Estimation of Relative Microscopic Affinity Constants of Agonists for the Active State of the Receptor in Functional Studies on M₂ and M₃ Muscarinic Receptors

Abstract

In prior work, we have shown that it is possible to estimate the product of observed affinity and intrinsic efficacy of an agonist expressed relative to that of a standard agonist simply through the analysis of their respective concentration-response curves. In this report, we show analytically and through mathematical modeling that this product, termed intrinsic relative activity (RA i ), is equivalent to the ratio of microscopic affinity constants of the agonists for the active state of the receptor. We also compared the RA i estimates of selected muscarinic agonists with a relative estimate of the product of observed affinity and intrinsic efficacy determined independently through the method of partial receptor inactivation. There was good agreement between these two estimates when agonist-mediated inhibition of forskolin-stimulated cAMP accumulation was measured in Chinese hamster ovary cells stably expressing the human M 2 muscarinic receptor. Likewise, there was good agreement between the two estimates when agonist activity was measured on the ileum from M 2 muscarinic receptor knockout mice, a convenient assay for M 3 receptor activity. The RA i estimates of agonists in the mouse ileum were similar to those estimated at the human M 3 receptor with the exception of 4-(m-chlorophenyl-carbamoyloxy)-2-butynyltrimethylammonium (McN-A-343), which is known to be an M 1 -and M 4 -selective muscarinic agonist. Additional experiments showed that the response to McN-A-343 in the mouse ileum included a non-M 3 muscarinic receptor component. Our results show that the RA i estimate is a useful receptor-dependent measure of agonist activity and ligand-directed signaling.Drug discovery often involves testing compounds in highthroughput screens to determine their activity at specific receptors. The process not only identifies useful drugs but also helps to explain how variation in the structure of a compound alters its pharmacological activity. With regard to agonists at G protein-coupled receptors (GPCRs), the most common measurements of functional activity are the maximal response (E max ) and the concentration of agonist required for half-maximal response (EC 50 ). These parameters can vary for the same agonist, however, depending on the coupling protein through which the receptor signals (e.g., G protein) and the nature of the response being measured. What is needed is a measure of agonist activity that is dependent solely on the agonist-receptor interaction and not on downstream elements in the signaling cascade.

The Effective Application of Biased Signaling to New Drug Discovery

“…Such a scale can be derived from the Black/Leff operational model of agonism (Black and Leff, 1983), which furnishes estimates of affinity in the form of K A values (equilibrium dissociation constants of agonist-receptor complexes) and agonist efficacy (in the form of t values for a given signaling pathway). A null method to derive such a factor (termed RA i denoted as receptor activity) has been published (Ehlert et al, 1999) and subsequently applied to agonist bias (Griffin et al, 2007;Figueroa et al, 2009;Tran et al, 2009;Ehlert et al, 2011).…”

Quantifying Agonist Activity at G Protein-Coupled Receptors

“…In our case, transfection of the M3 receptor in HEK 293 cells caused an increase in phosphoinositide hydrolysis that ranged from about 500 -1,000 cpm of If there are different active states of the receptor that signal through different coupling proteins (e.g., G proteins), then our method of analysis provides an accurate estimation of agonist Kb and RAi values for each effector pathway 3,6 . If more than one active state contributes to a single measured response, then our method of estimation of RAi and Kb represents a weighted average of different active states depending upon their relative abundance and activity 3 .…”

“…The analysis yields an estimate of the product of Kobs and a parameter proportional to efficacy (τ). The estimate of τKobs of one agonist, divided by that of another, is a relative measure of Kb (RAi) 6 . For any receptor exhibiting constitutive activity, it is possible to estimate a parameter proportional to the efficacy of the free receptor complex (τsys).…”

A Novel Method for Analyzing Extremely Biased Agonism at G Protein–Coupled Receptors

“…This ability provides a useful means of comparing agonist activity without the need to directly access the affinity of the agonist or the degree of receptor reserve present in a system. Specifically, it provides a relative measure of the active state affinity constant of the agonist for the particular signaling pathway under investigation (Tran et al, 2009).…”

“…At a given level, drug action is defined by unique pharmacologic parameters, which can be expressed mathematically in terms of the next deeper level parameters (Tran et al, 2009). For example, the EC 50 and E max values of agonists (level 1 parameters) can each be expressed in terms of observed affinity and intrinsic efficacy (level 2 parameters).…”