Interpretation of agonist affinity estimations: the question of distributed receptor states

Theoretical Aspects of GPCR-Ligand Complex Pharmacology

Over the past 50 years in pharmacology, an understanding of seven transmembrane (7TMR) function has been gained from the comparison of experimental data to receptor models. These models have been constructed from building blocks composed of systems consisting of series and parallel mass action binding reactions. Basic functions such as the the isomerization of receptors upon ligand binding, the sequential binding of receptors to membrane coupling proteins, and the selection of multiple receptor conformations have been combined in various ways to build receptor systems such as the ternary complex, extended ternary complex, and cubic ternary complex models for 7TMR function. Separately, the Black/Leff operational model has furnished an extremely valuable method of quantifying drug agonism. In the past few years, incorporation of the basic allosteric nature of 7TMRs has led to additional useful models of functional receptor allosteric mechanisms; these models yield valuable methods for quantifying allosteric effects. Finally, molecular dynamics has provided yet another new set of models describing the probability of formation of multiple receptor states; these radically new models are extremely useful in the prediction of functionally selective drug effects.

The mass action equation in pharmacology

The mass action equation is the building block from which all models of drug-receptor interaction are built. In the simplest case, the equation predicts a sigmoidal relationship between the amount of drug-receptor complex and the logarithm of the concentration of drug. The form of this function is also the same as most dose-response relationships in pharmacology (such as enzyme inhibition and the protein binding of drugs) but the potency term in dose-response relationships very often differs in meaning from the similar term in the simple mass action relationship. This is because (i) most pharmacological systems are collections of mass action reactions in series and/or in parallel and (ii) the important assumptions in the mass action reaction are violated in complex pharmacological systems. In some systems, the affinity of the receptor R for some ligand A is modified by interaction of the receptor with the allosteric ligand B and concomitantly the affinity of the receptor for ligand B is modified to the same degree. When this occurs, the observed affinity of the ligand A for the receptor will depend on both the concentration of the co-binding allosteric ligand and its nature. The relationships between drug potency in pharmacological models and the equilibrium dissociation constants defined in single mass action reactions are discussed. More detailed knowledge of efficacy has led to new models of drug action that depend on the relative probabilities of different states, and these have taken knowledge of drug-receptor interactions beyond Guldberg and Waage.

What is pharmacological 'affinity'? Relevance to biased agonism and antagonism

The differences between affinity measurements made in binding studies and those relevant to receptor function are described. There are theoretical and practical reasons for not utilizing binding data and, in terms of the quantification of signaling bias, it is unnecessary to do so. Finally, the allosteric control of ligand affinity through receptor-signaling protein interaction is discussed within the context of biased antagonism. In this regard, it is shown that both the bias and relative efficacy of a ligand are essential data for fully predicting biased effects in vivo.

5-Hydroxytryptamine receptor assays

5-Hydroxytryptamine (5-HT) receptors, by virtue of their broad expression pattern in peripheral and central tissues, regulate diverse physiological and behavioral responses through the activation of fourteen molecularly distinct receptor subtypes. The tissue-specific distribution of these receptors confers specificity for the actions of serotonin and highlights the therapeutic potential of serotonin receptor modulators. To better assess this therapeutic potential, it is useful to characterize serotonergic agonists and antagonists in physiologically relevant organ systems. Provided in this unit are twelve tissue bath assays using vascular and smooth muscle tissues isolated from guinea-pig, rat, and rabbit. These tests make possible the analyses of compounds at nine serotonin receptor subtypes.

5-HT4 receptor agonists: similar but not the same

5-Hydroxytryptamine(4) (5-HT(4)) receptors are an interesting target for the management of patients in need of gastrointestinal (GI) promotility treatment. They have proven therapeutic potential to treat patients with GI motility disorders. Lack of selectivity for the 5-HT(4) receptor has limited the clinical success of the agonists used until now. For instance, next to their affinity for 5-HT(4) receptors, both cisapride and tegaserod have appreciable affinity for other receptors, channels or transporters [e.g. cisapride: human ether-a-go-go-related gene (hERG) is K(+) channel and tegaserod: 5-HT(1) and 5-HT(2) receptors]. Adverse cardiovascular events observed with these compounds are not 5-HT(4) receptor-related. Recent efforts have led to the discovery of a series of selective 5-HT(4) receptor ligands, with prucalopride being the most advanced in clinical development. The selectivity of these new compounds clearly differentiates them from the older generation compounds by minimizing the potential of target-unrelated side effects. The availability of selective agonists enables the focus to shift to the exploration of 5-HT(4) receptor-related differences between agonists. Based on drug- and tissue-related properties (e.g. differences in receptor binding, receptor density, effectors, coupling efficiency), 5-HT(4) receptor agonists are able to express tissue selectivity, i.e. behave as a partial agonist in some and as a full agonist in other tissues. Furthermore, the concept of ligand-directed signalling offers great opportunities for future drug development by enlarging the scientific basis for the generation of agonist-specific effects in different cell types, tissues or organs. Selective 5-HT(4) receptor agonists might thus prove to be innovative drugs with an attractive safety profile for better treatment of patients suffering from hypomotility disorders.

Agonist binding, agonist affinity and agonist efficacy at G protein-coupled receptors

Measurements of affinity and efficacy are fundamental for work on agonists both in drug discovery and in basic studies on receptors. In this review I wish to consider methods for measuring affinity and efficacy at G protein coupled receptors (GPCRs). Agonist affinity may be estimated in terms of the dissociation constant for agonist binding to a receptor using ligand binding or functional assays. It has, however, been suggested that measurements of affinity are always contaminated by efficacy so that it is impossible to separate the two parameters. Here I show that for many GPCRs, if receptor/G protein coupling is suppressed, experimental measurements of agonist affinity using ligand binding (K(obs)) provide quite accurate measures of the agonist microscopic dissociation constant (KA). Also in pharmacological functional studies, good estimates of agonist dissociation constants are possible. Efficacy can be quantitated in several ways based on functional data (maximal effect of the agonist (E(max)), ratio of agonist dissociation constant to concentration of agonist giving half maximal effect in functional assay (K(obs)/EC50), a combined parameter E(max)K(obs)/EC50). Here I show that E(max)K(obs)/EC50 provides the best assessment of efficacy for a range of agonists across the full range of efficacy for full to partial agonists. Considerable evidence now suggests that ligand efficacy may be dependent on the pathway used to assess it. The efficacy of a ligand may, therefore, be multidimensional. It is still, however, necessary to have accurate measures of efficacy in different pathways.

Differential effects of 5-hydroxytryptamine4 receptor agonists at gastric versus cardiac receptors: an operational framework to explain and quantify organ-specific behavior

Quantification of different levels of 5-hydroxytryptamine4 (5-HT4) receptor agonism expression across animal species as well as across organs within the same animal species offers substantial potential for the separation of desired gastrointestinal versus undesired cardiac pharmacological activity of compounds in development. Since a detailed investigation of such properties is lacking to date, we set out to quantify gastric and cardiac effects of 5-HT4 receptor ligands in the pig, a model considered to be representative for the human situation. An in vitro test was developed to study the potentiating effect of 5-HT, prucalopride, tegaserod, R149402 (4-amino-5-chloro-2,2-dimethyl-2,3-dihydro-benzofuran-7-carboxylic acid [3-hydroxy-1-(3-methoxy-propyl)-piperidin-4ylmethyl]-amide), and R199715 (4-amino-5-chloro-2,3-dihydro-benzofuran-7-carboxylic acid [3-hydroxy-1-(3-methoxy-propyl)-piperidin-4ylmethyl]-amide) on electrically induced cholinergic contractions in longitudinal muscle strips of the proximal stomach. The results were compared with inotropic and chronotropic effects of these compounds in the electrically paced left atrium and spontaneously beating right atrium, respectively. To quantify the observed tissue-dependent responses, a nonlinear mixed-effects model based on the operational model of agonism was developed and successfully fitted to the data. The model quantified the tissue-dependent partial agonism of the selective 5-HT4 receptor agonists prucalopride, R149402, and R199715, whereas tegaserod and 5-HT were equiefficacious. The model was further extended to incorporate the responses to prucalopride in the presence of the 5-HT4 receptor antagonist GR113808 ([1-[2-[(methylsulphonyl)amino]ethyl]-4-piperidinyl-]methyl 1-methyl-1H-indole-3-carboxylate). The results indicate that these interactions do not follow a simple competitive pattern and that they differ between stomach and left atrium.

Agonist induction, conformational selection, and mutant receptors

Current models of receptor activation are based on either of two basic mechanisms: agonist induction or conformational selection. The importance of one pathway relative to the other is controversial. In this article, the impossibility of distinguishing between the two mechanisms under a thermodynamic approach is shown. The effect of receptor mutation on the constants governing ligand-receptor equilibria is discussed. The two-state model of agonism both in its original formulation (one cycle) and including multiple active states (multiple cycles) is used. Pharmacological equations for the double (two cycles) two-state model are derived. The simulations performed suggest that the double two-state model of agonism can be a useful model for assessing quantitatively the changes in pharmacological activity following receptor mutation.

Assessing the (a)symmetry of concentration-effect curves: empirical versus mechanistic models

Modeling the shape of concentration-effect curves is of prime importance in pharmacology. Geometric descriptors characterizing these curves (the upper and lower asymptotes, the mid-point, the mid-point slope, and the point of inflection) are used for drug comparison or for assessing the change in agonist function after a system modification. The symmetry or asymmetry around the mid-point of a concentration-effect curve is a fundamental property that, regretfully, is often overlooked because, generally, models yielding exclusively symmetric curves are used. In the present review, empirical and mechanistic models are examined in their ability to fit experimental data. The geometric parameters of a survey of empirical models, the Hill equation, a logistic variant that we call the modified Hill equation, the Richards function, and the Gompertz model are determined. To analyze the relationship between asymmetry and mechanism, some examples from the ionic channel field, in an increasing degree of complexity, are used. It is shown that asymmetry arises from ionic channels with multiple binding sites that are partly occupied. The operational model of agonism is discussed both in its empirical general formulation and including the signal transduction mechanisms through G-protein-coupled receptors. It is shown that asymmetry results from systems where receptor distribution is allowed. Developed mathematical models are compared for describing experimental data on alpha-adrenoceptors. The existence or not of a relationship between the shape of the curves and receptor reserve is discussed.

The ligand-receptor-G-protein ternary complex as a GTP-synthase. steady-state proton pumping and dose-response relationships for beta -adrenoceptors

Steady-state solutions are developed for the rate of G alpha.GTP production in a synthase model of the ligand-receptor-G-protein ternary complex activated by a ligand-receptor proton pumping mechanism. The effective rate, k(31), defining the proton transfer, phosphorylation and G alpha.GTP release is a controlling rate of the synthase in the presence of a ligand with an efficient mode of signal activation, the ligand-receptor interaction taking place under effectively equilibrium conditions. The composite rate, however, becomes an amplifying factor in any dose-response relationship. The amplification is a triple product of the rate, k(31), the equilibrium constant associated with the activation of the proton signal, K(act)and the fraction of agonist conformer transmitting the signal, f(*). Where the rate of activation of the proton signal becomes critically inefficient, the rate of activation, k(act 1)replaces k(31)K(act). A correlation between beta(1)-adrenergic receptor-stimulated GDP release and adenylate cyclase activation shows that this correlation is not unique to an exchange reaction. Within the initiating Tyr-Arg-Tyr receptor proton shuttle mechanism, the position of Arg(r156) paralleldictates the high-(R(p)) and low-(R(u)) ligand-binding affinities. These states are close to R(*)and R(0)of the equilibrium model (De Lean et al., 1980, J. Biol. Chem.255, 7108-7117). An increased rate of hydrogen ion diffusion into a receptor mutant can give rise to constitutive activity while increased rates of G-protein release and changes in receptor state balance can contribute to the resultant level of action. Constitutive action will arise from a faster rate of G-protein release alone if proton diffusion in the wild-type receptor contributes to a basal level of G-protein activation. Competitive ligand-receptor occupancy for constitutive mutants shows that, where the rate of G-protein activation from the proportion of ligand-occupied receptors is less than the equivalent rate that would be generated from this fraction by proton diffusion, inverse agonism will occur. Rate-dependent dose-responses developed for the proposed synthase mechanism give explicit definition to the operational model for partial agonism (Black & Leff, 1983, Proc. Roy. Soc. Lond. B220, 141-162). When comparable ligands have effectively identical conformational states at the transition state for signal activation, the antagonist component of the binding "in vitro" can be derived by multiplying the apparent binding constant by (1-e) where e is the maximum stimulatory response. This component should be consistent throughout the tissues.

Analysis of receptor inactivation experiments with the operational model of agonism yields correlated estimates of agonist affinity and efficacy

The aim of this study was to evaluate whether the operational model of agonism can yield independent estimates of agonist affinity (pK(A)) and efficacy (log tau) when Furchgott's method of irreversible receptor inactivation is employed. For this purpose, the interaction between noradrenaline and phenoxybenzamine was studied in rat small mesenteric artery using a paired-curve design. Phenoxybenzamine pretreatment produced a significant rightward shift and depression of the upper asymptote of the noradrenaline concentration-effect (E/[A]) curve. Although the operational model of agonism appeared to provide an adequate fit of the individual E/[A] curves, a highly significant correlation was found between the estimates of pK(A )and log tau (r = -0.80, p < 0.0001), inconsistent with the assumption that affinity and efficacy are independent parameters (best line fit: pK(A) = -0.96 x log tau + 6.75). The pK(A) and log tau estimates were not correlated with either the pEC50s of the control curves or upper asymptotes of the phenoxybenzamine-treated curves. Simulations showed that the correlation between affinity and efficacy can be explained by the effect on the outcome of the analysis of random errors in the response measurements. Therefore, although in theory the operational model of agonism should provide independent estimates of agonist affinity and efficacy, this is unlikely to be the case with experimental data.

The effect of the molecular mechanism of G protein-coupled receptor activation on the process of signal transduction

A thermodynamic model of signal transduction that incorporates the possibility of multiple conformational states between the inactive and the active forms of the receptor was developed. The obtained equilibrium model is equivalent to the extended ternary complex of Samama et al. (J. Biol. Chem. 268 (1993) 4625-4636) if only two states of the receptor exist. These multiple equilibria between receptor states are modeled by two sets of equilibrium constants: K(piAR) and K(sigma piAR), in the presence of the ligand; and K(piR) and K(sigma piR), in the absence of the ligand. The higher the value of these constants, the more efficiently the active form of the receptor is generated. Intrinsic efficacy of the agonist is defined in the present formulation as the molecular processes induced by ligands in the receptor that lead to the active form of the receptor. Both the energetics (associated to K[piAR]) and mechanism of the process of receptor activation (associated to K[sigma piAR]) are important in eliciting the maximum response. Moreover, analytical expressions of basal activity, potency and maximum response were obtained. These definitions were used to classify the extra cellular ligand as agonists (K[sigma piAR] > K[sigma piR]), inverse agonists (K[sigma piR] > K[sigma piAR] > 0), neutral antagonists (K[sigma piAR] = K[sigma piR]), and pure antagonists.

Analysis of the variation in the action of L-365,260 at CCKB/gastrin receptors in rat, guinea-pig and mouse isolated gastric tissue assays

1. Since L-365,260 was first described as a selective antagonist at cholecystokinin (CCK)B/gastrin receptors, we have used it periodically as a reference compound in isolated tissue assays of guinea-pig gastric muscle and lumen-perfused stomachs from mouse and immature rat. L-365,260 behaved as a surmountable antagonist and produced parallel rightward shifts of pentagastrin concentration-effect curves' in each of the replicate experiments. The experiments were performed by several different experimenters in the same laboratories over a five year period. 2. In the isolated, lumen-perfused, immature rat stomach assay, L-365,260 behaved as a simple competitive antagonist (Schild plot slope = 1.00 +/- 0.10, pKB = 7.54 +/- 0.03 from a global analysis of the data) acting at a homogeneous population of receptors in five separate, highly-reproducible, experiments. In contrast, the replicate data sets obtained from the interaction in the isolated, lumen-perfused mouse stomach and guinea-pig gastric muscle assays, over the same period, were not consistent with the presence of a single receptor population. The guinea-pig gastric muscle data were relatively reproducible between experiments but some individual Schild plot slopes and the slope estimated from a global analysis of all the data were significantly less than unity (slope = 0.80 +/- 0.07, pA2 = 8.56 +/- 0.05 from the global analysis). The data obtained in the mouse stomach were significantly more variable than that obtained in the same assay, during the same period, from the interaction between histamine and the H2-receptor antagonist, famotidine. The individual Schild plot slopes ranged from being very flat (0.20) to being not significantly different from unity (1.23) and the pA2 values ranged from 7.68 to 8.70. 3. Overall, the data could be accounted for by assuming the variable expression of two receptor subtypes across the assays. The rat stomach appeared to express a single receptor characterized by a low affinity constant for L-365,260 (pKB approximately 7.5). The guinea-pig gastric muscle and mouse stomach data could be explained by the presence of this receptor and a second one characterized by a high affinity constant for L-365,260 (pKB approximately 8.6). The activity of the two proposed receptor subtypes was consistent between experiments in the guinea-pig and the high affinity receptor appeared to be predominant. In contrast, the mouse stomach data could only be simulated by assuming that the proportion and absolute number of each subtype varied significantly between the replicate experiments. 4. The L-365,260 affinity estimates at the inferred receptor subtypes were indistinguishable from those obtained in a corresponding analysis of the behaviour of L-365,260 in CCKB/gastrin receptor radioligand binding experiments in guinea-pig gastric gland and mouse and rat cerebral cortex preparations.

Pharmacological analysis of dopamine stimulation of [35S]-GTP gamma S binding via human D2short and D2long dopamine receptors expressed in recombinant cells

1. The activation of G-proteins by agonist-occupied D2 or D3 dopamine receptors in membranes from recombinant cells expressing the cloned receptors has been analysed by a [35S]-guanosine 5'-[gamma-thio] triphosphate ([35S]-GTP gamma S) binding assay. 2. The rate of [35S]-GTP gamma S binding was increased by dopamine in a dose-dependent manner in membranes from CHO cells stably expressing either the D2short or D2long dopamine receptor. 3. The dopamine-induced stimulation of [35S]-GTP gamma S binding could be inhibited by a range of antagonists. Affinities for antagonists derived from the inhibition of the dopamine stimulation of [35S]-GTP gamma S binding correlated very well with affinities derived from radioligand binding studies. 4. When the maximum [35S]-GTP gamma S binding responses stimulated by dopamine acting at different receptor subtypes were compared, there was a tendency for the stimulation via the D2short receptor to be greater than via the D2long receptor and for the stimulation via the D3 dopamine receptor to be less than for either D2 receptor. These differences in maximal response were also seen when the inhibitory effects of dopamine on adenylyl cyclase via the three receptor subtypes were compared. 5. The stimulation of [35S]-GTP gamma S binding by dopamine in membranes from recombinant cells therefore provides an excellent system for studying the molecular nature of agonism and the receptor/G-protein interactions for these receptors.

Determination of KA values by controlled receptor expression in Xenopus oocytes

1. In the present study we estimated the KA value of endothelin-1 (ET-1) for ETA-receptors by a new method in which the level of expression of ETA-receptors in Xenopus oocytes was altered in a controlled way. 2. Kvl.2 (a delayed rectifier type K channel) c RNA at the fixed concentration of 0.2 micro g micro l(-1) was mixed with ETA-receptor cRNA at various concentration ratios (10(-3)-3). Oocytes were examined 2-4 days after the injection of the cRNA mixtures. 3. In these oocytes, ET-1 suppressed the amplitude of Kvl.2 current in a dose-dependent manner in the range of 0.1-100 nM; the maximum inhibition produced by ET-1 was larger and the EC50 value for the inhibition by ET-1 was smaller as the mixture ratio was increased. Double-reciprocal plots of equiactive concentrations of ET-1 in 1/1- and 1/30-injected oocytes yielded a KA for ET-1 of 7.4 nM. The number of ETA-receptors in 1/30-injected oocytes was 13% of that in 1/1-injected oocytes, whereas the inhibition of the current in 1/30-injected oocytes was about 60% of that in 1/1-injected oocytes. This suggests the presence of spare receptors of ETA in the latter. 4. A saturation binding experiment estimated a KD value of 0.1 nM for ET-1 at ETA-receptors and the number of ETA-receptors in 1/30-injected oocytes was 23% of that in 1/1-injected ones. This value was not significantly different from that estimated by the above new method. However, there was a discrepancy between KA and KD, which could be due to factors unique to the expression system employed in the present study.

2-Naphthalenesulphonyl L-aspartyl-(2-phenethyl)amide (2-NAP)--a selective cholecystokinin CCKA-receptor antagonist

1. The in vitro pharmacological characterization of the sodium salt of 2-naphthalenesulphonyl 1-aspartyl-(2-phenethyl)amide [2-NAP], a hydrophilic compound derived from the C-terminal aspartate-phenylalanine dipeptide of cholecystokinin (CCK), is described. 2. 2-NAP behaved as a competitive antagonist of sulphated cholecystokinin octapeptide (CCK-8) at CCKA-receptors in both intact tissue bioassays (guinea-pig gall bladder, pancreas and ileum, human and rabbit gall bladder) and a radioligand displacement assay (guinea-pig pancreatic cells). The mean pKB, over assays, was 6.5. 3. Compared to the other assays, the rabbit gall bladder assay gave a significantly higher pKB estimate [7.0] for 2-NAP and a significantly lower estimate [8.9] for devazepide (formerly L-364,718 and MK-329), a well-characterized CCKA-receptor antagonist; these anomalous results suggest that a different class of CCKA-receptors may be involved. 4. 2-NAP, was found to be highly selective, having at least 300 fold greater affinity for CCKA-receptors than for 50 other pharmacological loci, including gastrin/CCKB, as estimated by bioassay or radioligand displacement.