A mathematical model on the analysis of a one-ligand, one-binding group system when an unknown amount of endogenous ligand is present.

In the study of ligand-receptor interaction, binding studies using radiolabelled ligands are usually conducted and results analyzed according to the method originally described by Scatchard. When significant levels of endogenous ligands are present, assumption of a linear relationship between the bound-to-free ratio and the bound ligand may be erroneous and chemical methods have been described to resolve this problem. We present a mathematical approach to the system, using a method based on multiple regression of binding data. A three-dimensional graphic representation of the binding data analogous to the original Scatchard plot is proposed. When the endogenous and the exogenous ligands are different, the linear regression model is applicable only if their affinity constants are known. Non-linear curve-fitting computer programs should be used to resolve this problem when these constants are unknown.