Scatchard equation
The Scatchard equation is an equation used in molecular biology to calculate the affinity and number of binding sites of a receptor for a ligand. It is named after the American chemist George Scatchard.
Equation
Throughout this article, denotes the concentration of a receptor-ligand complex, the concentration of free receptor, and the concentration of free ligand. Let n be the number of binding sites for ligand on each receptor molecule, and let represent the average number of ligands bound to a receptor. Let Kd denote the dissociation constant between the ligand and receptor. The Scatchard equation is given byBy plotting / versus, the Scatchard plot shows that the slope equals to -1/Kd while the x-intercept equals the number of ligand binding sites n.
Derivation
''n''=1 Ligand
When each receptor has a single ligand binding site, the system is described bywith an on-rate and off-rate related to the dissociation constant through Kd=''koff/k''on. When the system equilibrates,
so that the average number of ligands bound to each receptor is given by
which is the Scatchard equation for n=1.
''n''=2 Ligands
When each receptor has two ligand binding sites, the system is governed byAt equilibrium, the average number of ligands bound to each receptor is given by
which is equivalent to the Scatchard equation.
General Case of ''n'' Ligands
For a receptor with n binding sites that independently bind to the ligand, each binding site will have an average occupancy of /. Hence, by considering all n binding sites, there willligands bound to each receptor on average, from which the Scatchard equation follows.