Schild equation

Rearrangement of these equations leads to the Schild equation (Equation 6.52) as well. 

However, the testing of a wide range of concentrations of an allosteric antagonist would show the saturation of the allosteric binding site as revealed by an approach to a maximal value for the antagonism. The Schild equation for an allosteric antagonist is given by (see Section 7.8.3)... 

This leads to the logarithmic metameter form of the Schild equation ... 

In the presence of a competitive antagonist, the EC50 of the agonist dose-response curve will be shifted to the right by a factor equal to the dose ratio. This is given by the Schild equation as [B]/Kb-I-1, where the concentration of the antagonist is [B] and KB is the equilibrium dissociation constant of the antagonist-receptor complex ... 

This is the Schild equation, which was first stated and applied to the study of competitive antagonism by H. O. Schild in 1949. It is probably the most important single quantitative relationship in... 

More usually, both (r - 1) and [B] are plotted on logarithmic scales (the Schild plot). The outcome should be a straight line with a slope of unity, and the intercept on the x-axis provides an estimate of log KB. The basis for these statements can be seen by expressing the Schild equation in logarithmic form ... 

How might the value of pA2 be interpreted in these terms If the Schild equation is obeyed,... 

The relationship between the magnitude of the shift (as expressed by the concentration ratio) and the antagonist concentration obeys the Schild equation. 

The initial near-parallel displacement of the curves in Figure 1.26B raises the question of whether the Schild equation would be obeyed under these conditions. If we consider the two concentrations of agonist that give equal responses before and during the action of the antagonist ([A] and r[A], respectively, where r is the concentration ratio) and repeat the derivation set out in Section 1.5.2 (but using Eq. (1.55) rather than (1.49)), we find that the expression equivalent to the Schild equation is ... 

Hence, the Schild equation would apply, albeit over a limited range of concentrations that is determined by the receptor reserve. Moreover, the value of KB obtained under such conditions will... 

A corollary is that a demonstration of the Schild equation holding over a small range of concentrations should not be taken as proof that the action of an antagonist is competitive. Clearly, as wide as practicable a range of antagonist concentrations should be tested, especially if there is evidence for the presence of spare receptors. 

Note, too, the convergence at low agonist concentrations of the curves plotted in Figure 1.27. The antagonist becomes less active when the response is small, because there are fewer receptors in the AR form available to combine with C. Again, in contrast to the other kinds of antagonism that have been described, there is no initial parallel displacement of the curves (even if many spare receptors are present), and the Schild equation is never obeyed. 

The Schild equation is thus obtained, where [D]/[d] is the dose ratio. From equation (2.17), [AJj, the antagonist concentration necessitating a doubling of the agonist concentration to achieve the pure agonist effect, is... 

Clark plot A graphical method of estimation of the affinity of a competitive antagonist from a linear plot of the Caddum-Schild equation. In practice, any advantages of this plot have been overlooked, and the logarithmic form of this equation is almost universally used in the Schild plot class The taxonomic group immediately ranking above the order and below the phylum. 

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