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.     

亲和层析法用于噬菌体抗体库的筛选

本研究报道一种基于固定化金属亲和层析(IMAC)的噬菌体抗体库液相筛选方法。将纯化的带有His标签的抗原与噬菌体抗体库混合,噬菌体抗体与抗原充分结合后再加入亲和介质,使噬菌体抗体抗原复合物通过His标签与介质结合,然后通过充分洗涤去除非特异性噬菌体抗体,最后将特异性噬菌体抗体洗脱下来,感染TG1,进行下一轮筛选。整个筛选过程中抗原与抗体的结合在液相中完成,不仅消除了固相介质对抗原表位的影响,也更有利于噬菌体抗体与抗原的充分作用。将此方法应用于HEV NE2蛋白特异性人源噬菌体抗体的筛选,抗原竞争ELISA,阳性血清阻断,可溶性单链抗体表达检测及测序结果表明,最终获得2个特异性人源抗体。     

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.     

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 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.     

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.     

High-affinity binding measurements of antibodies to cell-surface-expressed antigens

A simple method that allows affinity measurements of antibodies to integral membrane proteins is described. Kinetic Exclusion Assay was used to determine the concentration of free antibody that remains in solution after equilibrium has been established between the antibody and the cell-surface-expressed antigen, from which the equilibrium dissociation constant (Kd) was determined. It eliminates the requirement for soluble antigen and modifications such as radio-labeling or fluorescent labeling of the antibody. For one of the cell-surface-expressed antigens, it was determined that the affinity of the antibody to the cell-surface-expressed antigen was similar to that of the purified, soluble form of the antigen. In addition to the simplicity of the approach, the method provides a true measure of the affinity/avidity of the antibody to the native form of cell-surface-expressed targets, including antigens that cannot be produced in soluble forms, and to unknown cell surface antigens.     

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.     

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.     

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.     

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.     

Determination of rate constants of antigen-antibody reaction. A theory

A new method of determination of rate constants for antigen-antibody interactions is proposed. This method is based on a solid phase immunoenzymatic analysis of the dynamics of elution of immobilized antigen-bound antibodies in the presence of a free antigen. The kinetics of this process is described by a system of differential equations, whose solution results in expression defining the dynamics of antibody interaction with immobilized and free antigens. Simple formulas were derived for the calculation of the rate and equilibrium constants for the antibody-antigen reaction on the basis of experimental kinetic curves. The use of theoretical kinetic curves for antibody elution showed that these formulas reflect with a high degree of accuracy the kinetic properties of the reaction under study.     

Serologic aspects of IgG4 antibodies. II. IgG4 antibodies form small, nonprecipitating immune complexes due to functional monovalency

Human IgG4 antibodies directed against phospholipase A, the P1 antigen from Dermatophago?des pteronyssinus extracts, and cat albumin were found unable to cross-link antigen. Previously, it was demonstrated that IgG4 antibodies, in contrast to IgG1 antibodies, did not cross-link Sepharose-bound antigen and antigen added in solution. To eliminate the possibility that this phenomenon was caused by preferential binding of both IgG4 Fab fragments to the solid-phase-bound antigen, cross-linking of antigen was studied in a fluid-phase system. In this test, incapability of IgG4 antibodies to bridge two antigens was also found. As a result of such a phenomenon, it is expected that immune complexes formed by IgG4 antibodies will be considerably smaller than complexes formed by IgG1. This was confirmed by analysis of the molecular size profiles of IgG1- and IgG4-containing immune complexes in sucrose-density gradients. Moreover, IgG1 was able to precipitate antigen in a radioimmunoprecipitation test, whereas precipitation was not demonstrable by the same amount of IgG4 antibodies. Even 3% polyethylene glycol 8,000 did not precipitate the small IgG4-containing immune complexes efficiently. The antibodies studied were of a high-affinity type, and there was no significant difference in association constants between IgG1 and IgG4 antibodies. Therefore, we were not able to confirm observations reported in the literature that the IgG4 subclass is associated with a low-affinity antibody response; probably, the affinity of the IgG4 antibodies was underestimated by other investigators because of the polyethylene glycol precipitation technique used to separate antibody-bound and free antigen. Our findings stress the point that IgG4 antibodies take a special place in the immune response upon chronic exposure to antigen.     

基于生物膜干涉技术检测PDL1抗体与PDL1抗原的亲和力

生物膜干涉（biolayer interferometry,BLI）技术可对抗体与抗原的相互作用进行亲和力、动力学的全面分析。在抗体克隆筛选、动力学常数测定中对链霉亲和素（streptavidin,SA）生物传感器的需求量较大,但目前鲜有关于SA传感器重复利用的报道。基于BLI技术、再生SA生物传感器建立一种使用再生后的传感器检测PDL1抗体与PDL1抗原亲和力的方法。通过将生物素化的PDL1抗原偶联至SA生物传感器上,再与单链抗体、双价单链抗体、完整抗体和双特异性抗体这4类PDL1抗体结合,计算抗原抗体的亲和力常数,利用甘氨酸（10 mmol·L^-1,pH 1.7）再生SA传感器,再次进行分子间相互作用力分析。结果显示,重复性相对标准偏差（relative standard deviation,RSD）均值为6.87%,批间重复性RSD为0.82%,稳定性RSD均值为6.13%,说明运用甘氨酸再生后的SA生物传感器测分子间的亲和力数据可靠、重现性好、稳定性高,再生后的传感器可继续用于本样品的实时、无标记的抗原抗体相互作用力分析。BLI技术可节省检测成本,为SA传感器的重复利用提供理论依据。     

Primary antibody-Fab fragment complexes: a flexible alternative to traditional direct and indirect immunolabeling techniques.

Immunolabeling with immune complexes of primary and secondary antibodies offers an attractive method for detecting and quantifying specific antigen. Primary antibodies maintain their affinity for specific antigen after labeling with Fab fragments in vitro. Incubation of these immune complexes with excess normal serum from the same species as the primary antibody prevents free Fab fragments from recognizing immunoglobulin. Effectively a hybrid between traditional direct and indirect immunolabeling techniques, this simple technique allows primary antibodies to be non-covalently labeled with a variety of reporter molecules as and when required. Using complexes containing Fab fragments that recognize both the Fc and F(ab')2 regions of IgG, we show that this approach prevents nonspecific labeling of endogenous immunoglobulin, can be used to simultaneously detect multiple antigens with primary antibodies derived from the same species, and allows the same polyclonal antibody to be used for both antigen capture and detection in ELISA.     

A rapid method for determining dynamic binding capacity of resins for the purification of proteins

Biolayer interferometry is a novel method for quantifying macromolecules, such as proteins, in solution. The presence of other, non-binding molecules does not interfere with quantification, which allows one to measure the concentration of the molecule of interest in a crude mixture. Here we apply this method to determining the dynamic binding capacity of affinity resins.     

Antigen modulation of antibody forming cells: the relationship between direct plaque size, antibody secretion rate and antibody affinity.

Using the mathematical theory of direct plaque growth, we have analyzed the expected variation of plaque size with IgM affinity and secretion rate. We use the theory to comment on recent effector cell blockage experiments and show how the theory can be used to determine the change in the secretion rate of a single antibody-forming cell subjected to blockage by a multivalent antigen. We also argue, using the mathematical theory, that under the usual experimental conditions employed in the plaque assay, cells that produce low affinity IgM antibodies will give rise to smaller plaques than cells that produce high affinity IgM antibodies.     

A mathematical model for germinal centre kinetics and affinity maturation

We present a mathematical model which reproduces experimental data on the germinal centre (GC) kinetics of the primed primary immune response and on affinity maturation observed during the reaction. We show that antigen masking by antibodies which are produced by emerging plasma cells can drive affinity maturation and provide a feedback mechanism by which the reaction is stable against variations in the initial antigen amount over several orders of magnitude. This provides a possible answer to the long-standing question of the role of antigen reduction in driving affinity maturation. By comparing model predictions with experimental results, we propose that the selection probability of centrocytes and the recycling probability of selected centrocytes are not constant but vary during the GC reaction with respect to time. It is shown that the efficiency of affinity maturation is highest if clones with an affinity for the antigen well above the average affinity in the GC leave the GC for either the memory or plasma cell pool. It is further shown that termination of somatic hypermutation several days before the end of the germinal centre reaction is beneficial for affinity maturation. The impact on affinity maturation of simultaneous initiation of memory cell formation and somatic hypermutation vs. delayed initiation of memory cell formation is discussed.