146 INTRODUCTION TO IMMUNOCHEMICAL SPECIFICITY 



association constant K. Precise values of m are not yet available, 

 but Wurmser and Filitti-Wurmser devised methods of calculation 

 which did not require a knowledge of m. 



If we invert both sides of equation (6), we obtain 



\/r = \/m + \/mK(A) (7) 



This means that if we plot the reciprocal of the number of moles 

 of agglutinin combined with a mole of red cells against the reciprocal 

 of the concentration of free agglutinin, we should get a straight line 

 with slope 1/mK. If we make such determinations at two different 

 temperatures, the ratio of the two slopes (l/mK2)/{l/mKi) gives 

 us the ratio of the association constants at these two temperatures, 

 Kx/K2. From this we may calculate AH° from van't Hoff's equation 

 (25) (p. 133). 



The amount of isoagglutinin remaining free in equilibrated mix- 

 tures of erythrocytes and serum cannot be estimated with sufficient 

 accuracy by the method of serial dilutions generally used to estimate 

 the strength of an agglutinating serum, and the quantitative methods 

 of Heidelberger and his school are not sensitive enough. But the 

 Wurmsers hit upon the device of expressing the agglutinin con- 

 tent of their sera in terms of the maximum number of red cells 

 they agglutinate, and of determining the free agglutinin in the super- 

 natant of erythrocyte-agglutinin mixtures in the same way. This 

 enabled them merely by cell counting to obtain the data for determin- 

 ing the requisite slopes and ratios of slopes described in the last para- 

 graph (Fig. 10-6). 



The values of AH° calculated by these methods are shown in Table 

 10-2. It will be seen that these values of AH° are in several cases 

 larger than the rather small values calculated by other workers for 

 other antibody-antigen and antibody-hapten systems. The most sur- 

 prising feature of Table 10-2, however, is the marked differences in 

 the anti-B isoagglutinin values obtained from the blood of persons of 

 different blood group and even of different genotype. This has been 

 confirmed by the examination of the serum of 36 AiO individuals, six 

 of group AiAi, and eight of group OO. The anti-B in the serum of 

 any given individual seems always to be homogeneous. This homog- 

 eneity is in marked contrast to the heterogeneity found for immune 

 antibodies (p. 14) and, if confirmed, might go far toward supporting 



