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This study was concerned with the enhancement of affinity, due to bivalency, in the interaction of bivalent ligands with 7 S and IgM antibody. Three bivalent haptens with terminal lactosyl groups were synthesized and their binding by equine anti-lactosyl antibodies evaluated. Association constants were measured by equilibrium dialysis and by the ammonium sulfate precipitation method. The binding of two monovalent ligands was also evaluated for comparative purposes. From molecular models of the bivalent ligands it was found that the maximum distance between the lactosyl groups was 85·5 A in the largest ligand. The failure to observe any enhancement of affinity in the binding of the bivalent ligands was attributed to the inability of the ligands to span the minimum separation of the combining sites. This interpretation is in accord with the findings of Werner et al. (Werner T.C., Bunting J.R. and Cathou R. E. (1972) Proc. natn. Acad. Sci. U.S.A. 69 , 795) who concluded from energy transfer measurements that the minimum average distance between the combining sites was 92–102 A.

In an effort to induce the formation of antibodies of high affinity against a defined haptenic group two relatively large groups were conjugated to protein through the lysyl residue which thereby became part of the haptenic groups. A purification procedure has been developed involving semi-automatic operation of chromatographic and gel filtration columns. The final yield of purified anti-hapten γG-antibody was about 66% of the precipitable antibody in the rabbit antisera. Four haptens were synthesized which corresponded to increasing fractions of the haptenic group. The binding of these haptens was measured by equilibrium dialysis and fluorescence quenching. The measured association constants ranged from 1×10 5 m −1 to 2×10 7 m −1 . Three of these haptens exhibited a phototropism, associated probably with a cis-trans isomerism about azo group, such the exposure of the haptens to light their binding to antibody. The use of the method of fluorescence quenching in this system was not entirely satisfactory. A minimum estimate of the extent of complementary of the antibody site was provided by the binding of the largest of the haptens.

A double isotope method for the determination of antibody affinity using ammonium sulphate globulin precipitation is described and appraised. The incorporation of a 22Na-volume marker in addition to the 125I-labelled antigen eliminates the usual necessity to wash the globulin precipitates and enables larger numbers of samples to be assayed rapidly and reliably. Affinity values for anti-hapten and anti-protein antibodies determined by these two methods are compared and although higher values were obtained with the double isotope method, the affinities of sera assayed by both methods are ordered similarly.

Rabbits rendered immunologically tolerant to BSA produced antibodies capable of precipitating BSA following immunization with DNP—BSA. Antigen binding studies using purified `anti-BSA' antibodies produced by tolerant animals indicated that these antibodies bound DNP—BSA with far greater avidity than BSA. It was concluded that a true termination of tolerance had not occurred. The implications of the results with regard to induction of antibody formation and of tolerance are discussed.

The plaque inhibition method of measuring the affinity of single antibody-forming cells (AFC) developed by Andersson has been modified for use with haptens. Using this method, it was possible to make simultaneous determinations of the relative affinities of IgG and IgM plaques during the primary and secondary responses. It was shown that there was no maturation of the affinity of antibody-released IgM AFC in the primary response in mice. There was an increase in affinity of the antibody released from IgG AFC, which was antigen dose- and time-dependent, confirming results obtained by others. Furthermore, at any time during the course of the primary response, the affinity of the IgM antibody released by AFC was always lower than that of IgG plaque-forming cells. This difference averaged about 10-fold. The same factors were shown to influence the affinity changes of IgG AFC observed during the secondary response. In addition the booster, or secondary dose of antigen used, was important. Highest affinity antibody was produced in response to intermediate antigen doses. The maturation of affinity affects the generation of memory cells to the same degree as the antibody-secreting cells during the primary response, since similar affinity changes occurred in the absence of detectable primary responses. Finally, when the period between primary stimulation and challenge is 5 months, there is a decrease of between 2 and 2.6 log10 in the concentrations of DNP lysine needed to inhibit 50 % of the IgG antibody-forming cells depending on the doses used for priming. The variation of affinity of IgM antibody was much less obvious, with a 6-fold difference at the maximum, which was independent of the doses of antigen used for priming or boosting, and of the time elapsed between the two antigenic stimuli.

It was found that several DNP-hapten preparations contained low levels of contamination with radioactive, weakly bound impurities which could not be removed by routine methods. This contamination resulted in artificially low values for antibody affinity and artificially high values for the heterogeneity index. A mathematical model for the binding of contaminated hapten by homogeneous antibody was developed. This model predicted that the degree of distortion would be minimized by the use of large ‘outside’ volumes and low antibody concentrations for equilibrium dialysis measurements. Experimental data consistent with these predictions were obtained.

Antigen, diffusing into converging edges of an antibody depot, inhibits the precipitation unless the reaction is completed before an inhibiting antigen excess is established. Since the rate of the increase of antigen concentration depends on the size of the angle, relative avidities of similar preparations of antibody may be estimated from the angle just producing observable inhibition.

ANTIBODY affinity usually varies during the course of the immune response. This information has been acquired by studying antibodies present in the serum (for review see ref. 1), released by single cells in semi-solid media2–10 or, more recently, synthesized in vitro and released into liquid medium by lymph node microfragments11,12.