202 THE ANTIOEN-ANTIBODY REACTIONS 



These observations have since been confirmed by many other workers, and 

 with a number of different antigen-antibody systems. In these systems, the 

 optimal ratio as determined by Dean and Webb's method is a constant, and the 

 method affords a reliable method of determining (a) the antibody content of two 

 or more solutions in terms of a fixed amount of antigen, or (b) the antigen content 

 of two or more solutions of antigen in terms of a fixed amount of antibody. 



A few examples may make these points clear. 



Dean and Webb titrated 33 samples of rabbit-v-horse antisera, and found the optimal 

 ratio varied from 1 : 177 to 1 : 14. Taking the two sera exhibiting these extreme ratios, 

 we see that one part by volume of antigen (horse serum) gave optimal flocculation with 

 177 and with 14 parts by volume of the two antisera. Since one part by volume of antigen 

 requires a constant amount of antibody for optimal flocculation, this amount must be 

 contained in the one in 177 volumes, and in the other in 14 volumes ; and the second 

 serum contains 177/14 = 12-6 times the concentration of antibody in the first. 



Taylor, Adair and Adair (1932) have used this method to determine the amount of a 

 given antigen in a naturally-occurring mixture. Thus, they have estimated the percentage 

 of egg albumin in egg white, and the amount of globuUn in horse serum, using in each case 

 chemically purified antigens for their titrations. The results obtained were in close agree- 

 ment with previous determinations, carried out by the usual methods of chemical analysis, 

 as shown by the following comparative figures : 



Percentage of crystalline egg albumin in egg white. Per cent. 



Hopkins (1900) 6-0 



Wu and Ling (1927) . . '. 8-5 



Optimal ratio method , . . . . . . .7-29 



Percentage of globulin in horse serum. Per cent. 



Hammarsten (1878) 4-57 



Gibson and Banzhaf (1910) 4-07 



Optimal ratio method ........ 4-46 



The vahdity of the calculations depends among other things on the assumption that 

 there is one type of antibody reacting with a single antigen in solution. With solutions 

 containing two antibodies and two antigens the titration series may yield two distinct 

 zones, or a single zone that is narrow or broad according to the degree of coincidence of 

 two optimally reacting mixtures in the test-tubes. (See, for example Dean, Taylor and 

 Adair 1935, Goldsworthy and Rudd 1935, Pochon 1936). 



It will be noted that Dean and Webb, in determining the optimal ratio for 

 flocculation, kept the amount of antiserum constant, and varied the amount of 

 antigen. The ratio determined by this method may conveniently be referred to as 

 the constant-antihodij optimal ratio, or constant -antibody O.R. 



Prior to these studies, Ramon (1922) had shown that diphtheria antitoxin could 

 be titrated by mixing falling amounts of antitoxic serum with constant amounts of 

 toxin, and noting which tube in such a series first showed flocculation. The fact 

 that this technique was introduced as a practical method of standardizing an 

 important therapeutic reagent and that controversy centred round its relation to 

 the current in vivo methods of standardization probably delayed the recognition of 

 its wider theoretical significance. We may conveniently refer to the optimal 

 antigen-antibody ratio, as determined by Ramon's technique, as the constant- 

 antigen optimal ratio, or constant-antigen O.R. 



