Determination of the affinity of high- and low-affinity antibodies, which are in a mixture, using ELISA and the method of non-linear regression

It was shown that application of the method of non-linear regression for the solution of the equation, which relates the fraction of free antibodies in a mixture and antigen concentrations, allows to determine the affinity constants for two antibodies in a mixture. Such method is easier and more accurate than the suggested by us earlier method, which use the numerical solution of the appropriate four equations, that describe the relations between the experimental data obtained by ELISA, competing antigen concentration, and values of antibody affinity. In addition, the proposed method allows using much less quantity of experimental measurements without diminishing of the accuracy for the affinity constants evaluations.     

Determination of antibody affinity by ELISA. Theory

New approaches for the measurement of antibody affinity by ELISA are suggested and considered theoretically. It was shown that not only more precise and more convenient in comparison to that suggested earlier, but also more informative graphical representation of the experimental data in the appropriate coordinate could be used for evaluation of antibody affinity. The following cases were considered: (i) determination of antibody affinity for one kind of univalent antibodies, (ii) determination of antibody affinity for one kind of bivalent antibodies, (iii) determination of antibody affinity for two kinds of univalent antibodies, which are in a mixture, and (iv) determination of antibody affinity for two kinds of bivalent antibodies, which are in a mixture. Advantages and disadvantages of the different approaches are discussed.     

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.     

Analysis of the discrete structure of antibodies by affinity and antigen-binding capacity

Immune sera are a mixture of different groups of antibodies belonging to the same class of immunoglobulins, but differing in their affinity. The graphic analysis and numerical methods permit the determination of the size and affinity of each group of antibodies. Differences in affinity are manifested as differences in antigen-binding capacity. The antigen-binding capacity index, calculated as the product of the association constant multiplied by the concentration of the active centers of antibodies, is proposed.     

Purification of individual tRNAs using a monoclonal anti-AMP antibody affinity column

A murine monoclonal anti-AMP antibody affinity matrix was used for isolation of individual species of amino acid transfer nucleic acids (tRNAs). The antibodies had been prepared using 5'-AMP covalently attached to bovine serum albumin as antigen and exhibited high affinity for 5'-AMP but greatly reduced affinity for 3'-AMP. Native uncharged tRNAs that terminate in a 5'-AMP group on the amino acid acceptor arm of the molecule bind tightly to the anti-AMP affinity matrix, whereas aminoacylated tRNAs are not retained. This allows separation of a particular tRNA species as its aminoacyl derivative from a complex mixture of uncharged tRNAs under very mild conditions.     

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.     

Determination of the concentration of ligand-specific molecules, found in mixtures with ligand-nonspecific molecules

A new method, which allows determination of the concentration of ligand-specific molecules in a mixture of these molecules with biochemically similar but ligand-unspecific molecules, is suggested. The method is based on a partial exhaustion of the mixture on a column with immobilized ligand and determination of the part of ligand-specific molecules presented in exhausted mixture. The concentration of monoclonal antibodies specific to bovine serum albumin in a commercial "Sigma" preparation and concentration of polyreactive immunoglobulins in a commercial "Sigma" preparation of bovine immunoglobulins were determined by suggested method.     

Determination of antibody affinity by using antigenic and antibody immunosorbents

To determine the affinity of the active centers of antibodies, cellulose immunosorbents for antibodies and antigens have been used. The fixation of serum proteins on the sorbent, the interaction of fixed antibodies with a monovalent antigen and the graphic analysis of the results thus obtained allows one to assess not only the concentration of the effective active centers on the sorbent, but also all known characteristics of antibody affinity: the average association constant K0, the common association constant Kt, the geometric association constant Kg, the average association constants which determine the affinity of different antibody groups. The use of antigenic immunosorbent permits one to determine the value of the average internal association constant K0. The determination of antibody affinity in hyperimmune antiplague sera by means of immunosorbents and red blood cells coated with capsular antigen has resulted in obtaining similar values of affinity indices.     

Demonstration of an in vivo generated sub-picomolar affinity fully human monoclonal antibody to interleukin-8

The high specificity and affinity of monoclonal antibodies make them attractive as therapeutic agents. In general, the affinities of antibodies reported to be high affinity are in the high picomolar to low nanomolar range and have been affinity matured in vitro. It has been proposed that there is an in vivo affinity ceiling at 100 pM and that B cells producing antibodies with affinities for antigen above the estimated ceiling would have no selective advantage in antigen-induced affinity maturation during normal immune responses. Using a transgenic mouse producing fully human antibodies, we have routinely generated antibodies with sub-nanomolar affinities, have frequently rescued antibodies with less than 10 pM affinity, and now describe the existence of an in vivo generated anti-hIL-8 antibody with a sub-picomolar equilibrium dissociation constant. This confirms the prediction that antibodies with affinities beyond the proposed affinity ceiling can be generated in vivo. We also describe the technical challenges of determining such high affinities. To further understand the importance of affinity for therapy, we have constructed a mathematical model to predict the relationship between the affinity of an antibody and its in vivo potency using IL-8 as a model antigen.     

Immunochemical quantification of procion red HE-3B used as ligand in affinity chromatography.

The quantification of Procion Red HE-3B used as a ligand in affinity chromatography for proteins is reported. It's based on an enzyme-linked immunosorbent assay using antibodies against the dye. Polyclonal antibodies were classically prepared after conjugation of the dye on KLH and injection into rabbits. The development of the assay was based on the competitive inhibition between hemoglobin-dye complex and free dye. The sensitivity of this method was about 1000-times higher than a classical spectrophotometric assay, and was modulated by some chemical substituents attached on the native dye. It was demonstrated that the assay was applicable to the determination of dye traces that may be released from dye affinity sorbents. Moreover, the quantification of the dye was successfully applied to proteins that are being purified from a dye affinity column.     

Accurate determination of the oxidative phosphorylation affinity for ADP in isolated mitochondria

Background

Mitochondrial dysfunctions appear strongly implicated in a wide range of pathologies. Therefore, there is a growing need in the determination of the normal and pathological integrated response of oxidative phosphorylation to cellular ATP demand. The present study intends to address this issue by providing a method to investigate mitochondrial oxidative phosphorylation affinity for ADP in isolated mitochondria.

Methodology/Principal Findings

The proposed method is based on the simultaneous monitoring of substrate oxidation (determined polarographically) and phosphorylation (determined using the glucose - hexokinase - glucose-6-phosphate dehydrogenase - NADP⁺ enzymatic system) rates, coupled to the determination of actual ADP and ATP concentrations by bioluminescent assay. This enzymatic system allows the study of oxidative phosphorylation during true steady states in a wide range of ADP concentrations. We demonstrate how the application of this method allows an accurate determination of mitochondrial affinity for ADP from both oxidation (K_mVox) and phosphorylation (K_mVp) rates. We also demonstrate that determination of K_mVox leads to an important overestimation of the mitochondrial affinity for ADP, indicating that mitochondrial affinity for ADP should be determined using phosphorylation rate. Finally, we show how this method allows the direct and precise determination of the mitochondrial coupling efficiency. Data obtained from rat skeletal muscle and liver mitochondria illustrate the discriminating capabilities of this method.

Conclusions/Significance

Because the proposed method allows the accurate determination of mitochondrial oxidative phosphorylation affinity for ADP in isolated mitochondria, it also opens the route to a better understanding of functional consequences of mitochondrial adaptations/dysfunctions arising in various physiological/pathophysiological conditions.     

Enzyme kinetic assays with surface plasmon resonance (BIAcore) based on competition between enzyme and creatinine antibody

A procedure is described which allows the characterization of enzyme by a hybrid approach using an enzyme and an antibody. The presented method is related to the affinity determination of antibodies by the 'affinity in solution' procedure for BlAcore. The antibody is used as an indicator for the concentration of substrate, which is also the antigen. A mixture of enzyme, substrate and antibody is incubated, and an aliquot of this solution is injected periodically into a flowcell containing immobilized substrate, which is bound by the antibody, but not cleaved by the enzyme. The chosen initial concentration of substrate inhibits the binding of antibody to the immobilized substrate by 90%. During the enzymatic reaction, increased amounts of antibody bind to the surface, as the substrate concentration is decreased. With this method, the cleavage of creatinine with creatinine iminohydrolase (6 mU/ml) was monitored for up to 11 h. A recently developed monoclonal antibody against creatinine was used as the indicating protein. For the calculation of enzyme activity, the signals were compared with a calibration curve for inhibition of antibody binding to the chip by creatinine in solution.     

Traditional ELISA methods for antibody affinity determination fail to reveal the presence of low affinity antibodies in antisera: an alternative approach

Traditionally used methods of antibody affinity determination either by ELISA or by the surface plasmon resonance technique do not allow detection of the presence of low‐affinity antibodies in samples of high‐affinity antibodies. In this paper we demonstrate the possibility to reveal their presence and to determine the affinities of both categories of antibodies as well as the ratio of their concentrations. This is especially important since by using traditional methods for antibody affinity evaluation the admixture of low‐affinity antibodies in a sample diminishes the accuracy in determination of specific antibody affinity. In addition, the presence of an admixture of low‐affinity antibodies may be an important biological characteristic of the system under study; their revelation and the evaluation of their binding parameters may be valuable in many cases for obtaining a more complete characterization of the binding properties of the multiple antibodies generated in an immune response. Copyright © 2009 John Wiley & Sons, Ltd.     

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.     

Immunoenzyme method of sequential saturation for determining antigens using the model of insulin

The method for the determination of insulin by means of the enzyme immunoassay, based on the use of insulin-peroxidase conjugates, has been developed. In this assay the scheme of the successive saturation of the active sites of antibodies is used. The antigenic properties of two conjugates differing in the method of their preparation are compared. The conjugates were obtained by the covalent binding of peroxidase, oxidized in its carbohydrate component, with insulin (conjugate 1) or hexamethylene-diamine-modified insulin (conjugate 2). The conjugates represented a mixture of oligomers differing in their molecular weight. Conjugate 1 possessed higher affinity to antibodies and higher enzymatic activity than conjugate 2. The method for evaluating the quality of antisera to insulin used in the assay has been proposed. The time of the insulin assay is 5-16 hours, the limit of insulin detection is 5 microU/ml, the variation factor is 3-12%.     

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.     

Monoclonal antibodies for carcinoembryonic antigen and related antigens as a model system: determination of affinities and specificities of monoclonal antibodies by using biotin-labeled antibodies and avidin as precipitating agent in a solution phase immunoassay

A general method is described for the determination of affinity constants and antigen cross-reactivities of monoclonal antibodies. The method employs biotin-labeled antibody, radiolabeled antigen, and avidin as a precipitating agent in a homogeneous phase, competitive radioimmunoassay. This method eliminates incomplete or variable precipitation of antigen-antibody complexes often encountered in immunoassays in which monoclonal antibodies are employed. Using this assay system, we were able to rapidly determine the affinity constants for a number of monoclonal antibodies elicited to carcinoembryonic antigen (CEA). In the preceding paper it was shown that five of the monoclonal antibodies recognized distinct epitopes on CEA. In antigen-binding experiments with these five monoclonal antibodies, the percent of radiolabeled CEA bound in antibody excess ranged from 30 to 92%. The CEA cross-reacting antigens, normal cross-reacting antigen (NCA), and tumor-extracted, CEA-related antigen (TEX) were significantly bound by one, and to a lesser degree, by two of the five antibodies. Two antibodies did not bind significant amounts of NCA or TEX. In inhibition studies, the amount of unlabeled CEA leading to 50% inhibition of 125I-labeled CEA-binding was in the range of 3.7 to 760 ng per tube. The amount of TEX showing the same degree of inhibition was 23-fold greater than the amount of CEA for two antibodies and 351-fold greater than the amount of CEA for a third antibody. The affinity constants for CEA were in the range of 1.0 x 10(8) to 5.1 x 10(10) M-1. The affinity constants for NCA and TEX, determined for one of the antibodies, were three orders of magnitude lower in comparison to CEA. The heterogeneity of radiolabeled CEA as indicated by the low fraction bound by one of the monoclonal antibodies is shown to be most probably an artifact resulting from radioiodination damage. The application of the approach described in this report should eliminate the problems most commonly encountered in the determination of affinity constants for monoclonal antibodies or the use of monoclonal antibodies in competitive, homogeneous-phase immunoassays.     

The HSA affinity of warfarin and flurbiprofen determined by fluorescence anisotropy measurements of camptothecin

The determination of affinity of warfarin and flurbiprofen to human serum albumin (HSA) by fluorescence anisotropy measurements of carboxylate form of camptothecin (CPT-C) is the subject of this paper. A simple method based on measurements of fluorescence anisotropy of CPT-C allows to determine the affinity constant of CPT-C to HSA by computation of the fraction of bound CPT-C molecules with HSA It was observed, that adding of competing drug to plasma significant reduces the rate of increase of CPT-C fluorescence anisotropy with increase of albumin concentration and, the affinity constant of CPT-C to HSA decreases. The hypothesis of interactions between competing drug and CPT-C is presented. The results of these studies suggest that CPT-C displaces other drug from protein binding site and the degree of this displacement depends on concentration of drug and drug-HSA binding affinity. The presented in this paper biosystems research allows to estimate the affinity constant of warfarin and flurbiprofen. It was also confirmed that despite that most of drugs bind predominantly to Site I or Site II of HSA (only one of these sites is high-affinity site), at elevated concentrations, part of drug molecules can be bound to low-affinity site of HSA.