The theoretical consequences of ligand multivalency are introduced in the context of quantitative affinity chromatography; in this regard Chapter 1 provides the foundations upon which the rest of the thesis is developed. First, the problem of allowance for the effects of gel partitioning of the solute in quantitative affinity chromatography is re-examined, and new expressions are derived for the description of results obtained by frontal chromatography. Secondly, the theoretical expressions have been rearranged into forms suitable for determination of the relevant interaction parameters by simple graphical analysis, a procedure illustrated with results obtained in a partition equilibrium study of the NADH-dependent elution of the tetravalent enzyme, rabbit muscle lactate dehydrogenase, from Blue Sepharose.
Chapter 2 explores the potential of the theoretical expressions developed in Chapter 1 by noting that the linearized form of the quantitative affinity chromatographic expression is essentially a general counterpart of the Scatchard analysis which takes into account the valence of the ligand. Use of this multivalent Scatchard form is first demonstrated by application to binding data obtained by exclusion chromatography of mixtures of Dextran T2000 and concanavalin A (a bivalent ligand). A recycling partition equilibrium study with Sephadex G-100 as gel phase then provides a quantitative evaluation of the interaction between haemoglobin and a monoclonal mouse antihaemoglobin antibody preparation in order to emphasize the ability of the methodology to consider collectively binding results obtained with a range of acceptor concentrations. Finally, the use of the generalized Scatchard analysis to assess acceptor site homogeneity is illustrated by reappraisal of results for the binding of glyceraldehyde-3-phosphate dehydrogenase to erythrocyte membranes.
Chapter 3 sees a return to quantitative affinity chromatography in a study designed to examine the validity of considering successive interactions between an affinity matrix and a multivalent partitioning solute to be governed by a single intrinsic binding constant. To that end a value of 6,000M-1 has been obtained for the initial binding of the horse liver alcohol dehydrogenase enzyme to Blue Sepharose (pH 7.5, I 0.15), an interaction which leads to a three- to four-fold enhancement of the subsequent interaction of that molecule with the matrix. Although this evidence of positive cooperativity in the enzyme-matrix interaction points to a deficiency in quantitative affinity chromatography theory based on equivalence and independence of these interactions [Nichol, L.W., Ward, L.D., and Winzor, D.J. (1981) Biochemistry 20, 4856-4860 DOI:10.1021/bi00520a008], it is shown that such treatment leads to a much better description of the experimental situation than that provided by an alternative analysis based on cooperativity of enzyme-matrix interactions to the extent that only a single enzyme-matrix complex exists [Kyprianou, P., and Yon, R.J. (1982) Biochem. J. 207, 549-556 ].
The affinity chromatographic theme continues in Chapter 4 with a further methodological advancement that allows characterization of systems involving macromolecular ligands. This potential is demonstrated by using concanavalin A and ovalbumin as multivalent solute and macromolecular ligand, respectively, in an experimental study with Sephadex G-50 as affinity matrix. The effect of galactose on the chromatographic behaviour of Eicinus communis phyto-haemagglutinin on Sepharose 4B is also used to establish that quantitative affinity chromatography on polysaccharide matrices affords an unequivocal means of characterizing the interactions of lectins with monosaccharides in solution. Although no general solution to the problem of ligand multivalency in quantitative affinity chromatography has been found, an experimental protocol is devised for the situation in which the partitioning solute (lectin) is univalent.
Effects of antigen multivalency on procedures for the analysis of immuno-assays are examined in Chapter 5 on the basis of the theoretical expressions developed in Chapters 1 and 2. In section A quantitative relationships are generated which provide the basis for more rigorous logit-log analyses of radioimmunoassays in which the antigen is multivalent, and an additional, theoretically superior, linear transform of the basic expression is developed. Simulated binding data for a tetravalent antigen system are then used to demonstrate (i) the curvilinearity of the conventional Scatchard plot for such a system despite the homogeneity of binding sites, and (ii) the application of the various linear transforms involving logarithmic functions. Results obtained in a solid-phase radioimmunoassay for triiodothyronine are also presented to provide, for that system at least, experimental justification of the implicit assumption that the antigen-antibody interactions may be described in terms of a single intrinsic association constant. An enzyme-linked immunoassay of ferritin is then used to illustrate the possibility that a linear Scatchard plot may be obtained with a multivalent antigen under conditions where steric factors restrict participation of an antigen molecule to a single interaction with immobilized antibody. The potential of solid- phase immunoassay procedures as a means of evaluating binding constants for antigen-antibody interactions is examined in Section B. In an enzyme-linked immunosorbent assay developed for the herbicide, paraquat, an association constant of 2.1(±0.2)×105M-1 (pH 7.4, I 0.16) is evaluated for the interaction between this small monovalent antigen and its elicited monoclonal mouse IgG antibody. A similar value of 2.7(±0.3)×105M-1 is likewise obtained for the interaction of paraquat with the Fab fragment of the IgG antibody. The extension of the procedure developed in this section to quantitative analysis of interactions involving multivalent antigens is also explored; and expressions are presented to enable an experimenter to achieve this end.
In Chapter 6 theoretical consideration is given to the interaction of a bivalent solute with particulate receptor sites, not only from the viewpoint of quantitatively describing the binding behaviour but also from that of the kinetics of solute release upon infinite dilution of a solute-receptor mixture. In the latter regard a general expression is derived which describes the time-dependence of the amount of solute bound as a function of two rate constants for the stepwise dissociation of crosslinked solute-receptor complex, and a thermodynaraic parameter expressing the initial ratio of singly-linked to doubly-linked solute-receptor complexes. An experimental study of the interaction between Sephadex and concanavalin A is then used to illustrate application of this recommended theoretical approach for characterizing the binding behaviour and dissociation kinetics of a bivalent solute for a system in which all solute-receptor interactions may be described by a single intrinsic association constant. Published results on the interaction of phosphorylase 𝑏 with butyl-agarose are also shown to comply with this simplest model of the bivalent solute hypothesis; but those on the interaction between IgG dimers and Fc receptors require modification of the model by incorporation of different intrinsic association constants for the successive binding of receptor sites to a bivalent solute.