Antibody Affinity Is a Quantitative Measure of Binding Strength

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The combined strength of the noncovalent interactions between a single antigen-binding site on an antibody and a single epitope is the affinity of the antibody for that epitope. Low-affinity antibodies bind antigen weakly and tend to dissociate readily, whereas high-affinity antibodies bind antigen more tightly and remain bound longer. The association between a binding site on an antibody (Ab) with a monovalent antigen (Ag) can be described by the equation k1

VISUALIZING CONCEPTS

ANTIGEN

VISUALIZING CONCEPTS

ANTIGEN

ANTIBODY

-CH2 — OH ••• O = C — CH2— CH2— Hydrogen bond i2-ch2-nh3+ -o^

ffCH

ffCH

Interactions Bonds

Hydrophobic interactions van der Waals interactions

CH CH3

CH CH3

Hydrophobic interactions van der Waals interactions

FIGURE 6-1

The interaction between an antibody and an antigen depends on four types of noncovalent forces: (1) hydrogen bonds, in which a hydrogen atom is shared between two electronegative atoms; (2) ionic bonds between oppositely charged residues; (3) hydrophobic interactions, in which water forces hy drophobic groups together; and (4) van der Waals interactions between the outer electron clouds of two or more atoms. In an aqueous environment, noncovalent interactions are extremely weak and depend upon close complementarity of the shapes of antibody and antigen.

where k1 is the forward (association) rate constant and k_1 is the reverse (dissociation) rate constant. The ratio k1/k_1 is the association constant Ka (i.e., k1/k_1 = Ka), a measure of affinity. Because Ka is the equilibrium constant for the above reaction, it can be calculated from the ratio of the molar concentration of bound Ag-Ab complex to the molar concentrations of unbound antigen and antibody at equilibrium as follows:

The value of Ka varies for different Ag-Ab complexes and depends upon both k1, which is expressed in units of liters/mole/second (L/mol/s), and k_1, which is expressed in units of 1/second. For small haptens, the forward rate constant can be extremely high; in some cases, k1 can be as high as 4 X 108 L/mol/s, approaching the theoretical upper limit of diffusion-limited reactions (109 L/mol/s). For larger protein antigens, however, k1 is smaller, with values in the range of 105 L/mol/s.

The rate at which bound antigen leaves an antibody's binding site (i.e., the dissociation rate constant, k_1) plays a major role in determining the antibody's affinity for an antigen. Table 6-1 illustrates the role of k_1 in determining the association constant Ka for several Ag-Ab interactions. For example, the k1 for the DNP-l-lysine system is about one fifth that for the fluorescein system, but its k_1 is 200 times greater; consequently, the affinity of the antifluores-cein antibody Ka for the fluorescein system is about 1000fold higher than that of anti-DNP antibody. Low-affinity Ag-Ab complexes have Ka values between 104 and 105 L/mol; high-affinity complexes can have Ka values as high as 1011 L/mol.

For some purposes, the dissociation of the antigen-antibody complex is of interest:

The equilibrium constant for that reaction is Kd, the reciprocal of Ka

Kd = [Ab][Ag]/[Ab-Ag] = 1/Ka and is a quantitative indicator of the stability of an Ag-Ab complex; very stable complexes have very low values of Kd, and less stable ones have higher values.

The affinity constant, Ka, can be determined by equilibrium dialysis or by various newer methods. Because equilibrium dialysis remains for many the standard against which

Forward and reverse rate constants (k1 and k_-|) and association and dissociation constants (Ka and Kd) for three ligand-antibody interactions

TABLE 6-1

Antibody

Ligand ki

Anti-DNP e-DNP-L-lysine 8 X 107 1 1 X 10s

Anti-fluorescein Fluorescein 4 X 108 5 X 10~3 1 X 1011

Anti-bovine serum albumin (BSA) Dansyl-BSA 3 X 105 2 X 10~3 1.7 X 108 SOURCE: Adapted from H. N. Eisen, 1990, Immunology, 3rd ed., Harper & Row Publishers.

d other methods are evaluated, it is described here. This procedure uses a dialysis chamber containing two equal compartments separated by a semipermeable membrane. Antibody is placed in one compartment, and a radioactively labeled lig-and that is small enough to pass through the semipermeable membrane is placed in the other compartment (Figure 6-2). Suitable ligands include haptens, oligosaccharides, and oligo-peptides. In the absence of antibody, ligand added to compartment B will equilibrate on both sides of the membrane (Figure 6-2a). In the presence of antibody, however, part of the labeled ligand will be bound to the antibody at equilibrium, trapping the ligand on the antibody side of the vessel, whereas unbound ligand will be equally distributed in both compartments. Thus the total concentration of ligand will be greater in the compartment containing antibody (Figure 6-2b). The difference in the ligand concentration in the two compartments represents the concentration of ligand bound to the antibody (i.e., the concentration of Ag-Ab complex). The higher the affinity of the antibody, the more ligand is bound.

Control: No antibody present

(ligand equilibrates on both sides equally)

Control: No antibody present

(ligand equilibrates on both sides equally)

A

B

A

B

• •

• •

• • •

• •

• •

• •

Vs-

-6

-

Equilibrium

Initial state

Equilibrium

Experimental: Antibody in A

(at equilibrium more ligand in A due to Ab binding)

Antibody

Radiolabeled ligand

Initial state

Equilibrium

FIGURE 6-2

Determination of antibody affinity by equilibrium dialysis. (a) The dialysis chamber contains two compartments (A and B) separated by a semipermeable membrane. Antibody is added to one compartment and a radiolabeled ligand to another. At equilibrium, the concentration of radioactivity in both compartments is mea-

Control

Experimental

Experimental

Ligand bound by antibody

Time, h sured. (b) Plot of concentration of ligand in each compartment with time. At equilibrium, the difference in the concentration of radioactive ligand in the two compartments represents the amount of ligand bound to antibody.

Since the total concentration of antibody in the equilibrium dialysis chamber is known, the equilibrium equation can be rewritten as:

where r equals the ratio of the concentration of bound ligand to total antibody concentration, c is the concentration of free ligand, and n is the number of binding sites per antibody molecule. This expression can be rearranged to give the Scatchard equation:

Values for r and c can be obtained by repeating the equilibrium dialysis with the same concentration of antibody but with different concentrations of ligand. If Ka is a constant, that is, if all the antibodies within the dialysis chamber have the same affinity for the ligand, then a Scatchard plot of r/c versus r will yield a straight line with a slope of —Ka (Figure 6-3a). As the concentration of unbound ligand c increases, r/c approaches 0, and r approaches n, the valency, equal to the number of binding sites per antibody molecule.

Most antibody preparations are polyclonal, and Ka is therefore not a constant because a heterogeneous mixture of antibodies with a range of affinities is present. A Scatchard plot of heterogeneous antibody yields a curved line whose slope is constantly changing, reflecting this antibody heterogeneity (Figure 6-3b). With this type of Scatchard plot, it is possible to determine the average affinity constant, K0, by determining the value of Ka when half of the antigen-binding sites are filled. This is conveniently done by determining the slope of the curve at the point where half of the antigen binding sites are filled.

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  • Sofia
    How to measure binding affinity of an antibody?
    8 years ago
  • adela rivera
    What is high antibody affinity?
    8 years ago
  • james
    How to quantitatively measure antibody binding?
    8 years ago
  • Mikolaj
    How to determine antibody binding affinity?
    7 years ago
  • ada
    How to measure "off rate" of antibody?
    7 years ago
  • miranda
    How to measure affinity of antibody strength?
    7 years ago
  • lena
    How is antibody affinity measured?
    2 years ago
  • maxine
    What is an equilibrium state antibodyantigen binding?
    2 months ago

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