Estimation of ligand affinity constants for receptor states in functional studies involving the allosteric modulation of G protein-coupled receptors: Implications for ligand bias

Abstract

Introduction The affinity constants of a ligand for active and inactive states of a receptor ultimately determine its capacity to activate downstream signaling events. In this report, we describe a reverse-engineering strategy for estimating these microscopic constants. Methods Our approach involves analyzing responses measured downstream in the signaling pathway of a G protein-coupled receptor under conditions of allosteric modulation and reduced receptor expression or partial receptor inactivation. The analysis also yields estimates of the isomerization constant of the unoccupied receptor, the sensitivity constant of the signaling pathway, and the more empirical parameters of the receptor population including the observed affinities and efficacies of allosteric and orthosteric ligands – including inverse agonists – and the efficacy of the unoccupied receptor (i.e., constitutive activity). Results and Discussion We validate our approach with an analytical proof and by analysis of simulated data. We also use our method to analyze data from the literature. We show that the values of the microscopic constants of orthosteric and allosteric ligands are constant regardless of the allosteric interaction and the nature of the receptor-signaling pathway as long as the same active state mediates the response. Our analysis is useful for quantifying probe-dependent allosteric interactions and the selectivity of agonists for different signaling pathways. Knowing the isomerization constant and sensitivity constant of a signaling pathway in a given cell line or tissue preparation enables future investigators to estimate the affinity constants of agonists for receptor states simply through analysis of their concentration-response curves. Our approach also provides a means of validating in silico estimates of ligand affinity for crystal structures of active and inactive states of the receptor.

Estimation of the receptor-state affinity constants of ligands in functional studies using wild type and constitutively active mutant receptors: Implications for estimation of agonist bias

“…We have also shown that the function describing agonist-induced formation of this complex is consistent with a Monod-Wyman-Changeux model (Ehlert & Griffin, 2014). Hence, we used the following simplified form of the Monod-Wyman-Changeux model (one orthosteric binding site and no allosteric site; (Monod et al, 1965)) to simulate agonist-receptor activation: $$T_f=\frac{1}{1+\frac{{\mathit{\text{DK}}}_{\mathit{\text{inact}}}+1}{K_{q-\text{italicobs}}false({\mathit{\text{DK}}}_{\mathit{\text{act}}}+1false)}}$$…”

“…We have previously shown that, with regard to G protein signaling, agonist-induced receptor activation is proportional to the formation of a quaternary complex consisting of the active state of the agonist-receptor complex ( DR* ) associated with exchange state of the G protein ( G* ) bound with GDP ( DR*G*GDP ) (Ehlert, 2008; Ehlert & Griffin, 2014; Stein & Ehlert, 2015). We have also shown that the function describing agonist-induced formation of this complex is consistent with a Monod-Wyman-Changeux model (Ehlert & Griffin, 2014).…”

“…We recently described a protocol for estimating K act and K inact that relied on an allosteric agonist to push the equilibrium in the direction of the active state (Ehlert & Griffin, 2014). The approach involves measuring agonist responses under conditions of allosteric agonism and in the presence of partial receptor inactivation or reduced receptor expression.…”

Cooperativity Has Empirical and Ultimate Levels of Explanation

“…This is the ultimate mechanism of cooperativity in the two-state model. How the fundamental state parameters give rise to the more superficial population parameters is described in Table 1 [5,6]. These equations differ from those given by Zhang and Kavana [1].…”

Practical guide for calculating and representing biased signaling by GPCR ligands: A stepwise approach

“…What is common to these two types of influences and distinguishes them from proper ligand-bias is that the signaling imbalance they create influences all ligands in the same way. Methods that quantify the ligand-dependent component of a biased response 'dissect away' system and assay confounding influences [8][9][10][11]. One way of doing so is by normalizing, to a common standard, the response produced by each ligand in different pathways of interest.…”