Scatchard equation

The Scatchard equation is an equation for calculating the affinity constant of a ligand with a protein. The Scatchard equation is given by

${\frac {r}{c}}=nK_{a}-rK_{a}$

where r is the ratio of the concentration of bound ligand to total available binding sites, c is the concentration of free ligand, and n is the number of binding sites per protein molecule.

K_a is the association (affinity) constant from the equation

$K_{a}={\frac {[Ab-Ag]}{[Ab][Ag]}}$

where Ab is the binding site on the antibody, Ag is a monovalent antigen, and Ag-Ab is antigen-bound antibody.

The Scatchard equation is sometimes referred to as the Rosenthal-Scatchard equation.

Plotting these data, r/c vs r, yields the Scatchard plot with a slope -K_a and a Y-intercept of nK_a. Relative binding affinities between two sites can be distinguished with a line showing identical affinity and a curve showing different affinities.

The Scatchard equation is named after the former MIT Chemistry Department member George Scatchard, an American chemist, 1892–1973.

See

• lecture with derivation (Archived version at web.archive.org)