Design and models for estimating antagonist potency (pA2, Kd and IC50) following the detection of antagonism observed in the presence of intrinsic activity
Introduction
The potencies of pharmacological competitive antagonists are commonly expressed in terms of pA2 values or in general pAx 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 Kd, the dissociation constant of the antagonist for the receptor. Schild (1957) derived the followingwhere 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 fromwhich also permits estimation of the Schild slope. The parameter 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 Kd 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 (pAx), Kd, 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.
References (21)
- et al.
Constitutively active 5-hydroxytryptamine2C receptors reveal novel inverse agonist activity of receptor ligands
J. Biol. Chem.
(1994) - et al.
Improved method for the measurement of glutamate and aspartate using capillary electrophoresis with laser induced fluorescence detection and its application to brain microdialysis
J. Chromatogr. B.
(1997) - et al.
Pharmacological characterization of MCCG and MAP4 at the mGluRlb, mGluR2 and mGluR4a human metabotropic glutamate receptor subtypes
Neuropharmacology
(1995) - et al.
A GTPγS binding assessment of metabotropic glutamate receptor standards in Chinese hamster ovary cell lines expressing the human metabotropic glutamate receptor subtypes 2 and 4
Neuropharmacology
(1998) - et al.
Estimation of antagonist Kb from the inhibition curves in functional experiments: alternative to the Cheng–Prusoff equation
Trends Pharmacol Sci.
(1993) - et al.
Protein measurement with the folin phenol reagent
J. Biol. Chem.
(1951) - et al.
Synthesis and biological activity of cyclic analogues of MPPG and MCPG as metabotropic glutamate receptor antagonists
Bioorganic Med. Chem. Lett.
(1997) - et al.
A family of metabotropic glutamate receptors
Neuron
(1992) - et al.
Pharmacological antagonism of the actions of group II and III mGluR agonists in the lateral perforant path of rat hippocampal slices
Br. J. Pharmacol.
(1996) - et al.
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.
(1998)
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