220 THE ANTIGEN -ANT I BODY REACTIONS 



in characterizing antisera in terms of standard antigenic preparations and vice versa. 

 Antibody content may be expressed in terms of maximally precipitated nitrogen, and 

 degrees of antigenic similarity as the proportion of homologous antibody precipitable 

 by different antigenic preparations. Heterologous systems are not so readily characterized 

 by this method. For instance, Pennell and Huddleson (1938) found a good fit with the 

 precipitation of Brucella abortus and melitensis endo-antigens, by homologous antisera, 

 but the fit was poor with the cross-reacting systems, abortus antigen and melitensis anti- 

 serum. This may be due to pecuUarities of the antigenic relationship between these two 

 organisms (see Chapter 34). A more important objection is that the relation does not 

 hold for the region of antigen excess (Malkiel and Boyd 1937) ; though Heidelberger 

 (1939) points out that this region is characterized by the co-existence of soluble and 

 insoluble antigen-antibody complexes in equihbrium, and his original assumptions do not 

 necessarily apply. 



Hershey (1941a, b, 1942, 1943a) has expressed the main features of specific precipitation 

 in a descriptive theory that differs from those of Heidelberger and Kendall in a number 

 of respects. The mass law is not invoked. Hershey adopts the notion of competing 

 bimolecular reactions, but unlike Heidelberger and Kendall assumes that the initial 

 antigen-antibody combination is reversible. The compounds may be characterized in 

 terms of valency of antigen and of antibody, and a dissociation constant k. Of special 

 interest is his restricted theory, in which the lattice hypothesis is assumed. That is, 

 both antigen and antibody are multivalent, and not only the initial combination, but the 

 later aggregation is determined by antigen and antibody valencies. The original papers 

 must be consulted for the details of the theory. It may be noted that, by assuming that 

 aggregates as well as initial compounds have a determined lattice structure, the assump- 

 tion of irreversilnlity of reaction is not only unnecessary but is irreconcilable with the 

 lattice hypothesis (1943a). The agreement of the theory with available data is as good 

 as that of Heidelberger and Kendall's, and the theory is applicable over a wide range 

 of the precipitin reaction. The consequences of the restricted theory are compatible with 

 a large number of observed facts including insolubihty of precipitates, the different effects 

 of antigen and antibody excess, and the varying relation of optima with various points 

 of reference in the equivalence zone. Taken in conjunction with the experimental data, 

 the success of the restricted theory at least provides an additional reason for giving the 

 lattice hypothesis the first place among the working hypotheses of serology. (See also 

 Ghosh 1935, Kendall 1942, and Pauling, Pressman, Campbell and Ikeda 1942.) 



Tests of the Lattice Hypothesis. 



The description of the precipitin reaction in terms of Heidelberger and Kendall's 

 mass-law equations corresponds in essentials with the lattice hypothesis of Marrack. 

 Both depend on the assumption that antibodies are multivalent. The main objec- 

 tions advanced against the conception of multivalent antibody are firstly the 

 difficulty of conceiving the mode of formation of multivalent antibodies in the 

 animal, and secondly that the assumption of multivalence is unnecessary to describe 

 the phenomena of precipitation. The first point is dealt with more fully in a later 

 section (p. 251). Hooker and Boyd (1937) object to the assumption of multivalence 

 on the grounds that inhibition by antibody excess is rare ; that non-specific adj uvants 

 like electrolytes and lipins are necessary for precipitation ; that the surface properties 

 of bacteria sensitized by antibody are those of a hydrophobic, salt-sensitive, denatured 

 globulin ; and that in the presence of excess of antibody the rate of flocculation 

 of an antigen is similar to a simple colloid undergoing non-specific flocculation. 

 The same authors (1942) point out that analysis of precipitates formed in the 

 zone of antigen excess, where antibody is not likely to have all its valencies satisfied, 

 seldom reveals a molecular ratio of antigen to antibody of more than unity. 



