Schild plot
Schild regression analysis, named for Heinz Otto Schild, is a useful tool for studying the effects of agonists and antagonists on the cellular response caused by the receptor or on ligand-receptor binding.
Using a dose-response curve or an equivalent curve with concentration and binding %, it is possible to determine the dose ratio, this is a measure of the potency of a drug; it is obtained by dividing the increased equilibrium constant due to drug inhibition by the equilibrium constant without the drug. A Schild plot is a double logarithmic plot, typically Log(dr-1) as the ordinate and Log[B] as the abscissa. This is because a competitive drug B will have a linear plot with the . These experiments must be carried out on a very wide range (therefore the logarithmic scale) as the mechanisms differ over a large scale, such as at high concentration of drug.
![{\displaystyle dr=1+[B]/K_{B}}](https://wikimedia.org/api/rest_v1/media/math/render/svg/4a09a50395a6e7963545d47e75388442ca176f6b)
Although most experiments use cellular response as a measure of the effect, the effect is, in essence, a result of the binding kinetics; so, in order to illustrate the mechanism, ligand binding is used. A ligand A will bind to a receptor R according to an equilibrium constant :
Although the equilibrium constant is more meaningful, texts often mention its inverse, the affinity constant (Kaff = k1/k−1): A better binding means an increase of binding affinity.
The equation for simple ligand binding to a single homogeneous receptor is
This is the Hill-Langmuir equation, which is practically the Hill equation (biochemistry) described for the agonist binding. In chemistry, this relationship is called the Langmuir equation, which describes the adsorption of molecules onto sites of a surface (see adsorption).
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