In the preceding paper, general expressions are derived for an hypothetical initial equilibrium between multivalent antigen and multivalent antibody, which form the basis for a
General theory of precipitation, which postulates a minimal disturbance of the initial equilibrium during aggregation, and a
Restricted theory, which specifies the direction of disturbances of the initial equilibrium if antigen and antibody are indeed multivalent.
For the special case of lattice-formation, the restricted theory is developed in a preliminary way to permit quantitative description of the composition of precipitates, and more fully to deal with flocculation-times and the meaning of optimal proportions.
The restricted theory leads to the concept of selective precipitation,which is probably adequate to explain the small volume effect observed in precipitating systems, and the different effects of excess of either reagent.
The relation of structure .to the properties of lattices are considered in connection with the solubility of precipitates and the problem of reversibility of biologic effects of antigen-antibody reactions.
Experimental methods are suggested for the measurement of the parameters of lattice-systems, which are three: the maximal valence of antigen, the maximal valence of antibody, and the dissociation-constant of the unit-valence. These, together with concentration-factors, completely define an ideal lattice-system.
In the application of the theory to experimental precipitating systems additional parameters such as the homogeneity and functional symmetry of the reactants, and nonspecific associative forces, are considered. In no case do available data clearly show that these influences seriously prejudice the usefulness of the theory. It is likely, however, that such instances will be found.
It is suggested that the principal parameter defining the individuality of different immune sera to a given antigen is the dissociation-constant of the specific valence. At present there is no reason to suppose that the diverse properties of different antisera, including their specificity, in any way imply a corresponding diversity of the fundamental immune response.
The unit-valence appears to represent an area of contact of the order 10—3 cm2. The relation between the dissociationconstant of the unit-valence and the structure of the antigenic surface is discussed briefly. The dissociation-constant of the immunologic valence is believed to be strongly influenced by associated substances foreign to the specific antibody.
The evidence is overwhelmingly in favor of the hypothesis that antibody and antigen are multivalent, and that the maximal valence of antibody is small, probably two. The maximal valence of antigen is probably limited primarily by the physical surface of the molecule.
Several definitions of practical usefulness are proposed in part IIc.
The encouragement and instruction continuously offered by Dr. Bronfenbrenner have contributed decisively to the results achieved in this study.