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

This paper analyzes the equilibria between immunoglobulins (R(2)), homo-bifunctional ligands (L(2)), 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(2), L(2), and I, given the initial conditions defining the total concentration of R(2), L(2), I, and four dissociation constants (K(d)(inter), K(d)(intra), K(d)(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.