This paper presents the equations and methodology for the measurement and interpretation of apparent dissociation constants for polyclonal populations of antibodies, where antigen is kept trace relative to antibody concentration. Surface plasmon resonance is used to determine K(d)s for the binding of anti-DNA antibodies to trace amounts of DNA antigen on a chip. Since the approach taken relies on equilibrium measurements, kinetic mass transport artifacts are avoided. The apparent K(d) is a weighted average of all the K(d)s for the clonally related subpopulations within the polyclonal pool, where each weighting factor is the relative titer (fractional presence) of the subpopulation. Titration curves appear as if there is one monoclonal population with that titer-weighted-average K(d). Implications of changes in the antibody affinity distribution within the population are discussed. The equations described herein provide a better physical understanding of the apparent K(d) that is obtained when a heterogeneous population of receptors is titrated against a trace ligand.
Copyright 1999 Academic Press.