204 THE ANTIGEN-ANTIBODY REACTIONS 



Considering first the rows in the table, we see that the constant-antibody O.R. 

 is 1/5 : 1/200, 1/7-5 : 1/300, etc. ; that is, 1 : 40. Considering columns, the 

 constant-antigen O.R. is 1/5 : 1/1,200, 1/7-5 : 1/1,600 etc. ; that is 1 : 240. In 

 this instance, therefore, the constant-antigen optimal mixture contains six times 

 as much antibody as the constant-antibody optimal mixture. The two optima 

 are on the face of it quite arbitrary, depending on which reagent we vary in com- 

 paring reactions taking place in a constant volume. For a 1/30 dilution of 

 antibody, 1/1,200 antigen precipitates faster than any other dilution; but this 

 particular dilution of antigen can be made to precipitate even more quickly by 

 increasing the concentration of antibody to 1/5, when precipitation occurs in 10, 

 as compared with 20 minutes. 



The Two Optimal Ratios and Chemical Equivalence. 



If the precipitates are removed by centrifugation the supernatant fluid remain- 

 ing may be tested, by the addition of more antibody or more antigen, for the 

 presence of residual antigen or antibody. Dean and Webb (1926) found that at 

 constant-antibody optimum there was neither antigen nor antibody in the super- 

 natant fluid and confirmatory results have been recorded by Taylor (1931, 1933), 

 Smith (1932) and Duncan (1932a). Duncan also found that at the constant- 

 antigen O.R. of the system with which he was working the supernatant fluid 

 contained a gross excess of antibody. It seems that in many systems the amounts 

 of antibody and antigens in an optimally reacting mixture, as defined by the 

 constant-antibody titration, are equivalent. For this reason, the constant-antibody 

 optimal ratio is obviously important in determining the nature of the combination 

 between antigen and antibody. However, the Ramon method of titrating anti- 

 toxin gives a constant-antigen O.R. and the close agreement between in vitro and 

 in vivo tests indicates that the ratio corresponds to a mixture in which toxin is 

 first neutrahzed by antitoxin ; that is, an equivalent mixture. The fact is, how- 

 ever, not irreconcilable with the generally observed equivalence at the constant- 

 antibody O.R., for the two ratios in diphtheria toxin-antitoxin titrations happen 

 to differ very little from one another (see Miles 1933, Boyd 1941, Boyd and Purnell 

 1944). 



The second problem that falls for discussion at this stage is that raised by 

 Bordet's hypothesis. Do antigen and antibody combine in constant proportions, 

 or may they combine in varying proportions, according to their relative concentra- 

 tions in the reacting mixture ? The precipitin reaction affords particularly favour- 

 able opportunities for attacking this important problem. 



Confining ourselves to the constant-antibody titration, we may distinguish 

 three zones^ — the central equivalence zone, the zone of antigen excess and the 

 zone of antigen deficiency, which is usually referred to as antibody excess, though 

 this term should properly be used for the constant-antigen titration series. The 

 zone of antigen excess may be further divided into two — a region where a marked 

 excess of antigen totally inhibits precipitation, and a region of moderate excess, 

 where some precipitation occurs. The equivalence zone may be narrow and con- 

 fined to mixtures in the optimal ratio, or the range of complete precipitation of 

 both reagents may be so broad that the antigen concentration at the antigen 

 excess end of the equivalence zone may be eight times, and is often two or three 

 times, that at the antibody excess end of the zone. 



These are the kind of results obtained with rabbit and liorse antisera. With other 

 animals, notably the guinea-pig, it is sometimes impossible to obtain any zone of complete 



