The Schild regression in the process of receptor classification

Abstract

The history and derivation of the Schild equation is reviewed as well as the conditions under which the intercept of a Schild regression (the pA 2, an empirical quantity) can be considered to be an estimate of the equilibrium dissociation constant of the antagonist for the receptor (K B). This parameter is of value in the classification of receptors. To be considered competitive (and, therefore, to be described in molecular terms by a K B), an antagonist must produce parallel displacement of agonist concentration–response curves with no alteration in the maximal response and thereby yield unambiguous dose ratios of agonist which are independent of agonist concentration. These dose ratios (dr) then can be utilized in the Schild equation (log (dr − 1) = n ∙ log [B] − log K B, where [B] is the molar concentration of antagonist) in the form of a regression of log (dr − 1) on log [B]. If the regression is linear and has a slope of unity, the blockade is consistent with simple competitive antagonism and the intercept can be considered an estimate of the K B. Experimentally, the slope is a parameter critical to the assessment of competitivity. While a slope significantly different from unity may indicate that an antagonist is not competitive, it also may indicate that nonequilibrium conditions exist in the experimental procedures. The importance of uptake mechanisms for agonists, with regards to producing underestimations of antagonist potency, are reviewed along with a concise model by Furchgott which conveniently incorporates these concepts. The possible significance of Schild regression slopes < 1 and > 1 are discussed along with caveats regarding Schild regressions with slopes of unity but erroneous estimates at K B. Short discussions of the use of selective agonists, experiments in vivo, and the assessments of receptor differences from estimates of K B also are given.