Fundamentals of Immunology - Lecture Course by M. V. Skok - Kyiv 2002

Chapter I. Immunochemistry

Lecture 5. Antigen-Antibody Interaction and Methods for Its Study

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where k₁ is the association constant, and k₂ is the dissociation constant of the antigen-antibody (AgAb) complex. Their ratio characterizes the efficiency of complex formation and is referred to as the affinity constant, k_a. The rates of the forward and reverse reactions can be calculated. When the reaction reaches equilibrium, v₁ = v₂ and k_а can be calculated as

This equation shows that k_а is expressed in reciprocal moles and is equal to the inverse of the free antigen concentration at which half of the antibody binding sites are occupied by the antigen at equilibrium, [Ab] = [AgAb].

Specific binding is considered significant when k_а exceeds 10⁵ M^-1, meaning that The rate of complex formation exceeds the rate of its dissociation by 5 orders of magnitude. For high-affinity antibodies, k_а > 10⁸ M^-1.

The affinity constant is a crucial characteristic of antibodies, and therefore, The ability to calculate it is essential. Several mathematical approaches and equations have been developed for this purpose, with the Scatchard equation being the most widely used. It relies on such concepts as:

[B] (bound) - the concentration of bound antigen;

[F] (free) - the concentration of free antigen;

n - the number of antibody binding sites (an intact antibody has two binding sites, while a Fab fragment has one).

The Scatchard equation:

Imagine that we gradually add an antigen to an antibody solution. Initially, all the antigen binds, and [F] << [B]. As more antigen is added, [B] increases, but [F] increases as well, causing the [B]/[F] ratio to decrease. Graphically, this is expressed as a linear dependence of B/F on B, and k_а can be calculated as the slope of the line (Fig. 3A).

According to the proposed equation, the Scatchard plot is a straight line. However, when analyzing serum antibodies, it turns out that experimental Scatchard plots are non-linear, meaning that as the antigen concentration increases, k_а decreases (Fig. 3B). This phenomenon is due to the heterogeneity of serum antibodies. Serum antibodies are a mixture of antibodies with varying affinities for the antigen. When the first portions of antigen are added to the antibody solution, the highest-affinity antibodies react first, requiring the lowest antigen concentration. As antigen concentrations rise, lower-affinity antibodies begin to bind it, making the actual Scatchard plot an integral curve of k_а values for all serum antibody populations (which can number up to 300 for a single antigenic determinant). The classical, linear Scatchard plot can only be obtained with monoclonal (myeloma or hybridoma) antibodies. Additionally, one must account for the fact that we are dealing with bivalent antibodies (or pentavalent in the case of IgM). The binding of the two Fabs is not equivalent: the binding of the first Fab can either facilitate or hinder the binding of the subsequent ones.

Most natural Antigens are not monovalent; instead, they carry multiple antigenic determinants. Therefore, under physiological conditions, we speak not of affinity in the pure sense, but of an integral, averaged measure of antigen-antibody affinity known as avidity. In reality, avidity exceeds the sum of its constituent affinities, which is easily demonstrated through mathematical equations.

Thermodynamically, k_а is determined by the difference in Free energy ΔG between the unbound states of the antigen and Introduction/42.html">Antibodies and Their state after complex formation. R is the gas constant, and T is the absolute Temperature. For the Antigen-Antibody Reaction, ΔG = -31.5 to -43.2 kJ/mol (compared to -229.53 kJ/mol for The formation of two covalent H-O bonds in a Water molecule); that is, the reaction proceeds with a decrease in Free Energy and is energetically favorable. The excess energy is utilized for the necessary Conformational Changes in both the antigen and the antibody to achieve optimal complementarity. Given that both the antigenic determinants and the antibody combining sites exhibit high atomic mobility, it becomes clear that they mutually induce conformational adjustments in each other. When two antigenic determinants bind to two antibody combining sites, the sum of the released energy is proportional to the sum of Logarithms, meaning that k_а values are not added together, but multiplied.

The increase in avidity during multivalent antigen-antibody binding is of great physiological significance for enhancing the binding efficiency of Bacteria, their toxins, Viruses, and so forth.

Experimental Determination of k_а.

According to the Scatchard equation, K_а can be determined if one can measure the concentrations of free and bound antigen at several points of antibody-antigen titration. Several experimental approaches can be used for this purpose.

1. Equilibrium dialysis.

This method was proposed to determine the K_а of Antibody Binding to low-molecular-weight haptens that can dialyze across a semipermeable membrane. The Essence of the method is that the antigen is placed into two chambers separated by a membrane, allowing concentration equilibrium to establish between them. Upon adding antibodies to chamber 1, a portion of the antigen binds to them, causing the concentration of free antigen to drop. This triggers the diffusion of free antigen from chamber 2 into chamber 1, establishing a new equilibrium. Now, the antigen concentration in chamber 2 equals the free antigen concentration in chamber 1, and The amount of bound antigen can be calculated as the difference between the initial concentration of added antigen and the free antigen. By adding different concentrations of antibodies, one can find the concentrations of free and bound antigen at multiple points and construct a Scatchard plot. It was precisely this method that was first used to calculate K_a for myeloma antibodies.

2. Fluorescence quenching.

This method is used when the binding of an antigen alters the optical parameters of antibodies, such as quenching the fluorescence of Tryptophan residues in the Active Site. Each value of the antigen concentration corresponds to a specific fluorescence intensity, making it possible to calculate the concentrations of free and bound antigen.

Methods for determining K_a are part of a large group of techniques used to study antigen-antibody interactions, which are also employed to detect the presence and quantity of antigens and antibodies in biological mixtures. They are essential, for example, in diagnosing various physiological states of the Organism. Thus, Pregnancy testing often relies on determining trophoblast-specific globulin in a woman's Blood or urine. Diagnosing many endocrine disorders requires precise measurement of specific hormone levels. In myocardial infarction, one of the earliest indicators of necrotic processes is the appearance of Heart Muscle Myoglobin in the blood, the level of which correlates with the extent of the lesion. Immunochemical methods are preferable here because they are based on the high Specificity of the antigen-antibody interaction. The Use of Monoclonal Antibodies has helped to standardize these methods to the maximum extent, making them reliable and reproducible. On the otherخص, detecting antibodies in sera or other biological fluids is also frequently necessary, for instance, to evaluate the success of vaccination. Testing for antibodies against the AIDS virus is the primary diagnostic assay for infection with this pathogen. Consequently, the detection of antigens and antibodies is frequently required in clinical practice. It demands highly sensitive methods, as most Hormones, growth factors, and antibodies are present in the body in trace amounts. For this very reason, much attention has been devoted in recent decades to developing sensitive methods for antigen and antibody quantification.

Methods of Immunochemical Analysis.

1. Precipitation.

Classic precipitation in solution can be observed in the presence of a polyvalent antigen and at least bivalent antibodies. Upon the gradual addition of antigen to antibodies (or vice versa) at a specific ratio, the solution becomes turbid due to the formation of a precipitate. With the further addition of antigen (or antibodies), the precipitate redissolves. The appearance of a precipitate is driven by the formation of high-molecular-weight complexes—a spatial lattice composed of numerous antigen and antibody molecules. In the presence of either antigen excess or antibody excess, low-molecular-weight soluble complexes are formed (Fig. 4). The antigen-antibody ratio at which precipitation is observed is referred to as the equivalence point.

Observing and recording a precipitate in solution is not always straightforward, which led to The Development of gel precipitation methods. This is a highly visual approach. While it lacks the sensitivity of modern radioimmunoassay or enzyme-linked immunosorbent assays, it played a historically significant role in immunochemical analysis.

The core Principle of the method is that the antigen-antibody reaction takes place in an Agar or agarose gel, whose structure allows the diffusion of both antigens and antibodies. Upon reaching the equivalence point within the gel, a precipitation arc is formed, which can be easily visualized with the naked eye or enhanced with specific stains. Changing the concentration of the antigen or antibody in the added solution alters THE POSITION OF the precipitation arc. The shape and position of the arc can be used to estimate the approximate concentration of antibodies or antigens, their homogeneity (multiple arcs form when several antigens and antibodies are present), as well as the cross-reactivity of various antigens.

There are several modifications of this method.

1) Single radial immunodiffusion (Mancini method), where one of the components is incorporated directly into the gel, while the other is placed into a well cut into the gel. The diffusion of the antigen (or antibody) from the well forms a precipitation ring upon reaching the equivalence point, the radius of which depends on the concentrations of the antigen and antibodies.

2) Ouchterlony double immunodiffusion in gel. Both components are placed into wells cut into the gel and diffuse toward each other. Precipitation arcs are formed, whose position and shape depend on the concentrations of the antigen and antibodies.

3) Immunoelectrophoresis—a combination of Electrophoresis and immunoprecipitation. In the classical approach, the antigen is placed into a well, from which it migrates under METABOLISM/18.html">The Influence of an electric current, separating into fractions within the gel. Antibodies are placed into a trough cut parallel to the gel. The antigen fractions diffuse toward the antibodies and form precipitation arcs, the number and position of which characterize the specific antigen and antibodies. This approach is used to analyze antigen mixtures in biological fluids or complex bacterial antigens.

4) A modification of immunoelectrophoresis is electroimmunodiffusion (rocket immunoelectrophoresis), in which the antigen is separated electrophoretically, and the gel into which it subsequently diffuses contains antibodies. In this case, precipitation arcs take on a rocket-like shape; the higher the antigen concentration, the taller the “rocket.”

5) Crossed immunoelectrophoresis involves initially separating the antigen by electrophoresis, after which an electric current is applied in a perpendicular direction into a gel containing antibodies. This is a more quantitative method because the area under the peak can be used to calculate the antigen concentration.

2. Agglutination.

When antibodies are added to a particulate (corpuscular) antigen rather than a soluble one (such as bacterial Cells), an agglutinate is formed instead of a precipitate. Under natural conditions, this is a mechanism for destroying bacteria, but in experimental settings, it can be used to detect the presence of specific antigens or antibodies in a mixture. Erythrocytes are frequently used as particulate antigens. These red Blood Cells form an agglutinate that is clearly visible to the naked eye. Naturally, this approach only detects antibodies directed against erythrocyte antigens. To broaden the applicability of this method, erythrocytes can be modified with a desired antigen. Thus, the hemagglutination assay makes it possible to detect antibodies against any soluble antigen. Instead of erythrocytes, colored beads can be used—such as polymer latex particles modified with the target antigen; this is referred to as latex agglutination.

3. Label-based analysis of antigens and antibodies.

Agar precipitation methods allow for the detection of microgram quantities of antigen. A revolutionary step in immunochemical analysis was the introduction of radioactive labels in the 1970s, which increased the sensitivity of the method by six orders of magnitude, making it possible to detect picogram quantities of antigen.

The first isotope used to label Proteins was ¹³¹I. Working with it was complex and hazardous because this isotope emits high-energy gamma radiation and has a very short half-life of 8 days. Later, researchers transitioned to the more convenient ¹²⁵I isotope, which emits soft gamma and beta radiation and has a half-life of a month and a half. It readily binds to Tyrosine residues in proteins and remains widely used in experiments today. If a protein synthesized within studied cells needs to be labeled, ³⁵S-labeled Methionine is used; it is added to the culture medium and incorporated into Newly synthesized proteins—a technique known as a biosynthetic label.

Radioimmunoassay (RIA) is a powerful METHOD FOR DETERMINING k_a. Its principle relies on the fact that an antigen labeled with a radioactive isotope can be easily and quantitatively identified within any mixture. The task is to separate the bound antigen from the free antigen. Solution-phase precipitation is often used for this purpose, where the precipitate is separated from the soluble antigen by centrifugation. The formation of a precipitate can be facilitated by using secondary antibodies (anti-immunoglobulin antibodies) or by precipitating the complex with ammonium sulfate. This approach has certain limitations, as some antigens are also precipitated by ammonium sulfate. Alternatively, insoluble particles (most commonly agarose beads) can be used, which are conjugated with an agent that binds antibodies and their immune complexes with antigens. Such agents include proteins A and G. These proteins are components of staphylococcal Cell walls and possess the property of strongly binding specific classes of IMMUNOGLOBULINS via their Fc region. The experiment is conducted as follows: first, specific antibodies are added to the antigen and incubated together for a period to allow complex formation; then, agarose beads coupled with protein A (or G) are added, and the antigen-antibody complexes are separated from the unbound antigen by centrifugation. The bound antigen is measured in the precipitate, while the free antigen is measured in the supernatant.

Over the past twenty years, sorption-based immunological methods have become widespread. Their core principle is that one of the Components of the antigen-antibody system is adsorbed onto a solid phase (such as polystyrene or nitrocellulose). The antigen-antibody complex is likewise formed on the solid phase and can be separated from the free antigen through a simple washing step.

While radioimmunoassays are highly sensitive, they remain hazardous to the personnel performing them, requiring specialized radiation protection measures and strict protocols for radioactive waste disposal. The radioactive decay of the isotopes also imposes limitations on their shelf life and use. Consequently, substantial efforts have been directed toward developing a method that matches the sensitivity of radioimmunoassays while being more convenient and safe. Enzyme immunoassay methods proved to be the solution.

The essence of these methods is that antibodies are covalently conjugated with an enzyme whose reaction product can be easily detected via color development, fluorescence, changes in pH, or electrical potential.

The advantage of an enzymatic label over a radioactive one is that Enzymes are:

- harmless to human health;

- stable upon storage;

- the reaction progresses over time, and the amount of accumulated reaction product increases accordingly.

The most common enzymes used as labels are peroxidase and alkaline phosphatase. The substrate for peroxidase is hydrogen peroxide. Typically, a so-called chromogenic substrate is added to the reaction, which is converted in a coupled reaction by the hydrogen peroxide decomposition product. This results in a colored product that can be identified visually, under a Microscope, or photometrically, depending on the type of experiment. Examples of such substrates for peroxidase include o-phenylenediamine, diaminobenzidine, and α-chloro-1-naphthol.

Experimental Design.

1. Labeled Antigen. Determination of Antigen Concentration in Biological Material.

The labeled antigen is mixed with specific antibodies in various ratios to obtain a binding curve and determine the amount of antigen required to bind all the antibodies (Fig. 5A). An antigen concentration is chosen such that antibody binding falls within the linear range of the curve, typically 50% saturation. Next, having mixed the labeled antigen and antibodies at this ratio, unlabeled antigen is added to generate a competitive binding curve of the labeled antigen by the unlabeled one (Fig. 5B). If a sample containing an unknown amount of antigen is now added instead of the unlabeled antigen, the amount of antigen in the sample can be calculated using the competition curve.

In this method, much like determining k_a, it is necessary to separate the labeled antigen bound to antibodies from the free antigen. Precipitation or sorption approaches are used for this purpose as well. Typically, a radioactively labeled antigen is used.

2. Labeled Antibodies. Determination of Antibodies.

Currently, the most common approach is enzyme-linked immunosorbent assay, widely known by the acronym ELISA. Its core principle involves sorbing an antigen onto The surface of a polystyrene microplate well. This sorption is non-specific and follows physicochemical laws. The Nature of the bonds between proteins and the plastic surface remains unclear. If the amount of antigen is insufficient to cover all potential binding sites, the second step involves blocking the well with a neutral protein (such as serum albumin). A solution containing antibodies is then added. The antibodies bind to the sorbed antigen, while the unbound ones are washed away (using a special buffer or simply water). Next, the bound antibodies must be detected. For this purpose, enzyme-labeled secondary antibodies (antibodies directed against the primary antibodies) are typically used. They are also incubated in the wells, the unbound ones are washed away, and a substrate solution is added. The enzyme begins to convert the substrate, and the accumulation of the colored product is proportional to the amount of bound secondary antibodies, and consequently, primary antibodies as well (Fig. 6A).

Antigen can also be quantified using this experimental setup. If a soluble antigen is added along with the primary antibodies, it will compete with the sorbed antigen for antibody binding. Consequently, fewer antibodies will bind to the solid phase the more soluble antigen is added (Fig. 6B).

For antigen detection, the so-called sandwich method is also widely used, where primary antibodies are sorbed onto plastic, a sample containing the antigen is added, and then secondary antibodies directed against a different antigenic determinant of the antigen are introduced to bind it as well. These antibodies may be directly labeled or detected using secondary labeled antibodies (Fig. 6C). The amount of bound "top" antibodies is proportional to the amount of antigen in the sample.

The purpose of using secondary antibodies is to amplify the final signal recorded in the immunoassay and, accordingly, increase the sensitivity of the method, since multiple molecules of labeled secondary antibodies can bind to a single primary antibody molecule. If the use of secondary antibodies is undesirable for any reason, alternative Amplification systems are employed, such as proteins A and G, or the currently very popular Avidin-biotin complementary pair.

Avidin is a chicken egg white protein characterized by its ability to tightly bind vitamin H (biotin). Streptavidin, derived from Streptomyces species, is also commonly used. Biotin can be easily attached to antibodies, and its presence can be detected using labeled avidin (streptavidin). The method can be further elaborated by adding another step: biotinylated antibodies, streptavidin, and biotinylated peroxidase. The more steps involved, the greater the signal amplification, but also the higher the potential for complications. Overall, immunoassays are generally less sensitive than radioimmunoassays, but optimal setups have achieved comparable sensitivity, especially when utilizing fluorescent or chemiluminescent substrates. Today, a wide range of commercial products is available to perform any assay variant, and specialized equipment has been developed for rapid high-throughput sample Processing, with many processes fully automated.

THE PRINCIPLE OF sorptive EIA is not limited to standard ELISA formats. Alternative solid phases can be used instead of polystyrene microplates, such as nitrocellulose, which also non-specifically binds proteins. In this case, the method is called dot blot. The use of nitrocellulose as a carrier has allowed the combination of immunochemical techniques with electrophoresis, known as Western blot. Here, antigens are separated into fractions by Polyacrylamide gel electrophoresis, transferred onto nitrocellulose by simple diffusion or electroblotting, and then detected using antibodies following the same principles as in ELISA. The key difference is that Western blotting utilizes alternative chromogenic substrates—those that yield an insoluble product remaining bound to the nitrocellulose.

Latex beads can also serve as the solid phase, onto which antigens or antibodies are sorbed. Finally, similar approaches are applied when antigens are naturally associated with a solid phase, such as On the surface or inside cells. This principle forms The basis of immunocytochemistry and flow cytometry.

If the antigen is located on The Cell surface, the cells are treated with antibodies on ice or after fixation with paraformaldehyde. Secondary antibodies (or avidin, or protein A) can be labeled with an enzyme (allowing visualization under a microscope via color development), a radioactive label (measuring bound antibodies with a counter), or a fluorochrome. In the latter case, cells can be analyzed directly under a fluorescence microscope or via flow cytometry. The instrument designed for this type of analysis is called a flow cytometer. It incorporates a laser, in the beam of which cells are separated based on whether they fluoresce or not, and they can even be sorted into distinct populations. Cells can also be simultaneously labeled with two or three (or even four in advanced setups) different antibodies conjugated to distinct fluorochromes. Typically, these are excited by a single wavelength of light while emitting in different spectral ranges, allowing the simultaneous detection of multiple cellular antigens.

To determine intracellular antigens, Cells must be made permeable to antibodies (since antibodies do not normally penetrate living cells unaided). To achieve this, cells are fixed with an ethanol-containing mixture. This approach enables the visualization of plasma cells packed with antibodies under a microscope.

To identify antibody-secreting cells, a modification of ELISA known as ELISPOT is used. In this method, cells are cultured on nitrocellulose filters coated with an antigen. The secreted antibodies bind to the surrounding antigen and, following detection with secondary antibodies and a substrate, appear as distinct rings or spots. This method originated as a simplified version of the local hemolysis-in-gel assay, which was very popular a decade ago. In that variant, cells were embedded in an agar gel containing erythrocytes (either native or antigen-modified). Secreted antibodies bound to the erythrocytes, and upon Complement addition, zones of erythrocyte hemolysis—clear plaques against the red gel Background—formed around the cells. (This exact method was used by Köhler to discover hybridomas secreting specific antibodies). ELISPOT can also be performed in agar within polystyrene microplate wells.

Thus, the principle of immunochemical analysis of antigens and antibodies features numerous modifications and can be applied to solve a wide range of experimental and diagnostic tasks. The appropriate modification for each specific task is selected based on sensitivity requirements and the detection capabilities of the final product.