P. Leff

Operational models of pharmacological agonism

The traditional receptor-stimulus model of agonism began with a description of drug action based on the law of mass action and has developed by a series of modifications, each accounting for new experimental evidence. By contrast, in this paper an approach to modelling agonism is taken that begins with the observation that experimental agonist-concentration effect, E/[A], curves are commonly hyperbolic and develops using the deduction that the relation between occupancy and effect must be hyperbolic if the law of mass action applies at the agonist-receptor level. The result is a general model that explicity describes agonism by three parameters: an agonist-receptor dissociation constant, KA; the total receptor concentration, [R0]; and a parameter, KE, defining the transduction of agonist-receptor complex, AR, into pharmacological effect. The ratio, [R0]/KE, described here as the ‘transducer ratio’, τ, is a logical definition for the efficacy of an agonist in a system. The model may be extended to account for non-hyperbolic E/[A] curves with no loss of meaning. Analysis shows that an explicit formulation of the traditional receptor-stimulus model is one particular form of the general model but that it is not the simplest. An alternative model is proposed, representing the cognitive and transducer functions of a receptor, that describes agonist action with one fewer parameter than the traditional model. In addition, this model provides a chemical definition of intrinsic efficacy making this parameter experimentally accessible in principle. The alternative models are compared and contrasted with regard to their practical and conceptual utilities in experimental pharmacology.

An operational model of pharmacological agonism: the effect of E/[A] curve shape on agonist dissociation constant estimation.

1 An operational model of pharmacological agonism has been analysed to predict the behaviour of rectangular hyperbolic and non‐hyperbolic agonist‐concentration effect, E/[A], curves with variation in receptor concentration, [Ro]. 2 Irreversible antagonism is predicted to cause E/[A] curve gradient changes in non‐hyperbolic cases but not in hyperbolic cases; in both cases estimation of agonist dissociation constants (KAS) is theoretically valid. 3 5‐Hydroxytryptamine (5‐HT) produced ‘steep’ E/[A] curves in contracting the rabbit isolated aorta preparation. Irreversible antagonism by phenoxybenzamine (Pbz) produced a flattened E/[A] curve, consistent with theoretical predictions. 4 Fitting 5‐HT E/[A] curves in the presence and absence of Pbz to the model provided an estimate of KA for 5‐HT which was not significantly different from the estimate obtained using Furchgotts null method. 5 The operational model of agonism appears to account qualitatively and quantitatively for the effects of [Ro] changes on hyperbolic and non‐hyperbolic E/[A] curves. Under conditions where irreversible antagonism may be used to estimate KAS, fitting the operational model directly to E/[A] data represents a valid, economical and analytically simple alternative to the conventional null method.

Further analysis of anomalous pKB values for histamine H2‐receptor antagonists on the mouse isolated stomach assay

1 Agonist‐antagonist interactions at histamine receptors have been re‐examined using improved techniques, on the mouse isolated, lumen‐perfused, stomach gastric acid assay. 2 Using histamine as agonist, pKB values have been estimated for burimamide, metiamide, cimetidine, ranitidine, oxmetidine and famotidine on both the gastric and guinea‐pig isolated right atrium assays. With the exception of oxmetidine on the atrial assay, these compounds behaved as competitive antagonists on both assays. 3 Oxmetidine significantly depressed basal rate on the atrial assay and the Schild plot slope parameter (0.81) was significantly less than one. 4 The pKB values estimated on the gastric assay were lower than those on the atrial assay. However, the difference between the values on the gastric and atrial assays was not constant. The difference between the two assays for famotidine was not significant. 5 We conclude that the apparent varying selectivity of the antagonists for gastric and atrial histamine H2‐receptors may be explained by the differential loss of antagonists into the gastric secretion from the receptor compartment and that there is no need to postulate heterogeneity of histamine H2‐receptors.

Analysis of competitive antagonism when this property occurs as part of a pharmacological resultant

1 In this paper, pharmacological resultant is defined as the net effect of a single compound resulting from the simultaneous expression of two or more specific actions. 2 The principles of concentration‐ratio analysis are extended to develop a method for detecting and quantifying competitive antagonism when this property is a component of a pharmacological resultant. The method is general to the extent that it allows analysis of competitive antagonism in combination with all types of post‐receptor intervention. Essentially it depends on the altered expression of competition by a reference antagonist. It incorporates tests for validating its application and it is independent of agonist concentration‐effect curve shape: in these respects the method is analogous to Schild plot‐analysis of simple competition. 3 The methodology for the practical application of the analysis is exemplified by studying the net effect of a combination of a phosphodiesterase inhibitor (isobutylmethylxanthine) and histamine H2‐ receptor antagonist (metiamide) on histamine‐stimulated tachycardia in guinea‐pig, isolated, right atrium. Cimetidine was used as the reference antagonist. 4 The equation used in this analysis is similar in form to one recently described by Hughes & Mackay (1985) to elucidate the situation when competitive antagonism occurs in combination with functional interactions. The relation between their method and the present analysis is discussed.

Pharmacological analysis of the pentagastrin‐tiotidine interaction in the mouse isolated stomach

1 The pentagastrin‐tiotidine interaction has been analysed, using improved techniques, in the mouse isolated, lumen‐perfused, stomach assay. For comparison and quantification of the H2‐receptor blocking activity of tiotidine, histamine‐tiotidine interactions have also been analysed in the mouse stomach and guinea‐pig isolated right atrial preparation. 2 Tiotidine behaved as a competitive antagonist of histamine both in the guinea‐pig right atrium (pKB 7.57) and mouse stomach (pKB 6.96). The difference in pKB was attributed to the loss of tiotidine into the gastric secretion. 3 On the stomach assay, pentagastrin concentration‐effect curves were significantly flatter with lower maximal responses than those obtained to histamine. In addition the profile of inhibition observed with tiotidine was different in that the pentagastrin curve maxima were depressed with only a small concomitant dextrad shift. 4 A mathematical model has been developed which accounts for the differences in agonist concentration‐effect curves and describes in a quantitative manner the expectations for the competitive antagonism of endogenous histamine assumed to be released by pentagastrin. Fitting of the pentagastrin‐tiotidine data to this model provided a reasonable goodness‐of‐fit. 5 The results are discussed in terms of the role of endogenous histamine in gastrin‐stimulated acid secretion. We conclude that the results are consistent with the hypothesis that pentagastrin stimulates acid secretion via the release of endogenous histamine under the present experimental conditions.

Pharmacological analysis of β‐adrenoceptor‐mediated agonism in the guinea‐pig, isolated, right atrium

1 The recently developed, operational model of pharmacological agonism defines the efficacy of agonists by τ = [Ro]/KE, where [Ro] is the total functional concentration of receptors and KE is the concentration of agonist‐occupied receptors for half‐maximal effect. Theoretically, variations in [Ro] and KE affect τ and in turn, E/[A] curve profiles similarly. 2 Using the β‐adrenoceptor mediated chronotropic responses of the guinea‐pig isolated right atrial preparation we have investigated the consequences of experimental [Ro] and KE variation. 3 Bromoacetylalprenolol menthane (M‐75) produced displacements of isoprenaline and dichloroisoprenaline E/[A] curves consistent with [Ro] reduction. Cholera toxin produced displacements consistent with decreases in KE. 4 . The operational model provides a simple conceptual framework for the prediction and interpretation of changes in E/[A] curve profile resulting from experimental interventions at the post‐receptor (KE) level as well as at the receptor ([Ro]) level.

An operational model of pharmacological agonism: the effect of E/[A] curve shape on agonist dissociation constant estimation: E/[A] curve shape and KA estimation

1 An operational model of pharmacological agonism has been analysed to predict the behaviour of rectangular hyperbolic and non-hyperbolic agonist-concentration effect, E/[A], curves with variation in receptor concentration, [Ro]. 2 Irreversible antagonism is predicted to cause E/[A] curve gradient changes in non-hyperbolic cases but not in hyperbolic cases; in both cases estimation of agonist dissociation constants (KAs) is theoretically valid. 3 5-Hydroxytryptamine (5-HT) produced ‘steep’ E/[A] curves in contracting the rabbit isolated aorta preparation. Irreversible antagonism by phenoxybenzamine (Pbz) produced a flattened E/[A] curve, consistent with theoretical predictions. 4 Fitting 5-HT E/[A] curves in the presence and absence of Pbz to the model provided an estimate of KA for 5-HT which was not significantly different from the estimate obtained using Furchgott’s null method. 5 The operational model of agonism appears to account qualitatively and quantitatively for the effects of [Ro] changes on hyperbolic and non-hyperbolic E/[A] curves. Under conditions where irreversible antagonism may be used to estimate KAs, fitting the operational model directly to E/[A] data represents a valid, economical and analytically simple alternative to the conventional null method.

Differences in asthma study models and the effectiveness of β2‐adrenoceptor ligands: response to Lipworth et al.

These Tables list key protein targets and ligands in this article which are hyperlinked guidetopharmacology.org/, the common portal for data from the IUPHAR/BPS Guide to PHAR permanently archived in the Concise Guide to PHARMACOLOGY 2013/14 ( Alexander et al., 20 LINKED ARTICLES This article is a reply to Lipworth BJ, Anderson WJ and Short PM (2016). From mouse to blockers in asthma. Br J Pharmacol 173: 248–249. doi: 10.1111/bph.13335, commentin Forkuo GS, Parra S, Knoll BJ, Bouvier M, Leff P and Bond RA (2015). Beta-blockers have d phenotype. Br J Pharmacol 172: 4833–4846. doi: 10.1111/bph.13253.