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

Quantitative receptor model for responses that are left- or right-shifted versus occupancy (are more or less concentration sensitive): the SABRE approach

Simple one-to three-parameter models routinely used to fit typical dose-response curves and calculate EC50 values using the Hill or Clark equation cannot provide the full picture connecting measured response to receptor occupancy, which can be quite complex due to the interplay between partial agonism and (pathway-dependent) signal amplification. The recently introduced SABRE quantitative receptor model is the first one that explicitly includes a parameter for signal amplification (γ) in addition to those for binding affinity (K d), receptor-activation efficacy (ε), constitutive activity (ε R0), and steepness of response (Hill slope, n). It can provide a unified framework to fit complex cases, where fractional response and occupancy do not match, as well as simple ones, where parameters constrained to specific values can be used (e.g., ε R0 = 0, γ = 1, or n = 1). Here, it is shown for the first time that SABRE can fit not only typical cases where response curves are left-shifted compared to occupancy (κ = K d/EC50 > 1) due to signal amplification (γ > 1), but also less common ones where they are right-shifted (i.e., less concentration-sensitive; κ = K d/EC50 < 1) by modeling them as apparent signal attenuation/loss (γ < 1). Illustrations are provided with μ-opioid receptor (MOPr) data from three different experiments with one left- and one right-shifted response (G protein activation and β-arrestin2 recruitment, respectively; EC50,Gprt < K d < EC50,βArr). For such cases of diverging pathways with differently shifted responses, partial agonists can cause very weak responses in the less concentration-sensitive pathway without having to be biased ligands due to the combination of low ligand efficacy and signal attenuation/loss-an illustration with SABRE-fitted oliceridine data is included.

Therapeutic potential of allosteric modulators for the treatment of gastrointestinal motility disorders

Gastrointestinal motility is tightly regulated by the enteric nervous system (ENS). Disruption of coordinated enteric nervous system activity can result in dysmotility. Pharmacological treatment options for dysmotility include targeting of G protein-coupled receptors (GPCRs) expressed by neurons of the enteric nervous system. Current GPCR-targeting drugs for motility disorders bind to the highly conserved endogenous ligand-binding site and promote indiscriminate activation or inhibition of the target receptor throughout the body. This can be associated with significant side-effect liability and a loss of physiological tone. Allosteric modulators of GPCRs bind to a distinct site from the endogenous ligand, which is typically less conserved across multiple receptor subtypes and can modulate endogenous ligand signalling. Allosteric modulation of GPCRs that are important for enteric nervous system function may provide effective relief from motility disorders while limiting side-effects. This review will focus on how allosteric modulators of GPCRs may influence gastrointestinal motility, using 5-hydroxytryptamine (5-HT), acetylcholine (ACh) and opioid receptors as examples.

C5aR2 receptor: The genomic twin of the flamboyant C5aR1

The complement fragment C5a is one of the most potent proinflammatory glycoproteins liberated by the activation of the biochemical cascade of the complement system. C5a is established to interact with a set of genomically related transmembrane receptors, like C5aR1 (CD88, C5aR) and C5aR2 (GPR77, C5L2) with comparable affinity. The C5aR1 is a classical G-protein-coupled receptor (GPCR), whereas C5aR2 is a nonclassical GPCR that tailors immune cell activity potentially through β-arrestins rather than G-proteins. Currently, the exact function of the C5aR2 is actively debated in the context of C5aR1, even though both C5aR1 and C5aR2 are coexpressed on myriads of tissues. The functional relevance of C5aR2 appears to be context-dependent compared to the C5aR1, which has received enormous attention for its role in both acute and chronic inflammatory diseases. In addition, the structure of C5aR2 and its interaction specificity toward C5a is not structurally elucidated in the literature so far. The current study has attempted to close the gap by generating highly refined model structures of C5aR2, respectively in free (inactive), complexed to C-terminal peptide of C5a (meta-active) and the C5a (active), embedded to a model palmitoyl-2-oleoyl-sn-glycero-3-phosphocholine bilayer. The computational modeling and the 1.5-μs molecular dynamics data presented in the current study are expected to further enrich the understanding of C5a-C5aR2 interaction compared to C5a-C5aR1, which will surely help in elaborating the currently debated biological function of C5aR2 better in the foreseeable future.

Community Guidelines for GPCR Ligand Bias: IUPHAR Review XX

G protein-coupled receptors modulate a plethora of physiological processes and mediate the effects of one-third of FDA-approved drugs. Depending on which ligand activates a receptor, it can engage different intracellular transducers. This 'biased signaling' paradigm requires that we now characterize physiological signaling not just by receptors but by ligand-receptor pairs. Ligands eliciting biased signaling may constitute better drugs with higher efficacy and fewer adverse effects. However, ligand bias is very complex, making reproducibility and description challenging. Here, we provide guidelines and terminology for any scientists to design and report ligand bias experiments. The guidelines will aid consistency and clarity, as the basic receptor research and drug discovery communities continue to advance our understanding and exploitation of ligand bias. Scientific insight, biosensors, and analytical methods are still evolving and should benefit from and contribute to the implementation of the guidelines, together improving translation from in vitro to disease-relevant in vivo models.

Emerging therapeutic opportunities for integrin inhibitors

Integrins are cell adhesion and signalling proteins crucial to a wide range of biological functions. Effective marketed treatments have successfully targeted integrins αIIbβ3, α4β7/α4β1 and αLβ2 for cardiovascular diseases, inflammatory bowel disease/multiple sclerosis and dry eye disease, respectively. Yet, clinical development of others, notably within the RGD-binding subfamily of αv integrins, including αvβ3, have faced significant challenges in the fields of cancer, ophthalmology and osteoporosis. New inhibitors of the related integrins αvβ6 and αvβ1 have recently come to the fore and are being investigated clinically for the treatment of fibrotic diseases, including idiopathic pulmonary fibrosis and nonalcoholic steatohepatitis. The design of integrin drugs may now be at a turning point, with opportunities to learn from previous clinical trials, to explore new modalities and to incorporate new findings in pharmacological and structural biology. This Review intertwines research from biological, clinical and medicinal chemistry disciplines to discuss historical and current RGD-binding integrin drug discovery, with an emphasis on small-molecule inhibitors of the αv integrins.

Integrins are key signalling molecules that are present on the surface of subsets of cells and are therefore good potential therapeutic targets. In this Review, Hatley and colleagues discuss the development of integrin inhibitors, particularly the challenges in developing inhibitors for integrins that contain an αv-subunit, and suggest how these challenges could be addressed.

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

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).

Analysis of Biased Agonism

Agonists and most natural ligands bind to receptors in their inactive state and quickly induce an active receptor conformation that initiates cell signaling. The active receptor state initiates signaling because of its structural complementariness with coupling proteins that activate signaling pathways, such as G proteins and G protein-coupled receptor kinases. Agonist bias refers to the propensity of an agonist to direct receptor signaling through one pathway relative to another. Thus, if the agonist exhibits much higher affinity for active state 1 compared to active state 2, it will cause a robust activation of receptor coupling protein 1 but not 2, and ultimately, a preferential stimulation of signaling pathway 1. Biased agonists are potentially more selective therapeutic agents because there are numerous cases where the therapeutic and adverse effects of an agonist are mediated by distinct pathways involving G proteins and β-arrestin. Given the mechanism for agonist bias, the most straightforward approach for quantifying bias involves the estimation of agonist affinity for the inactive receptor state and the active receptor states involved in signaling through different pathways. The approach provides quantitative estimates of the sensitivities of different signaling pathways, enabling one to determine to what extent the observed selectivity is caused by agonist or system bias. In addition, the approach is a powerful adjunct to in silico docking studies and can be applied to in vivo assays, structure-activity relationships, and the analysis of published agonist concentration-response curves.

A method for the quantification of biased signalling at constitutively active receptors

BACKGROUND AND PURPOSE

Biased agonism, the ability of an agonist to differentially activate one of several signal transduction pathways when acting at a given receptor, is an increasingly recognized phenomenon at many receptors. The Black and Leff operational model lacks a way to describe constitutive receptor activity and hence inverse agonism. Thus, it is impossible to analyse the biased signalling of inverse agonists using this model. In this theoretical work, we develop and illustrate methods for the analysis of biased inverse agonism.

EXPERIMENTAL APPROACH

Methods were derived for quantifying biased signalling in systems that demonstrate constitutive activity using the modified operational model proposed by Slack and Hall. The methods were illustrated using Monte Carlo simulations.

KEY RESULTS

The Monte Carlo simulations demonstrated that, with an appropriate experimental design, the model parameters are 'identifiable'. The method is consistent with methods based on the measurement of intrinsic relative activity (RA_i ) (ΔΔlogR or ΔΔlog(τ/K_a )) proposed by Ehlert and Kenakin and their co-workers but has some advantages. In particular, it allows the quantification of ligand bias independently of 'system bias' removing the requirement to normalize to a standard ligand.

CONCLUSIONS AND IMPLICATIONS

In systems with constitutive activity, the Slack and Hall model provides methods for quantifying the absolute bias of agonists and inverse agonists. This provides an alternative to methods based on RA_i and is complementary to the ΔΔlog(τ/K_a ) method of Kenakin et al. in systems where use of that method is inappropriate due to the presence of constitutive activity.

A three-parameter two-state model of receptor function that incorporates affinity, efficacy, and signal amplification

A generalized model of receptor function is proposed that relies on the essential assumptions of the minimal two-state receptor theory (i.e., ligand binding followed by receptor activation), but uses a different parametrization and allows nonlinear response (transduction) for possible signal amplification. For the most general case, three parameters are used: Kd, the classic equilibrium dissociation constant to characterize binding affinity; ε, an intrinsic efficacy to characterize the ability of the bound ligand to activate the receptor (ranging from 0 for an antagonist to 1 for a full agonist); and γ, a gain (amplification) parameter to characterize the nonlinearity of postactivation signal transduction (ranging from 1 for no amplification to infinity). The obtained equation, E/Emax=εγLεγ+1-εL+Kd, resembles that of the operational (Black and Leff) or minimal two-state (del Castillo-Katz) models, E/Emax=τLτ+1L+Kd, with εγ playing a role somewhat similar to that of the τ efficacy parameter of those models, but has several advantages. Its parameters are more intuitive as they are conceptually clearly related to the different steps of binding, activation, and signal transduction (amplification), and they are also better suited for optimization by nonlinear regression. It allows fitting of complex data where receptor binding and response are measured separately and the fractional occupancy and response are mismatched. Unlike the previous models, it is a true generalized model as simplified forms can be reproduced with special cases of its parameters. Such simplified forms can be used on their own to characterize partial agonism, competing partial and full agonists, or signal amplification.

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 describe a method for estimating the affinities of ligands for active and inactive states of a G protein-coupled receptor (GPCR). Our protocol involves measuring agonist-induced signaling responses of a wild type GPCR and a constitutively active mutant of it under control conditions and after partial receptor inactivation or reduced receptor expression. Our subsequent analysis is based on the assumption that the activating mutation increases receptor isomerization into the active state without affecting the affinities of ligands for receptor states. A means of confirming this assumption is provided. Global nonlinear regression analysis yields estimates of 1) the active (K_act) and inactive (K_inact) receptor-state affinity constants, 2) the isomerization constant of the unoccupied receptor (K_q-obs), and 3) the sensitivity constant of the signaling pathway (K_E-obs). The latter two parameters define the output response of the receptor, and hence, their ratio (K_q-obs/K_E) is a useful measure of system bias. If the cellular system is reasonably stable and the K_q-obs and K_E-obs values of the signaling pathway are known, the K_act and K_inact values of additional agonists can be estimated in subsequent experiments on cells expressing the wild type receptor. We validated our method through computer simulation, an analytical proof, and analysis of previously published data. Our approach provides 1) a more meaningful analysis of structure-activity relationships, 2) a means of validating in silico docking experiments on active and inactive receptor structures and 3) an absolute, in contrast to relative, measure of agonist bias.

Functional studies cast light on receptor states

Contemporary analysis of the functional responses of G-protein-coupled receptors (GPCRs) usually addresses drug-receptor interactions from the perspective of the average behavior of the receptor population. This behavior is characterized in terms of observed affinity and efficacy. Efficacy is a measure of how well a drug activates the receptor population and observed affinity a measure of how potently a drug occupies the receptor population. The latter is quantified in terms of the dissociation constant of the ligand-receptor complex. At a deeper level of analysis, drug-receptor interactions are described in terms of ligand affinity constants for active and inactive receptor states. Unlike observed affinity and efficacy, estimates of receptor state affinity constants are unperturbed by G proteins, guanine nucleotides, or other signaling proteins that interact with the receptor. Recent advances in the analysis of the functional responses of GPCRs have enabled the estimation of receptor state affinity constants. These constants provide a more fundamental measure of drug-receptor interactions and are useful in analyzing structure-activity relationships and in quantifying allosterism, biased signaling, and receptor-subtype selectivity.

What is biased efficacy? Defining the relationship between intrinsic efficacy and free energy coupling

A G protein-coupled receptor (GPCR) is only biologically active when associated with a transduction protein, but it can also switch function by interacting with different types of transduction proteins. Biased agonism arises when the ligand induces the receptor to engage distinct transduction proteins with different efficacies. We briefly review the concept of ligand efficacy, from the classical empirical idea to the current mechanistic views of allosteric regulation in proteins. A combination of these theoretically distinct ideas and methodologies allows us to distinguish true ligand bias from divergences of signalling caused by the system. We also demonstrate a rigorous mathematical connection between the intrinsic efficacy of classical receptor theory and the energetic effect that makes a ligand capable of stabilizing receptor-transducer association in the ternary complex model. This relationship unifies different definitions of efficacy and provides a rational basis for quantifying biased agonism.

A kinetic model of GPCRs: analysis of G protein activity, occupancy, coupling and receptor-state affinity constants

CONTEXT

G protein-coupled receptors are vital macromolecules for a wide variety of physiological processes. Upon agonist binding, these receptors accelerate the exchange of GDP for GTP in G proteins coupled to them. The activated G protein interacts with effector proteins to implement downstream biological functions.

OBJECTIVE

We present a kinetic, quaternary complex model, based on a system of coupled linear first-order differential equations, which accounts for the binding attributes of the ligand, receptor, G protein and two types of guanine nucleotide (GDP and GTP) as well as for GTPase activity.

METHODS

We solved the model numerically to predict the extents of G protein activation, receptor occupancy by ligand and receptor coupling that result from varying the ligand concentration, presence of GDP and/or GTP, the ratio of G protein to receptor and the equilibrium constants governing receptor pre-coupling and constitutive activity. We also simulated responses downstream from G protein activation using a transducer function.

RESULTS

Our model shows that agonist-induced G protein activation can occur with either a net decrease or increase in total receptor-G protein coupling. In addition, we demonstrate that affinity constants of the ligand for both the active and inactive states of the receptor can be derived to a close approximation from analysis of simulated responses downstream from receptor activation.

DISCUSSION AND CONCLUSION

The latter result validates our prior methods for estimating the active state affinity constants of ligands, and our results on receptor coupling have relevance to studies investigating receptor-G protein interactions using fluorescence techniques.

Mechanistic analysis of the function of agonists and allosteric modulators: reconciling two-state and operational models

Two-state and operational models of both agonism and allosterism are compared to identify and characterize common pharmacological parameters. To account for the receptor-dependent basal response, constitutive receptor activity is considered in the operational models. By arranging two-state models as the fraction of active receptors and operational models as the fractional response relative to the maximum effect of the system, a one-by-one correspondence between parameters is found. The comparative analysis allows a better understanding of complex allosteric interactions. In particular, the inclusion of constitutive receptor activity in the operational model of allosterism allows the characterization of modulators able to lower the basal response of the system; that is, allosteric modulators with negative intrinsic efficacy. Theoretical simulations and overall goodness of fit of the models to simulated data suggest that it is feasible to apply the models to experimental data and constitute one step forward in receptor theory formalism.

What ligand-gated ion channels can tell us about the allosteric regulation of G protein-coupled receptors

The GABA(A) receptor is the target for a number of important allosteric drugs used in medicine, including benzodiazepines and anesthetics. These modulators have variable effects on the potency and maximal response of macroscopic currents elicited by different GABA(A) receptor agonists, yet this modulation is consistent with a two-state model in which the allosteric ligand has invariant affinity constants for the active and inactive states. Analysis of the effects of an allosteric agonist, like etomidate, on the population current provides a means of estimating the gating constant of the unliganded GABA(A) receptor (∼10(-4)). In contrast, allosteric interactions at the M(2) muscarinic receptor are often inconsistent with a two-state model. Analyzing allosterism within the constraints of a two-state model, nonetheless, provides an unbiased measure of probe dependence as well as clues to the mechanism of allosteric modulation. The rather simple allosteric effect of affinity-only modulation is difficult to explain and suggests modulation of a peripheral orthosteric ligand-docking site on the M(2) muscarinic receptor.

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

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.

Allosteric transition: a comparison of two models

Introduction

Two recent models are in use for analysis of allosteric drug action at receptor sites remote from orthosteric binding sites. One is an allosteric two-state mechanical model derived in 2000 by David Hall. The other is an extended operational model developed in 2007 by Arthur Christopoulos’s group. The models are valid in pharmacology, enzymology, transportology as well as several other fields of biology involving allosteric concentration effects.

Results

I show here that Hall’s model for interactions between an orthoster, an alloster, and a receptive unit is the best choice of model both for simulation and analysis of allosteric concentration-responses at equilibrium or steady-state.

Conclusions

As detailed knowledge of receptors systems becomes available, systems with several pathways and states and/ or more than two binding sites should be analysed by extended forms of the Hall model rather than for instance a Hill type exponentiation of terms as introduced in non-mechanistic (operational) model approaches; yielding semi-quantitative estimates of actual system parameters based on Hill’s unlikely simultaneity model for G protein-coupled receptors.

Application of receptor theory to allosteric modulation of receptors

In this chapter, three topics are considered. The allosteric two-state model (ATSM) is compared with explicit multiconformational models. This demonstrates that the ATSM encapsulates the common behaviors of any model with at least two active and two inactive conformations: the "states" of the model represent ensembles of active and inactive conformations. A matrix representation of multiconformational models is introduced to provide a compact notation for models with arbitrarily large numbers of conformations. Allosteric modulation is further explored in the context of an operational model of receptor activity which includes constitutive receptor activity. Fitting this model allows the apparent affinity, intrinsic efficacy, and cooperativity constants of a pair of allosteric ligands to be determined. It is also demonstrated that, within certain limits, it is possible to estimate the parameters of the ATSM. Finally, a novel operational model is developed that may allow the analysis of protean ligands. This model requires a nonlinear stimulus function and two parameters to define the efficacy of a ligand. Expressions describing competitive and allosteric interactions under this model are developed and the results of applying null analyses to the data are determined.

Development of operational models of receptor activation including constitutive receptor activity and their use to determine the efficacy of the chemokine CCL17 at the CC chemokine receptor CCR4

BACKGROUND AND PURPOSE The operational model provides a key conceptual framework for the analysis of pharmacological data. However, this model does not include constitutive receptor activity, a frequent phenomenon in modern pharmacology, particularly in recombinant systems. Here, we developed extensions of the operational model which include constitutive activity and applied them to effects of agonists at the chemokine receptor CCR4. EXPERIMENTAL APPROACH The effects of agonists of CCR4 on [(35) S]GTPγS binding to recombinant cell membranes and on the filamentous (F-) actin content of human CD4(+) CCR4(+) T cells were determined. The basal [(35) S]GTPγS binding was changed by varying the GDP concentration whilst the basal F-actin contents of the higher expressing T cell populations were elevated, suggesting constitutive activity of CCR4. Both sets of data were analysed using the mathematical models. RESULTS The affinity of CCL17 (also known as TARC) derived from analysis of the T cell data (pK(a) = 9.61 ± 0.17) was consistent with radioligand binding experiments (9.50 ± 0.11) while that from the [(35) S]GTPγS binding experiments was lower (8.27 ± 0.09). Its intrinsic efficacy differed between the two systems (110 in T cells vs. 11). CONCLUSIONS AND IMPLICATIONS The presence of constitutive receptor activity allows the absolute intrinsic efficacy of agonists to be determined without a contribution from the signal transduction system. Intrinsic efficacy estimated in this way is consistent with Furchgott's definition of this property. CCL17 may have a higher intrinsic efficacy at CCR4 in human T cells than that expressed recombinantly in CHO cells.

Quantifying agonist activity at G protein-coupled receptors

When an agonist activates a population of G protein-coupled receptors (GPCRs), it elicits a signaling pathway that culminates in the response of the cell or tissue. This process can be analyzed at the level of a single receptor, a population of receptors, or a downstream response. Here we describe how to analyze the downstream response to obtain an estimate of the agonist affinity constant for the active state of single receptors. Receptors behave as quantal switches that alternate between active and inactive states (Figure 1). The active state interacts with specific G proteins or other signaling partners. In the absence of ligands, the inactive state predominates. The binding of agonist increases the probability that the receptor will switch into the active state because its affinity constant for the active state (K(b)) is much greater than that for the inactive state (K(a)). The summation of the random outputs of all of the receptors in the population yields a constant level of receptor activation in time. The reciprocal of the concentration of agonist eliciting half-maximal receptor activation is equivalent to the observed affinity constant (K(obs)), and the fraction of agonist-receptor complexes in the active state is defined as efficacy (ε) (Figure 2). Methods for analyzing the downstream responses of GPCRs have been developed that enable the estimation of the K(obs) and relative efficacy of an agonist. In this report, we show how to modify this analysis to estimate the agonist K(b) value relative to that of another agonist. For assays that exhibit constitutive activity, we show how to estimate K(b) in absolute units of M(-1). Our method of analyzing agonist concentration-response curves consists of global nonlinear regression using the operational model. We describe a procedure using the software application, Prism (GraphPad Software, Inc., San Diego, CA). The analysis yields an estimate of the product of K(obs) and a parameter proportional to efficacy (τ). The estimate of τK(obs) of one agonist, divided by that of another, is a relative measure of K(b) (RA(i)). For any receptor exhibiting constitutive activity, it is possible to estimate a parameter proportional to the efficacy of the free receptor complex (τ(sys)). In this case, the K(b) value of an agonist is equivalent to τK(obs)/τ(sys). Our method is useful for determining the selectivity of an agonist for receptor subtypes and for quantifying agonist-receptor signaling through different G proteins.