ANTIGEN-ANTIBODY REACTIONS 459 



and prevented from contact with solvent molecules, so 

 that the complex composed of antigen or hapten and a 

 few antibody molecules becomes lyophobic and insoluble. 

 He accounts for the observed failure of some multivalent 

 liaptens to cause precipitation as being due to the too 

 close proximity of the determinant polar groups so that 

 there is not room for two or more antibody molecules to 

 be brought into such positions that their polar groups 

 are occluded, the complex, therefore, remaining soluble. 

 If the hapten molecule is larger, for instance if R of the 



above formulae is — N=N<Q ^N=N 



the polar groups are further apart, steric hindrance is 

 less, more antibody molecules may be able to react with 

 occlusion of a larger number of their polar groups and 

 consequent precipitation. 



The evidence for making a definite decision between 

 the " framework " and " occlusion " hypotheses of 

 precipitation is at present not adequate, but the balance 

 seems in favour of the former. 



Pauling and his collaborators have proposed equations 

 to account quantitatively for the reactions between 

 multivalent antigen molecules and divalent antibody 

 molecules, assuming equilibrium between antigen- 

 antibody soluble complexes of the types AB, A^B and 

 AB^ and the precipitate ABp, where A represents 

 antigen and B represents antibody. The resulting 

 expression has been shown to hold for relatively simple 

 systems, such as those composed of divalent antigen 

 and divalent antibody. 



Hershey has also proposed a rather elaborate series 

 of equations which account fairly well for quantitative 

 findings and also enable deductions to be made as to the 

 results to be expected from alteratioixs in the systems. 



The Reacting Groups in Precipitin Reactions. — At 

 present comparatively little is loiown of this subject, but 

 some data are available. Chow and Goebel showed that 



