Thermodynamics of antibody-antigen reactions. 2. The binding of bivalent synthetic random coil antigens to antibodies having different antigen precipitating properties.

The objects of this study were the equine IgG and IgG(T) classes of antibodies with immunologic specificity for the dinitrophenyl group and bivalent antigens consisting of linear poly(ethylene glycol) polymers which terminated at both ends in dinitrophenyl groups. Complex formation between antibodies of both classes and one of several sharp fractions of antigen having number average molecular weights in the range 25 000 to 75 000 were studied by measuring the light scattered from solutions containing equimolar amounts (approximately 5 x 10(-6) mol/L) of one of the antibodies and one size fraction of antigen, and variable amounts of monovalent hapten. The data were analyzed in the context of a model that accounted for the formation of linear and cyclic complexes of all extents of aggregation. Two parameters in addition to the intrinsic antibody-dinitrophenyl group association constant were found to be necessary in the assumed equilibrium model to account for the behavior of the system. One of these accounted for the looses in configuration entropy that resulted when a random-coil polymer became bound at one end to a space-occupying antibody. The other was a ring closure factor for the formation of cyclic complexes. Ring closure factors for the formation of larger cyclic complexes (present in only small amounts under the conditions studied) were related to the ring closure factor for the formation of the smallest, which was found to increase as antigen size decreased, and for each antigen size to be consistently higher for IgG(T) antibody than for IgG antibody. Comparison of the theoretically estimated values of the two parameters within their measured values indicated that the average conformation of IgG antibodies in solution is open ("T" shaped) but the average inter-Fab are angle in IgG(T) antibodies is approximately 60 degrees or less.