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 (K = k/k): 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 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).
 is the total number of binding sites, and when the equation is plotted it is the horizontal asymptote to which the plot tends; more binding sites will be occupied as the ligand concentration increases, but there will never be 100% occupancy.  The binding affinity is the concentration needed to occupy 50% of the sites; the lower this value is the easier it is for the ligand to occupy the binding site.
The binding of the ligand to the receptor at equilibrium follows the same kinetics as an enzyme at steady-state (Michaelis–Menten equation) without the conversion of the bound substrate to product.
Agonists and antagonists can have various effects on ligand binding.  They can change the maximum number of binding sites, the affinity of the ligand to the receptor, both effects together or even more bizarre effects when the system being studied is more intact, such as in tissue samples. (Tissue absorption, desensitization, and other non equilibrium steady-state can be a problem.)
A surmountable drug changes the binding affinity:
* competitive ligand: 
* cooperative allosteric ligand: 
A nonsurmountable drug changes the maximum binding:
* noncompetitive binding: 
* irreversible binding
The Schild regression also can reveal if there are more than one type of receptor and it can show if the experiment was done wrong as the system has not reached equilibrium. <br/>