Schild Analysis
Experimentally, a KB is estimated by studying the interaction of an agonist and antagonist over a wide range of antagonist concentrations (the wider, the better). This is necessary because drugs that are not reversible competitive antagonists may appear to be so within a narrow range of concentrations. If the antagonist is truly competitive, it should produce parallel rightward displacement [i.e., no change in midpoint slope (m) occurs] of the E/log[A] curves with no change in the maximal response (a) (see Fig. 8ae). This is intuitively obvious, since the antagonist is merely decreasing the probability that an agonistreceptor interaction will occur, an effect that can always be overcome by increasing the agonist concentration. The analysis involves fitting experimentally derived values of r at different concentrations of antagonist to the following form of Eq. (10) (34) (See Fig. 8f):
Adherence of the data to this equation is judged by the finding of a linear plot with unit slope. Under these conditions the intercept on the Xaxis
Figure 8
Schild analysis: homogenous receptor system. Antagonism of the b2adrenoceptormediated relaxant effects of isoprenaline by the competitive antagonist ICI 118, 551, in the guinea pig isolated trachea. The data shown is from a single experiment. In each tissue (ae), the first isoprenaline E/[A]
curve performed was a control (
circle.gif
118,551 at concentrations of 3 nM (
bcircle.gif
); the second, was in the presence of ICI
), 30nM( A ), 100 nM( E ), triangle.gif and 300 nM (
bsquare.gif
). Note the concentrationdependent parallel rightward displacement of the control curves. (f) illustrates these displacements (r values) in Schild plot form. The plot has a slope of unity and the intercept on the Xaxis yields an estimate of 9.24 for the pKB (log10KB).
(log10[B]) gives an estimate of KB. If the slope (n) is not statistically different from the theoretically expected value of 1, then the data should be refitted to Eq. (11) with the slope constrained to unity. When n is significantly different from 1, the intercept gives an estimate of pA2 ( log10KB/n). The pA2 is an empirical estimate of antagonist affinity and equates to the negative logarithm of the concentration of antagonist that produces a twofold rightward shift (r = 2) of the control E/[A] curve. Nonlinearity and slopes other than unity can result from many causes. For example, a slope of greater than 1 may indicate incomplete equilibration with the antagonist or removal of the antagonist from the biophase. A slope that is significantly less than 1 may indicate removal of the agonist by a saturable uptake process, or it may result from the interaction of the agonist with more than one receptor. In the latter case the Schild plot may be nonlinear with a clear inflexion. All of these potential complicating factors have been described in detail previously by Kenakin (35) as have experimental manipulations and mathematical models that allow reliable antagonist affinity information to be extracted from such "nonclassic" data (see next section).
It should be emphasized that the finding that experimental data adheres to the Schild equation over a wide range of concentrations does not prove that the agonist and antagonist act at the same site. All that may be concluded is that the data is consistent with the hypothesis of mutually exclusive binding. Nevertheless, the estimation of antagonist affinities by Schild analysis currently forms the basis of classification schemes for the major hormone receptors, and its application will undoubtedly contribute significantly to future classifications.
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