Mathematical model for determining the binding constants between immunoglobulins, bivalent ligands, and monovalent ligands.

This paper analyzes the equilibria between immunoglobulins ( R), homo-bifunctional ligands ( L), monovalent ligands ( I), and their complexes. We present a mathematical model that can be used to estimate the concentration of each species present in a mixture of R, L, and I, given the initial conditions defining the total concentration of R, L, I, and four dissociation constants ( $$ K_{\rm{d}}^{\rm{inter}} $$, $$ K_{\rm{d}}^{\rm{intra}} $$, $$ K_{\rm{d}}^{\rm{mono}} $$, and α). This model is based on fewer assumptions than previous models and can be used to describe exactly a broad range of experimental conditions. A series of curves illustrates the dependence of the equilibria upon the total concentrations of receptors and ligands, and the dissociation constants. We provide a set of guidelines for the design and analysis of experiments with a focus on estimating the binding constants from experimental binding isotherms. Two analytical equations relate the conditions for maximum aggregation in this system to the binding constants. This model is a tool to quantify the binding of immunoglobulins to antigens and a guide to understanding and predicting the experimental data of assays and techniques that employ immunoglobulins. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]