Scatchard equation

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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.

Ka 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 this data, r/c vs r, yields the Scatchard plot with a slope -Ka and a Y-intercept of nKa. 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.