Determination of antibody affinity using ELISA

Some new approaches for the determination of antibody affinity were proposed. It was pointed out that the proposed methods are more simple, convenient, precise, and informative than that of Friguet et al. (1985). The approach that allows determination of two-valence antibodies affinity was also proposed. The example of two monovalent antibodies presented in the examined mixture was considered. It allows to estimate the affinity of both kinds of antibodies as well as to determine their concentration relations in the mixture.     

Avidity of bivalent antibodies. Problems of its experimental determination and theoretical evaluation

Some problems of experimental determination or theoretical evaluation of antibody avidity are considered. It was shown that in order to determine the fraction of nonoccupied antibodies in their mixture with the excess of the corresponding antigen which is required to estimate avidity the methods should be used which are more sensitive than ELISA. The available methods did not allow determining the avidity of bivalent antibodies because of many reasons. However, in the recent years new methods were suggested that make it possible to evaluate the avidity of bivalent antibodies and that of the receptors which consist of two binding sites connected by a flexible linker of the known length. Thus, there are all possibilities now for determining the avidity of bivalent antibodies in experiments or by theoretical methods.     

The kinetics of antibody binding to membrane antigens in solution and at the cell surface.

The reaction kinetics of 125I-labelled mouse monoclonal antibodies binding to three cell-surface antigens of rat thymocytes (Thy-1.1, W3/25) were studied. The differences between bivalent and univalent interactions were determined by using antibody in the F(ab')2 or Fab' form and by using antigen in polymeric or monomeric forms. Association rate constants (k+1), dissociation rate constants (k-1) and equilibrium constants were determined. Also, the dissociation kinetics of rabbit antibodies against rat Thy-1 antigen were studied. The major findings were as follows. (i) With F(ab')2 antibody there was no simple relationship between antigen density at the cell surface and extent of bivalent binding. Extensive univalent binding was observed unless the antibody had a high k-1 for the univalent interaction, in which case all binding was bivalent. (ii) k+1 values were similar for F(ab')2 or Fab' antibody, and for the different antibodies were in the range 0.8 x 10(5)--1.1 x 10(6) M-1.s-1. These differences were sufficient to affect the interpretation of serological assays with the different antibodies. (iii) Antibody bound bivalently dissociated much more slowly than that bound univalently. However, the k-1 values for the univalently bound antibody were sufficiently low in most cases that the lifetime of the univalent complex was similar to or greater than the time needed for the assay. Thus the results could be interpreted on the basis of irreversible reactions. The overall conclusion from the study is that for an understanding of the binding of antibody to cell-surface antigens the kinetics of the interaction are of major importance and theories based on equilibrium binding are inappropriate.     

New approach in evaluating affinity of bivalent antibodies by the method of surface plasmon resonance. Theory

Theoretical aspects of the affinity evaluation for the interaction between bivalent receptors (or antibodies) and corresponding ligands (or antigens) are considered. It was shown that the ligand presence in the solution at the stage when the receptor dissociation occurs leads to the increase of the affinity evaluation accuracy. We demonstrated that the analysis of the dissociative curve of the receptor from the chip is not necessary for affinity determination; the analysis of associative curve is sufficient for this purpose. We also suggested a new approach for evaluating the affinity of bivalent receptors (or antibodies) when these reagents are present in the studied solution and the correspondent ligand (or antigen) is immobilized on the chip.     

Analysis of some "insoluble" problems of determining the binding parameters of ligand-receptor interaction and methods of their solving

Some problems of the estimation of the parameters of ligand-receptor interaction (affinity, rate constants, valency, etc.) were considered. It was demonstrated that not only the Scatchard plot but also Klotz plot could be used for determining the parameters of ligand-receptor interaction for two types of binding sites of different affinity. A new approach and new coordinate systems for the estimation of the parameters of ligand-receptor interaction were suggested. It was shown that for the estimation of the affinity of putative monovalent antibodies by ELISA various equations, which are more precise and convenient than the Friguet et al. equations, could be obtained by the transformation of mass action law equation. The problem solution for the estimation by ELISA the affinity of two types of bivalent antibodies with different affinity and their concentrations for the case of the mixture of these antibodies was also suggested. The application of the proposed coordinate of dilution allows to solve the problem of determination of the parameters of ligand-receptor interaction (including antigen-antibody system) for the pre-existing ligand-receptor mixture without their preliminary separation and purification. This approach is especially important for the cases when the receptor is not stable enough to be isolated in the intact form from this mixture. It was shown that the well-known phenomenon of the prozone often observed under the titration of serum antibodies by the method of agglutination may get a mathematical explanation. Analytical solution of the problem of determining the velocity constant and the amount of the end product of the first order irreversible and reversible reaction kinetics was suggested, despite the fact that the process is described by the system of irrational equations. Mehods of asymptotic solution of transcendental irrational equations which describe the dynamics of reactions which mechanisms are subject to the so-called heterogeneous, successive, or competitive models have been considered. These methods permit the finding of the reaction rate constants and the amount of the end product, if the kinetics of the transformation of either initial, or end product of the reaction is known.     

A new method for the evaluation of antibody affinity based on serial dilutions of studied antibody-antigen mixture

A new method for the evaluation of the affinity of bivalent antibodies were suggested. This method is based on the previously published by the author the idea of using so-called coordinates of dilutions. It was shown that the suggested method allows to evaluate the affinity of antibodies with high accuracy using this simple approach. It is supposed that at some conditions the suggested method could have substantial advantages in comparison to the traditional methods. This method allows to analyze situations when antibodies are already in a mixture with antigen, for example in the bloodstream in the case of infections or autoimmune diseases. The method provides useful approach for the evaluation not only antibody affinity, but also the concentration of circulated antigen.     

The binding of monoclonal antibodies to cell-surface molecules. A quantitative analysis with immunoglobulin G against two alloantigenic determinants of the human transplantation antigen HLA-A2.

Monoclonal IgG1 (immunoglobulin G1) PA2.1 and MA2.1 antibodies recognize polymorphic sites of the human transplantation antigen HLA-A2. They are distinguishable because MA2.1 binds HLA-A2 and HLA-B17, whereas PA2.1 binds HLA-A2 and HLA-A28. The affinities of PA2.1-Fab for HLA-A2, three HLA-A2 variants and HLA-A28 are similar and relatively low (1.9 X 10(7) M-1). The affinities of MA2.1-Fab for HLA-A2, three HLA-A2 variants and HLA-B17 are similar and high (1.2 X 10(9) M-1). The difference in affinity is due to the rates of dissociation, which give half-times of dissociation of 290 min for MA2.1-Fab and 4 min for PA2.1-Fab. For both Fab, equilibrium measurements and kinetic determinations gave consistent estimates for affinity. When PA2.1-F(ab)2 or IgG is incubated with cells it reaches equilibrium within 3 h, with most molecules bound bivalently to the cell. Under similar conditions, MA2.1-F(ab)2 does not reach equilibrium and a significant proportion of molecules bound with one and two sites are found. For the lower-affinity antibody (PA2.1), estimates of the binding constants for one- and two-site interactions could be made. By simple Scatchard analysis the avidity of F(ab)2 or IgG is 1.3 X 10(9) M-1, giving an enhancement factor of 68 between bivalent and univalent binding. This is a measure of the equilibrium constant for the interchange between bivalent and univalent binding. Analysis of the results with more realistic models indicates that the actual value is larger (10(3)-10(4) M-1) than 68 M-1. The avidities of F(ab)2 and IgG for HLA-A2 are identical, showing the Fc does not interfere with bivalent binding to cells.     

ELISA-based method for determining the affinity of bivalent antibodies of two specificities in a mixture

The problem of the evaluation of the affinity for two types of bivalent antibodies in a mixture is considered. It is shown that the binding curve in appropriate coordinates can be used to compose either a system of four equations with four unknowns or a system of two equations with two unknown variables. The numerical solution of these equation systems yields affinity constants for both antibodies and the relationship between concentrations of antibodies studied in the mixture.     

Analysis of the interaction of antibodies with immunoglobulin idiotypes on neoplastic B lymphocytes: implications for immunotherapy

We have examined the reactions of a panel of nine monoclonal anti-idiotype antibodies with the surface immunoglobulin in situ on guinea pig L2C leukemic lymphocytes. Equilibrium binding constants were shown to range between 10(7) and 10(8) M-1 for univalent Fab' gamma fragments and between 10(8) and 10(9) M-1 for intact IgG. Saturation of the cell surface binding sites was achieved with 2.9 X 10(5) Fab' gamma molecules/cell and 1.2 X 10(5) IgG molecules/cell for each antibody, a result that is consistent with a bivalent mode of interaction for the IgG. Despite these overall similarities in binding characteristics antibodies showed striking differences in their ability to clear Ig from the cell surface by antigenic modulation in vitro. This suggested differences in the readiness with which the antibodies cross-linked neighboring surface Ig molecules. Such an interpretation was supported by differences in the times required to achieve bivalent binding at 0 degree C, and in the rates at which labeled antibody dissociated from the cell surface in the presence or absence of an excess of unlabeled antibody. The data are consistent with there being two functionally distinct types of anti-idiotype antibody: those that form predominantly intra-Ig bridges, with each antibody Fab being linked to an Fab on one target molecule ("monogamous" binding) and not favoring modulation; and those that form predominantly inter-Ig bridges ("bigamous" binding) and favor modulation. The nature of interaction is presumably dictated by the orientation of the particular idiotope concerned. This distinction could be of great importance in the therapeutic use of anti-idiotype to ablate B cell neoplasms.     

Advantages of two- or polyvalent binding of a receptor to the corresponding ligand in comparison to univalent binding

The features of monovalent and bivalent binding of receptors (or antibodies) with a polyvalent ligand (or with an antigen) are considered. It is shown that the rigid connection of the binding sites of the receptor brings to high increase of binding affinity for the corresponding ligand, but only in case if its epitopes are fully complementary to both sites of the receptor binding. If not, then there is no advantage of the binding of bivalent receptor before univalent binding. If the binding sites of the receptor are connected by a flexible linker, then regardless of location of epitopes of the corresponding ligand there is the successful fastening of receptor and ligand. Exactly the connection by a flexible linker is used by Nature in most cases at constructing of polyvalent receptors.     

The problem of prozone in serum antibody titration and its mathematical interpretation

The question of the mechanism of "prozone" creation was considered from the point of view of the concentrations of free and semi-blocked bivalent antibodies in the mixture of these antibodies with monovalent antigen. Using the so called "coordinates of dilution", suggested by the author earlier, it was possible to calculate the relationships between the concentrations of either free or semi-blocked bivalent antibodies and the dilution of the antigen-antibody mixture. It was shown that dilution of antigen-antibody mixture leads to an increase of the concentration of free bivalent antibodies and simultaneous sharp decrease of the concentration of semi-blocked antibodies. It is suggested, that such a relationship is quite enough for the creation of prozone effect in reactions, when only bivalent antibodies are active and semi-blocked antibodies compete with free antibodies, providing inhibition of the reaction.     

Cell adhesion molecules: detection with univalent second antibody

Identification of cell surface molecules that play a role in cell-cell adhesion (here called cell adhesion molecules) has been achieved by demonstrating the inhibitory effect of univalent antibodies that bind these molecules in an in vitro assay of cell-cell adhesion. A more convenient reagent, intact (divalent) antibody, has been avoided because it might agglutinate the cells rather than blocking cell-cell adhesion. In this report, we show that intact rabbit immunoglobulin directed against certain cell surface molecules of Dictyostelium discoideum blocks cell-cell adhesion when the in vitro assay is performed in the presence of univalent goat anti-rabbit antibody. Under appropriate experimental conditions, the univalent second antibody blocks agglutination induced by the rabbit antibody without significantly interfering with its effect on cell-cell adhesion. This method promises to be useful for screening monoclonal antibodies raised against potential cell adhesion molecules because: (a) it allows for the screening of large numbers of antibody samples without preparation of univalent fragments; and (b) it requires much less antibody because of the greater affinity of divalent antibodies for antigens.     

Novel and simple ELISA-based method for antibody affinity determination

New coordinates for antibody affinity determination by ELISA are suggested. The suggested approach is very simple but at the same time it is more convenient and is deprived of the drawbacks inhered in the earlier suggested methods. The examples of antibody affinity determination by the suggested methods for both simulative and experimental binding curves are considered. It was demonstrated that the suggested methods allow getting more precise values of antibody affinity.     

Expression of multivalency in the affinity chromatography of antibodies. Appendix: Derivation and evaluation of equations for independent bivalent interacting systems in quantitative affinity chromatography.

The expression of multivalency in the interaction of antibody with immobilized antigen was evaluated by quantitative affinity chromatography. Zones of radioisotopically labeled bivalent immunoglobulin A monomer derived from the myeloma protein TEPC 15 were eluted from columns of phosphorylcholine-Sepharose both in the absence and presence of competing soluble phosphorylcholine. At sufficient immobilized phosphorylcholine concentration, the variation of elution volume of bivalent monomer with soluble ligand was found to deviate from that observed for the univalent binding of the corresponding Fab fragment. In addition, the apparent binding affinity of the bivalent monomer increased with immobilized antigen density. Use of equations relating the variation of elution volume with free ligand concentration for a bivalent binding protein allowed calculation of microscopic single-site binding parameters for the bivalent monomeric antibody to both immobilized and soluble phosphorylcholine. The chromatographic data not only demonstrate the effect of multivalency on apparent binding affinity but also offer a relatively simple means to measure microscopic dissociation constants for proteins participating in bivalent interactions with their ligands.     

A new method of determining antibody heterogenicity (among them, monoclonal) by affinity

In this assay, cellulose antigenic immunosorbent was used as solid phase and preparations of polyclonal and monoclonal bivalent antibodies as antibodies. The new method is based on the assumption that definite relationship exists between some of free molecules and some of bound active centers of antibodies in the process of the interaction of antibodies and antigenic immunosorbent. Groups of antibodies with different affinity were detected in hyperimmune horse serum, in immune mouse serum and in the monoclonal preparation, which, on the one hand, confirms our earlier data and, on the other hand, demonstrates the possibility of using the new method for determination of antibody affinity.     

Model immune complexes formed between monoclonal antibodies and a novel bivalent affinity label

Murine monoclonal anti-dinitrophenyl antibodies were produced by lymphocyte hybridomas and incubated with a new bivalent affinity label, bis-(dinitrofluorobenzene)-pimelic acid amide. Stable dimers were isolated from the resulting mixture of immune complexes in high purity. Experiments were performed to show that the immune complexes are covalently cross-linked through antibody active sites. Model dimers were also formed with varying ratios of monoclonal anti-hapten antibodies based on immunoglobulin isotype. The potential uses of these complexes for analyses of the biological activites of immune aggregates are discussed.     

Attack on neoplastic cell membranes by therapeutic antibody

Mouse monoclonal antibody is not well fitted to destroying tumour cell targets. Complement and cellular effectors are inefficiently recruited, the cells can undergo antigenic modulation, antigen-negative mutants can arise, and the tumour-bearing subject can amount an immune response against the therapeutic antibody.This paper describes the preparation of two chimeric antibody derivatives designed to cirvumvent some of these problems. The first derivative is FabFc, prepared by linking Fab' from monoclonal antibody to Fc from human IgG. The bismaleimide linking agent forms a thioether bond with an SH group released by reduction of SS bonds in the hinge of each constituent. The second derivative is bisFabFc, formed by a bismaleimide in this case joining two FabFc molecules via a free SH in the Fc hinge of each. As regards antibody activity against target cells bisFabFc can be univalent (one active, one inactive Fab arm), bivalent, or bispecific (with each Fab arm directed against a different cell surface antigen). Its juxtaposed dual Fc regions are designed to promote cooperative binding of effectors.Some preliminary characterization in vitro has employed antibodies of anti-idiotypic specificity directed against guinea-pig L₂C leukaemic B lymphocytes. The parent mouse IgG1 antibody failed to invoke complement cytotoxicity or antibody-dependent cellular cytotoxicity, while the chimeric derivatives yielded good killing in both systems. In complement lysis bivalent bicFabFc outperformed univalent, which in turn outperformed the FabFc monomer.     

Determination of the binding parameters for a pre-existing antigen-antibody mixture

A new method, which allows to evaluate parameters of interaction between antibodies (or receptors) and an antigen (or ligand) is suggested. The method is based on the use of so-called coordinates of dilution suggested by the author earlier. Representation of the data of the titration curves for the mixtures of antibodies (or receptors) and antigen (or ligand) in these coordinates allows one to determine the affinity of interaction and the concentration of antigen (or ligand), which can reversibly block antibodies (or receptors). Simple formulas, which allow to estimate which part of paratopes or bivalent antibodies is free and which part is blocked by the antigen, depending on dilution of the considered system, are also suggested. Such a method could be useful for characterization of infection and autoimmune processes when the antigen and antibodies circulate together in the bloodstream.     

Theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody: application to histamine release from basophils.

We present a theory of equilibrium binding of symmetric bivalent haptens to cell surface antibody in the presence or absence of monovalent hapten. Bivalent haptens can link together antibodies to form linear chains or rings on cell surfaces. We show how to calculate the amount of any complex of bound bivalent hapten, monovalene fraction of antibody involved in complexes made up of two or more antibodies, i.e., the fraction of antibody that is cross-linked (Xpoly). We treat the case when the antibody on the cell surface, which is specific for the hapten, is homogeneous. For this case we prove a number of general properties about Xpoly: 1) Xpoly approaches zero at both high and low bivalent hapten concentration. 2) Xpoly becomes a maximum when the bivalent hapten concentration equals Amax, where Amax = 1/H + B/2. H is twice the equilibrium constant for the binding of a single hapten site to a single antibody site and B is the monovalent hapten concentration. 3) a plot of Xpoly vs the log of the bivalent hapten concentration is symmetric about the maximum value of Xpoly. We use these and other properties of Xpoly in this paper to clarify the relationship between cross-link formation and histamine release.     

Enhanced modulation of antibodies coating guinea pig leukemic cells in vitro and in vivo. The role of Fc gamma R expressing cells.

We have investigated the antigenic modulation induced by a number of antibody fragments and derivatives directed against the idiotype of the surface Ig of the L2C guinea pig B lymphoblastic leukemia, and studied the effects upon such modulation of the simultaneous presence of cells expressing Fc gamma receptors (FcR). In vitro studies confirmed previous work showing that antibody bivalency is required to induce modulation in vitro in simple systems. However, in the presence of isolated Kupffer cells, Fc-containing univalent antibodies were found to induce significant antigenic modulation, and the modulation induced by intact IgG was also found to be more rapid and extensive. Fragments that did not contain Fc regions behaved similarly in the presence or absence of Kupffer cells. Further investigations demonstrated that all three classes of human FcR can mediate modulation enhancement, and suggest that the mechanism involves indirect cross-linking of cell surface Ag via the antibody and effector cell FcR. In vivo studies showed that univalent antibody derivatives containing Fc regions did induce antigenic modulation, but that this was significantly reduced in comparison with bivalent antibodies, confirming their potential advantage for immunotherapy.