Use of the average antibody-antigen bond concept and probability theory to simplify modeling of linear and circular antibody-antigen complex formation.

We illustrate use of a simple approach to describe the equilibrium interactions of mixtures of monoclonal antibodies and antigens. This procedure is based on elementary concepts in probability theory and is readily suited to describing interactions of antibodies and antigens which form circular as well as linear complexes. The method is also suited to describing the inhibitory effects of antibodies which compete for overlapping epitopes and an example is provided to show how the procedure can be used to describe the interactions of antibodies which inhibit circular complex formation. We also outline simple strategies for preparing computer programs to simulate binding of antigens to defined antibody mixtures. The methods described should facilitate design of immunoassay procedures based on the use of defined mixtures of monoclonal antibodies.