Analysis of functional responses at G protein-coupled receptors: estimation of relative affinity constants for the inactive receptor state.

We describe a modification of receptor theory that enables the estimation of relative affinity constants for the inactive state of a G protein-coupled receptor. Our approach includes the traditional parameters of observed affinity (K(obs)) and efficacy (fraction of ligand-receptor complex in the active state, ε) and introduces the concept of the fraction of the ligand-receptor complex in the inactive state (intrinsic inactivity, ε(i)). The relationship between receptor activation and the ligand concentration is known as the stimulus, and the operational model expresses the response as a logistic function of the stimulus. The latter function includes K(obs) and the parameter τ, which is proportional to ε. We introduce the parameter τ(i), which is proportional to ε(i). We have previously shown that the product, K(obs)τ, of one agonist, expressed relative to that of another (intrinsic relative activity, RA(i)), is a relative measure of the affinity constant for the active state of the receptor. In this report, we show that the product, K(obs)τ(i), of one agonist, expressed relative to that of another (intrinsic relative inactivity, RI(i)), is a relative measure of the affinity constant for the inactive state of the receptor. We use computer simulation techniques to verify our analysis and apply our method to the analysis of published data on agonist activity at the M(3) muscarinic receptor. Our method should have widespread application in the analysis of agonist bias in drug discovery programs and in the estimation of a more fundamental relative measure of efficacy (RA(i)/RI(i)).