Theory of affinity electrophoresis : Evaluation of the effects of protein multivalency, immobilized ligand heterogeneity and microdistribution and determination of effective concentration of immobilized ligand

Abstract

Equations are presented which describe the effects of multivalency of protein molecules on electrophoretic mobility in an affinity gel with respect to the possibility of the quantitative evaluation of the strength of protein-ligand interactions under these conditions. At low concentrations of immobilized ligand ( c im), fairly exact K and L/n values can be obtained, even for multivalent proteins from linear plots ( K = intrinsic dissociation constant of the protein-mobile ligand complex; L = intrinsic dissociation constant of the protein-immobilized ligand complex; n = the number of independent, identical ligand-binding sites in the protein molecule). At higher c m conventional plotting of variables obtained by affinity electrophoresis yields curvilinear plots usually deviating only slightly from straight lines, the evaluation of which yields usually apparent K and L values lower than the true values, i.e. the strength of interaction is overestimated under these conditions. The importance of c m for the degree of restriction of multivalent interactions with immobilized ligand is stressed. No simple means of estimating n by affinity electrophoresis has been found. For a bivalent protein with two independent non-identical ligand-binding sites, apparent K and L values are obtained which lie between the true K 1, K 2 or L 1, L 2 values characterizing the two sites. Effective c im values can be obtained by following the dependence of the mobility of a protein in affinity gels containing a fixed c im on the protein concentration. The effects of non-homogeneity of immobilized ligand molecules ( i.e., the presence of different types of immobilized ligands within the gel) are quantitatively evaluated. The effects of steric non-homogeneity of the distribution of immobilized ligand molecules within the gel are considered qualitatively. The results of some experiments aimed at verifying the equations describing the effects of immobilized ligand concentration and microdistribution on the values of K and L for bivalent lectins are presented; experimental approaches for testing the other theoretical conclusions reached are suggested. Most of the equations derived should also be applicable, after minor modifications, for the quantitative description of affinity chromatography systems.