(obs)/τ(sys) and τ(i)K(obs)/τ(i-sys), respectively. We verify our method with computer simulation techniques and apply it to the analysis of M(2) and M(3) muscarinic receptors. Our method is applicable in the analysis of ligand bias in drug discovery programs.