Evaluation of equilibrium constants by affinity chromatography

Theoretical expressions are derived for affinity chromatography of systems comprising an acceptor A with one binding site for attachment to a functional group X on the column matrix and one site for interaction with a small ligand B that specifically affects its elution. From a general relationship covering all possible interactions between A, B and X simpler expressions are derived for affinity systems in which only two equilibria operate. Methods are suggested whereby these simpler systems may be characterized in terms of the two pertinent equilibrium constants and the concentration of matrix-bound constituent. The means by which the theory may be adapted to affinity chromatography of acceptors with multiple binding sites for ligand is also illustrated. Results of partition experiments on the Sephadex G-100-lysozyme-d-glucose system in acetate-chloride buffer (I=0.17m), pH5.4, are used to demonstrate the feasibility of evaluating quantitatively affinity-chromatography interactions. Values of 30m(-1) and 1.2x10(6)m(-1) are obtained for the equilibrium constants for the reactions of lysozyme with glucose and Sephadex respectively, there being only an occasional binding site in the polysaccharide matrix (approximately 1 in 10(5) glucose residues). In a second experimental study the phytohaemagglutinin from Ricinus communis is subjected to frontal chromatography on Sepharose 4B in the presence of different concentrations of d-galactose, the results illustrating some of the difficulties and limitations that are likely to be encountered in quantitative studies of affinity-chromatographic systems.