Design and models for estimating antagonist potency (pA2, Kd and IC50) following the detection of antagonism observed in the presence of intrinsic activity

doi:10.1016/S0028-3908(98)00185-3

Neuropharmacology

Volume 38, Issue 3, 14 March 1999, Pages 361-373

https://doi.org/10.1016/S0028-3908(98)00185-3 Get rights and content

Abstract

The antagonist activity of the metabotropic glutamate receptor ligand (2S,1′S,2′S)-2-methyl-2(carboxycyclopropyl)glycine (MCCG) was examined using the [³⁵S]GTPγS binding and forskolin (FSK)-stimulated adenosine 3′:5′-cyclic monophosphate (cAMP) assays with recombinant Chinese hamster ovary (CHO) cells expressing the G protein-coupled human subtype 2 metabotropic glutamate (hmGlu₂) receptor. Whereas MCCG proved to be a partial agonist in the GTPγS binding assay, it not only antagonized the agonist effect of (1S,3R)-ACPD in the cAMP assay but further produced an anomalous increase of the cAMP level relative to baseline. The anomalous MCCG response was also observed following treatment of the cells with MCCG in the absence of added agonist. Determination of the glutamate concentration in the incubate at the start and end of the cAMP reaction revealed the existence of micromolar concentrations of cellularly released glutamate throughout the course of the assay, reaching levels which exceeded its reported affinity for the mGlu₂ receptor. Considering MCCG’s partial agonist effect in the GTPγS binding assay and its pseudo-inverse agonist effect in the cAMP assay, available methods of estimating its antagonist potency were inappropriate since the classical Schild method and the alternative model suggested by Waud both assume the antagonist to lack a concentration-response relationship. We derived an alternate design and models that permit estimation of the pA₂ (pA_x), K_d and IC₅₀ for antagonists which produce a concentration related effect when applied by themselves. With their use, the data acquired in both assays support the designation of MCCG as a competitive antagonist of the hmGlu₂ receptor and provide similar pA₂ estimates between assays. In addition, the newly derived models and design permit the determination of antagonist potency for partial and inverse agonists so characterized in studies employing the Schild design.

Introduction

The potencies of pharmacological competitive antagonists are commonly expressed in terms of pA₂ values or in general pA_x values. The term pA₂ is defined as the negative logarithm to base 10 of the antagonist concentration (expressed in molar units) corresponding to a dose-ratio of 2 (i.e. the concentration that produces a 2-fold shift in the agonist concentration-response curve). The potencies of competitive antagonists are also expressed in terms of K_d, the dissociation constant of the antagonist for the receptor. Schild (1957) derived the following $log_{10} DR−1 =− log_{10} K_{d} + log_{10} ANAG$ where DR is the dose ratio and [ANAG] is the molar concentration of the antagonist. A Schild plot of log₁₀(DR-1) against log₁₀[ANAG], that allows calculation of Kd, is generally constructed from $log_{10} DR−1 =− log_{10} K_{d} + Schild·log_{10} ANAG$ which also permits estimation of the Schild slope. The parameter $pA_{2} = − log_{10} K_{d} Schild$ can be estimated from Eq. (2). We refer to this method as the ‘Schild Method’. For a competitive antagonist, the law of mass action further dictates that the Schild slope equals unity and that the maximum agonist responses observed in the absence and presence of different antagonist concentrations be not significantly different from each other.

Procedures (both design and model) for estimating K_d and pA₂ have also been developed from the results of an antagonist inhibition curve in the presence of a fixed concentration of the agonist (Waud, 1975, Waud, 1976). Lazareno and Birdsall (1993a) have studied this method extensively by comparing it to Gaddum, 1957, Schild, 1957 and Cheng and Prusoff (Cheng and Prusoff, 1973) equations. A six parameter nonlinear model (Eq. (A5) in the Appendix) is generally fit in such a situation. This nonlinear model simultaneously uses both the agonist and antagonist concentrations. The model constructs dose ratios as the ratio of two EC₅₀ values of the agonist in the presence and absence of the antagonist, where both the EC₅₀ values produce the same response. This definition of dose ratio is valid only under the assumption that the curves have the same minima and maxima. The pA₂ and IC₅₀ values for the antagonist are obtained by expressing these quantities as functions of the six parameters (first Eq. in (A6) and (A7)). We refer to this method as the ‘Waud Method’.

Neither of these approaches permit the evaluation of antagonist potencies for compounds that are not pure antagonists (e.g. partial and inverse agonists) since each alter baseline minima and maxima, respectively. For the same reason, they are also inadequate in situations where antagonists, though lacking intrinsic activity are studied in the presence of receptor stimulation, be it agonist-independent (e.g. constitutive) or agonist-dependent (e.g. the study of glutamate antagonists in situations where the cellular release of glutamate into the incubate permits stimulation of expressed mGlu receptors) activity. In these situations, we propose models or extensions of the Waud model for the estimation of pA₂ (pA_x), K_d, and IC₅₀. The derivations of the proposed models are presented in the Appendix section. The proposed models have been examined using data sets from actual experiments and the results are discussed.

Section snippets

Chemicals

The mGlu receptor specific agonist (1S,3R)-1-aminocyclopentane-1,3-dicarboxylate ((1S,3R)-ACPD) and mGlu₂ receptor selective antagonist (2S,l′S,2′S)-2-methyl-2(carboxycyclopropyl)glycine (MCCG) were purchased from Tocris Cookson, St Louis, MO. Concentrations of these compounds were expressed in micromolar (μM) units.

Biological assays

Since receptor stimulation results in responses that are either directly or inversely proportional to agonist concentration, separate mathematical models have been derived to

Results

Results obtained in the [³⁵S]GTPγS binding assay, where the agonist response is directly proportional (Case I) to receptor stimulation are presented graphically in Fig. 1. The graph reveals the concentration-dependent responses, measured in dpms obtained following treatment of the homogenate with the agonist (1S,3R)-ACPD (□). An inverse prediction calculated on the basis of this regression analysis revealed the EC₉₀ to be approximately 10 μM. Responses obtained following application of the

Discussion

Two biological assays were selected to examine mathematical models derived to assess the potency and the competitive nature of the antagonism observed with MCCG, an antagonist that displays intrinsic activity. Both assays were based on the interaction between the agonist (1S,3R)-ACPD and/or the antagonist MCCG with the G protein-coupled hmGlu₂ receptor. Although (1S,3R)-ACPD is generally accepted as a non-selective mGlu receptor agonist, the partial agonist activity displayed by MCCG has

Acknowledgements

The authors gratefully acknowledge the support of Dr Thomas Copenhaver, Director of Biometrics Research at Wyeth–Ayerst Research.

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Design and models for estimating antagonist potency (pA2, Kd and IC50) following the detection of antagonism observed in the presence of intrinsic activity

Abstract

Introduction

Section snippets

Chemicals

Biological assays

Results

Discussion

Acknowledgements

J. Biol. Chem.

J. Chromatogr. B.

Neuropharmacology

Neuropharmacology

Trends Pharmacol Sci.

J. Biol. Chem.

Bioorganic Med. Chem. Lett.

Neuron

Pharmacological antagonism of the actions of group II and III mGluR agonists in the lateral perforant path of rat hippocampal slices

Br. J. Pharmacol.

Characterization of [3H](2S,2′R,3′R)-2-(2′,3′-dicarboxycyclopropyl)glycine ([3H]-DCG IV) binding to metabotropic mGlu2 receptor-transfected cell membranes

Br. J. Pharmacol.

Design and models for estimating antagonist potency (pA₂, K_d and IC₅₀) following the detection of antagonism observed in the presence of intrinsic activity

Characterization of [³H](2S,2′R,3′R)-2-(2′,3′-dicarboxycyclopropyl)glycine ([³H]-DCG IV) binding to metabotropic mGlu2 receptor-transfected cell membranes