Competitive Antagonism in Pharmacology: A Proposed Single Step Evaluation
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0092-8615/97 Copyright 0 1997 Drug Information Association Inc.
COMPETITIVE ANTAGONISM IN PHARMACOLOGY A PROPOSED SINGLE STEP EVALUATION* LISAM A ~ F I SAND S
CORINNE
THOMAS-HAIMEZ
Statistical Department, Servier Research Institute, Suresnes, France
PR
JEANMACCARIO
Inserm U 169, Villejuif Cedex, France
The inhibitory capacity of a competitive antagonist is measured using the pA2 (the negative logarithm of the antagonist dissociation constant). The conventional two-step procedure, based on Schild’s regression, neglects a portion of the errors. New single step methods are proposed based on nonlinear regression on dose-effect. Whereas verification of the competition hypothesis o f e n inte$eres with pA2 estimation, the development of improved nonlinear models could explain and partially incorporate the reasons for noncompetition. The improvements are of two kinds: I . Pharmacological, based on the inclusion of suspected pharmacological mechanisms such as spare receptors or transduction into a nonlinear fixed-effects model (with examples from the literature); and 2. Experimental, incorporating biovariability as a random effect into a mixed-effects model. Key Words: pA2; Competitive inhibition; Schild’s regression; Nonlinear regression; mixed models
INTRODUCTION AN ANTAGONIST IS considered competitive and reversible when it binds to the same recognition site on the receptor as the agonist and if an equilibrium exists between the agonist and antagonist so that an increase in the concentration of one decreases the binding of the other. Unlike the agonist, the antagonist has no intrinsic activity. The power of a competitive antagonist is evaluated by the pA2, or negative logarithm, of the concentration of antagonist causing the agonist to double its concentration in order to obtain the same effect. It can be shown that the pA2 is also equivalent to the negative logarithm of the dissociation constant of the antagonist with the receptor (-log Kantagonlst), representing its capacity to move from the receptor site.
*Based on a presentation made at the DIA Workshop “Statistical Methodology in Non-clinical and Toxicological Studies,” March 25-27, 1996, Bruges, Belgium. The article presented was called “The pA2 in pharmacology: a need for a new way of estimation.” Reprint address: Lisa MaYofiss, Institut de Recherches Servier, 11 rue des Moulineaux, 92150 Suresnes, France.
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Lisa Maibfss, Corinne Thomas-Haimez, and Pr Jean Maccario
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The pA2 is used to evaluate antagonism and compare drugs with an antagonistic action in preclinical screening. Some questions, however, remain unanswered: Should the pA2 be estimated if the competition hypothesis is not verified? and What is the best method, given the many disadvantages of the conventional Schild procedure (l)?
VERIFICATION OF THE COMPETITION HYPOTHESIS In practice, the pharmacological event is based on a set of agonist dose-response curves in the absence or presence of several c
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