11 Avidity: The nature of antigen-antibody interactions

Dr. M. N. Gupta

1. Objectives

• To understand the nature of binding site on Fab in more detail

• To understand the origin of multispecificity

• To understand forces which govern the binding between antigen and antibody

• To understand the concept of avidity

• To understand the techniques of equilibrium dialysis

2. Concept Map

3. Description

Much of our insight about the interactions between antigen and antibody has come from simple systems such as haptens interaction with Fab fragments, X-ray crystallography has contributed a lot at the early phase of these studies.

The binding between a hapten and Fab largely depends upon close complementarity of the shapes of the two entities. This is due to the inherent nature of the weak forces which are involved in the binding.

Nature of the antigen binding site

The elegant studies of Wu and Kabat in identifying the hypervariable regions gave the first clear clue about the nature of the antigen binding site. Subsequent affinity labelling experiments by S.J. Singer confirmed the role of these regions in binding the antigen.

The early X-ray studies indicated that the Fab fragment and Bence Jones dimer have very similar structural features. More extensive studies carried out later led us to believe that the present antibody molecule evolved from a single domain polypeptide.

Structure of the antibody

Each domain is characterized by two sheets of antiparallel beta strands joined by a S-S bond. This is infact now called the immunoglobulin fold.

The divergent evolution of the duplicate genes led to one evolving as the constant region and another as the variable region.

The evolutionary changes in the amino acid sequence led to the concave shape of the antigen combining site.

The shape of the site exposes a large surface area to the antigen and allows a close fit between the antigen and the combining site.

As an early example, X-ray studies revealed the binding of the hapten phosphorylcholine to the wedge shaped cavity of the Fab fragment of a mouse immunoglobulin.

The choline group of the hapten interacts with the hypervariable loops from both H- and L-chains. Its positively charged N is in a position to interact with the negative charge on the Glu side chain.

These early studies indicated that the antigen combining sites consist of loops of hypervariable sequences fixed to more rigidly constructed other parts of the variable domain which have more of a framework function.

Similarity between antigen binding site and the active site of enzymes

In a way, the antigen binding sites of antibodies are not very different from the active sites of the enzymes. That should not be surprising as both classes of proteins require specific molecular recognition of other molecules. There are many similarities and among them we start with the length of the binding site.

a.) Length of the binding site

The classical studies on lysozyme by John Rupley had indicated that hexaoligosaccharide of N-acetyl glucosamine fits well with the binding site of the enzyme.

An antibody against dextran was raised and its binding constants with oligomers of glucose were determined. The studies revealed that Ig binding sites has space of six glucose residues with a length of about 25 Angstrom.

b.) Microenvironment of the binding site

Dansyl lysine is an interesting hapten which has both hydrophilic and hydrophobic component. The fluorescence emission spectra of the free hapten compared with its spectra when bound to its antibody showed decrease in the λmax emission and significant increase in the fluorescence intensity. Both indicate that the microenvironment of the hapten binding site is predominantly non-polar.

It is known that the active site of enzymes also have predominantly hydrophobic character.

Thus, Both the antigen binding site and the enzyme active site have non-polar micro environment.

c.) Binding constants

The binding constants for many haptens fall in the range of 10-4 to 10-10. The standard free energy of binding are generally in the range of -6 to -15 kCal/mol.

These ranges are similar to what are found for many enzyme-substrate and enzyme-coenzyme interactions.

Difference

However, there is a fundamental difference between the two classes of proteins. In the case of enzymes, binding of substrates lead to catalysis. In case of antibodies, haptens or antigens are not chemically transformed. We will later on talk of catalytic antibodies to take the analogy between the two classes of proteins further.

In this respect, antibodies are closer to lectins. Lectins also specifically bind to sugars, polysaccharides or glycoconjugates but do not transform these molecules into different chemical entitites. The biochemistry of lectin is a relatively newer area. It is interesting to note that the early work on lectins was pioneered by the same groups of scientists who earlier worked with immunoglobulins.

Multispecificity of antibodies

We have so far focused on how the recognition of an antigen by antibody become specific. How do we reconcile this with cross reactivity of antibodies? How does that occur?

A single antibody can infact bind to more than one antigen. We are not referring to many antigenic determinants on a single antigen.

Antibodies can bind to the antigenic determinants which was used to raise the antibody. It can also bind to the antigenic determinants with similar structures. This is referred to as cross reacting antigens.

Antigenic determinants with very different structures can also bind to an antibody.

A stable antigen-antibody complex can form if there are enough short range interactions. The nature and number of these short range interactions may be different from what are involved in the recognition of specific antigenic determinant.

This phenomenon is called multispecificity of antibodies and in fact also contribute to the diversity of the antigen binding capacity of the immune system.

Dan Tawfik‟s group at the Weizmann Institute of Science in Israel has been looking at instances of multispecificity shown by some antibodies. Tawfik‟s group incidentally also studies the phenomenon of catalytic promiscuity by enzymes. We have earlier discussed the similarity between enzyme-substrate and antigen-antibody recognition phenomenon. Catalytic promiscuity also refers to multispecificity of enzymes!

Tawfik‟s group used X-ray crystallography and pre-steady kinetics to look at the phenomenon of multispecificity of antibodies. These studies have led him to the conclusion that one of the conformational isomer which is a part of several conformations of antibodies in equilibrium with each other can possess a low affinity promiscuous binding site for many haptens. It is the subsequent induced fit which leads to the high affinity complex formation. In the latter, antigen binding sites assume a narrower and deep shape.

Binding constants of the antibodies

The antibody molecule can exist in a conformation Ab1 which does not bind to an antigen and thus has a low constant K-value. Ab2 is the binding constant with low affinities. Ab3 is the conformation which forms high affinity complex via induced fit.

An “unrecognized” antigen may interact with Ab2 . The transient complex of Ab2 can revert back to the non-binding conformer Ab1 with a fast relaxation time of ~58 sec-1. The fast dissociation rate is nearly 100 sec-1. If the binding leads to induced fit, high affinity complex of Ab3 with antigen is formed.

Hence this works like a proof reading mechanism to ensure that lack of discrimination by Ab2 is checked within limits.

The overall view is that Binding with an unacceptable ligand leads to its dissociation due to global or local conformational change.

Specific ligands on the other hand lead to lock-in conformational isomer.

These results help us to understand not only cross reactivity but also autoimmune responses.

The binding sites for a hapten are deep narrow cavities. Antigens, on the other hand, bind to a long and flat shaped surface of the binding site. Thus, antibodies have binding capabilities to a very wide range of antigens which differ in size (and shapes).

Nature of the forces which bind antigen with antibodies

1. Electrostatic Forces

It has already been pointed out that there is a great similarity between the recognition of an antigen by an antibody and enzyme substrate interactions. IN the latter case, in many cases, it is now well established that subsequently covalent enzyme-substrate intermediate are formed. In the case of antigen and antibody, the binding forces are purely non-covalent. These are similar to those which operate in many specific biomolecular recognition phenomenon.

•  Antibodies are protein in nature and many amino acid side chains carry charges at physiological pH.

•  Lys and Arg are positively charged; Asp and Glu are negatively charged

•  The force of attraction (F) between the two charged species with charges q1 and q2 follow

Where D is the dielectric constant and d is the distance which separate the two charges.

Hence, as two charges come closer, the force of attraction increases rapidly.

The dielectric constant of water is quite high with a value of 80. In vacuum D=1. Hence exclusion of water molecules between the two interacting charged surfaces will greatly enhance the force of binding.

In addition to charges, dipoles on the antigen and antibody can also contribute to such forces.

Charge transfer complexes because of electron donating groups on antibody and electron accepting group on antigen (such as dinitrophenol, DNP) can also be formed.

Because of the nature of the electrostatic interactions, the binding between antigen and antibody becomes large if the fit is close and shapes are complementary

Figure 10: The structure of the contact regions between a monoclonal Fab anti-lysozyme and lysozyme. (a) Space-filling model showing the Fab and lysozyme molecules fitting together smugly to form the complex. The antibody heavy chain is shown in blue, the light chain in yellow, lysozyme in green with its glutamine 121 in red. (b) Fab and lysozyme models pulled apart to show how the protuberances and depressions of each are complementary to each other.

2. H-Bonding

H-bonds can form between charged as well as uncharged specie.

The one to which H-atom is originally attached is called H-donor. The specie which starts sharing this H atom is called H-acceptor.

Typically, N and O atoms bound to H in biological systems act as H-donors. Similarly, atom on the acceptor specie is also N and O.

The bond energies of H-bonds are in the range of 3-7 kCal/mole. That is why H-bonds are included in the list of weak bonds. While weaker than covalent bonds, H-bonds are stronger than van der Waal‟s bonds.

H-bonds are directional in nature. Thus, H-bond is strongest when donor, H and acceptor are co-linear.

3. Van der Waal’s forces

Thus, a significant contribution of these forces to the overall interactions between antigen and antibody arises from complementarity of the surfaces between the two. That allows multiple van der Waals bonds to form simultaneously between the antigen and the antibody.

These are non-specific attractive forces which start operating where two atoms are at about 3-4 angstrom from each other.

These forces arise from the fact that at this distance, transient asymmetry of charge around an atom induces similar distribution of charges

At a shorter distance, there is strong repulsion. The distance at which attractive forces are strongest, is called van der Waal‟s contact distance. This is equal to sum of contact radii of the two atoms.

The bond energy of a van der Waals bond is ~1 kCal/mole. How weak is that can be appreciated from the fact that at room temperature, the average thermal energy of molecules is about 0.6 kCal/mole.

4. Hydrophobic Bonds

Water is a polar molecule and water molecules can form H-bonds with each other.

In water these H-bonded structures are continuously forming and breaking apart. Statistically there is some order in the structure of water.

What happens when a non-polar molecule is introduced in such a structure? Water molecules cannot form any bonds with the molecule. The earlier H-bonds among the water molecules in the vicinity of this non-polar molecules are disturbed. The modes by which these water molecules could form H-bonds are now fewer. In that sense, the non-polar molecule has introduced some order in the water molecules around it. These entropic considerations lead to non-polar molecules coming together rather than forming “islands” of ordered water molecules at several places in the liquid water. This is thermodynamically favoured and is the basis of the so called hydrophobic bond among the non-polar molecules. It is not their affinity for each other but it arises out of the fact that water molecules are able to form H-bonds in a more facile fashion when non-polar molecules cluster together.

In some species Gln121 of hen egg white lysozyme is replaced by His121. Monoclonal Fab against hen egg white lysozyme binds very poorly with these lysozyme molecules. Loss of a single bond disturbs the synergy of several weak bonds which contribute to the affinity between the antigen and the antibody.

Affinity and Avidity

While the term affinity or affinity constant is well understood, the term avidity has often been a source of confusion in older books (literature).

The term avidity is used to express the binding between multivalent antigen and antibody:

nAb + mAg = AbnAgm

It is applicable even when antisera is used as an antibody preparation and thus consists of a population of antibodies, each binding to the antigen (or antigenic determinant) with a different binding constant.

It also includes the binding between an antibody molecule to different but similar antigenic determinants on the antigen.

The familiar analogy is from the co-ordinate chemistry here chelates have high binding constants!

More important, it arises from the fact that strength of multi-links is more than the sum of strength of individual links.

Figure 13: Heterogeneity of IgG anti-hapten (dinitrophenyl: DNP) antibodies from the serum of an immunized animal contrasting with the homogeneity of a monoclonal Ig G anti-DNP (a) Scatchard plot of hapten binding to antibodies purified from the serum.  (b) Histogram showing a typical distribution of antibody affinities in the anti-DNP serum.

Thus if individual links have K1 and K2  as affinity constants and

∆G1=- RT ln K1 and ∆G2 =- RT ln K2

∆Gavidity = ∆G1  + ∆G2           = -RT (ln K1  + ln K2 ) = -RT ln K1K2  = -RT ln Kavidity

Polyvalent interactions are actually very common in biological systems. Avidity refers to association constant of a polyvalent interaction.

Equilibrium Dialysis

The technique of equilibrium dialysis was introduced by Eisen and Karush to determine the binding constant between a hapten and an antibody. As Ig have molecular weight of >150 kDa, these do not pass through semi-permeable membrane of a dialysis bag.

Haptens upto 10 kDa can easily pass through most membrane of a dialysis bag which are commonly used in enzymology.

To start with the antibody is placed in the dialysis sac and the sac is suspended in a vessel containing hapten solution. Hapten can diffuse into the bag.

The hapten can be either measured spectroscopically or labelled with a radioisotope.

The reversibility of the process (single equilibrium) can be checked by continually changing the buffer in which the hapten was dissolved in the vessel (outside the sac).

Measurement of the total hapten concentration in the dialysis bag enables the amount bound to the antibody to be calculated.

Scatchard analysis

The data can be plotted in terms of Scatchard Plot.

r/c vs. r

where r= moles of antigen bound per mole of antibody; c= molar concentration of free antigen

r/c = Kn – Kr

where n= valence f the antibody

It allows one to calculate the number of binding sites in the antibody molecule. This is how the presence of two binding sites (for antigens) in IgG was determined.

At infinite c, r/c = o. At that pint, the equilibrium reduces to: Kn =Kr . Hence the intercept on the x-axis equals n (the number of binding sites)

If all the antibody molecules in the preparation are identical as in the case of a monoclonal antibody, the slope of the scatchard plot gives the association constant K. Otherwise, the plot will give the average association constant.

In the case of a hapten, the mixture of antibodies produced by raising antisera against hapten-carrier conjugate will in fact give number of binding sites <2 as many will not bind hapten at all.

At a certain value of c (concentration of free hapten), half of the antibody sites are occupied.

At that point

[Ab-hapten] = [Ab]

As K = ([Ab-hapten] )/ ([Ab][hapten]);

at that point

K= 1/[hapten]

Thus K, the binding constant is defined as the affinity constant and is equal to the hapten concentration when half the binding site of the antibodies are occupied.

Many other methods for determining binding constants between antigen and antibody are available. These include gel filtration, spectroscopic techniques (when binding changes a special characteristic of antigen or antibody). A technique which has proved very useful in calculating „on‟ rates and „off‟ rates is BIACORE. We will discuss it in the context of its applications which will come up in the later lectures.

Summary:

•  The binding of a hapten with an antigen binding site involves many weak forces. The binding depends upon their synergy.

•  Antibodies can cross react and show multispecificity.

•  It is necessary to think in terms of avidity rather than affinity constant while discussing antigen-antibody binding