BINDING-EQUATIONS FOR INTERACTING SYSTEMS COMPRISING MULTIVALENT ACCEPTOR AND BIVALENT LIGAND - APPLICATION TO ANTIGEN-ANTIBODY SYSTEMS

Consideration is given to the reversible interaction of a bivalent ligand, B, with a multivalent acceptor, A (possessing f reactive sites) which leads to the formation of a series of complexes, AiBj, comprising networks of alternating acceptor and ligand molecules. A binding equation is derived on the basis of a site association constant, k, defined in terms of reacted site probability functions. This equation, which relates the binding function, r (the moles of ligand bound per mole of acceptor) to the concentration of unbound ligand, mb, is used to show that plots of r vs. 2kmB constructed with fixed but different values of kmA intersect at the point (mB = 1 2k, r = f 2) where the extent of reaction and the concentrations of those complexes for which j i = f 2 attain maximal values. Corresponding Scatchard plots are shown by numerical example to be non-linear, their second derivative being positive for all r. It follows that such deviations from linearity cannot be taken alone as evidence for site heterogeneity in cross-linking systems. The binding equation obtained directly is shown to be identical with that obtained with f = 2 by summation procedures involving the general expression for concentrations of complexes, mA, formulated in terms of appropriate statistical factors. In this way, previous findings on precipitation and gel formation in cross-linking systems are correlated with the present development of binding theory. © 1979.