Antibodyhapten Interactions

Specific, rapid, and high-affinity recognition of antigens by antibodies is essential for the host's immune system to respond to invasion by foreign cells and pathogens. Pecht and Lancet1 have presented a cogent analysis of antibody interactions with haptens, and the interested reader will find their examination of the kinetics and thermodynamics to be particularly lucid. Briefly, for the simple one-step binding scheme,

Antibody + Hapten = Complex their examination of the literature indicated the following interesting information about the magnitudes for the forward and reverse rate constants: (a) kon varies over a range of three orders of magnitude (from 0.005 to 5 x 108 M^V1); (b) koff varies over a range of eight powers of ten (from 3 x 10_5 s_1 to 6 x 103 s_1); (c) rigorous treatment of the kinetics requires an additional isomerization step typical of most binding reactions. The latter is suggested, because the limiting rate of diffusion places an upper bound on the magnitude of the equilibrium constant for a one-step binding mechanism. Thus, in a one-step reaction mechanism, the value of koff must be particularly important in models that attempt to explain wide variations in binding affinity that are achieved with different haptens as ligands.

A general two-step ligand-induced isomerization mechanism, as described by Eigen2, can be written as:

His treatment puts the values for the first-step rate constants as and k+i = (4^ M1000){(Da + DB)/RABj k-i = 3(Da + Db)/Rab2

where N equals Avogadro's number, DA and DB are the diffusion constants, and RAB is the so-called encounter distance. Pecht and Lancet1 estimate the latter to be 3

to 15 A, and for a hapten of molecular weight ~400, they use a diffusivity DB of about 5 x 10_5 cm2/s and an Rab value of 7.5 A. Taking a typical diffusivity for an immunoglobulin (DA = 3 x 10_9 cm2/sec), the values of k+1 and k_1 turn out to be 3 x 109 M_1s_1 and 3 x 109 s1, suggesting that the equilibrium constant K1 for the weakly interacting, encounter-controlled first step is around 1 M. The second step involves the hapten-in-duced conformational change from species AB to form species C. For the encounter step, Pecht and Lancet1 suggest that k_1 (as well as the AH^* and AS_1i) may be considered to be constant for virtually all hapten-immunoglobulin reactions. On the other hand, values of k+1 and AS+1* fall within a range that depends on the geometry of ligand approach to its receptor site. For the isomerization step, unimolecular rate constants range from 10 to 100 per second, and the slowness of the transition is suggestive of long-range conformational changes that involve more than a few residues contacting each other in the complex.

1l. Pecht & D. Lancet (1977) in Chemical Relaxation in Molecular Biology (I. Pecht & R. Rigler, eds.) pp. 2-3, Springer-Verlag, Berlin. 2M. Eigen (1974) in Quantum Statistical Mechanics in the Natural Sciences (S. L. Minz & S. M. Wiedermayer, eds.) pp. 37-61, Plenum Press, New York.

Selected entries from Methods in Enzymology [vol, page(s)]: Basic Principles of Antigen-Antibody Reactions: Proteins and polypeptides as antigens, 70, 49; the experimental induction of antibodies to nucleic acids, 70, 70; the preparation of antigenic hapten-carrier conjugates: a survey, 70, 85; production of reagent antibodies, 70, 104; preparation of Fab fragments from IgGs of different animal species, 70, 142; use of carbodiimides in the preparation of immunizing conjugates, 70, 151; use of glu-taraldehyde as a coupling agent for proteins and peptides, 70, 159; immunochemical analysis by antigen-antibody precipitation in gels, 70, 166

Methods for the Detection of Antigens/Antibodies: Equilibrium and kinetic inhibition assays based upon fluorescence polarization, 70, 3; fluorescence excitation transfer immunoassay (FETI), 70, 28; indirect quenching fluoroimmunoassay, 70, 60; the homogeneous substrate-labeled fluorescent immunoassay, 70, 79; fluorescence immunoassays using plane surface solid phases (FIAPS), 70, 87.

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