Scatchard equation

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

$\frac{r}{[L]} = nK_a - rK_a$

where

$r = \frac{[L]_{bound}}{[P]_0}$

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

K_a is the association (affinity) constant from the equation

$K_a = \frac{[LP]}{[L][P]}$

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

Plotting these data, r/[L] 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.

Scatchard plot

File:Scatchard Plot.gif

Scatchard plot

A Scatchard plot is a plot of the ratio of concentrations of bound ligand to unbound ligand versus the bound ligand concentration. It is a method for analyzing data for freely reversible ligand/receptor binding interactions. The plot yields a straight line of slope -K, where K is the affinity constant for ligand binding. The affinity constant is the inverse of the dissociation constant. The intercept on the X axis is Bmax. It is sometimes the case that binding data does not form a straight line when plotted in a Scatchard plot. Such is the case when ligand bound to substrate is not allowed to achieve equilibrium before the binding is measured or binding is cooperative.

In a Scatchard plot, assumptions of independence in linear regression model is violated because B (bound ligand) is used in the X and Y axes. Generally, Scatchard and Lineweaver-Burk plots are outdated. Their original intention was to transform the data into linear representations of the original data such that linear regression methods could be applied. These transformations frequently distort experimental error and can be misleading if results are not accurate.

Further reading

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