136 INTRODUCTION TO IMMUNOCHEMICAL SPECIFICITY 



What we are interested in, however, is the strength of a single 

 antibody-antigen bond. The compound Ad:- contains two such bonds, 

 and each mole of free antigen G contains %' moles of free combining 

 sites, where v is the valence of the antigen. Consequently, we have to 

 obtain the value of K\ where K' is the equilibrium constant corre- 

 sponding to the equilibrium 



(antibody-antigen bonds)/ 



(free antigen sites) (free antibody sites) = K' (3) 



by waiting 



2(AG2)A(G) (AG) = K' 

 or 



K' = {2/v)K (4) 



Therefore, the standard free energy of a single antibody-antigen bond 



A7^°, equals -RTXnK' = -RTlnK - RT\n{2/v),or 



AF°, = -RTlnK + RT\niv/2) (5) 



The exact value of the correction will depend on the valence of the 

 antigen and the exact nature of the reaction the equilibrium state of 

 which is being studied. 



As an illustration, let us consider the results of Baker et al. (1956) 

 on the reaction of anti-benzenearsonic acid antibodies with ben- 

 zenearsonic acid-azo-bovine serum albumin (bovine serum albumin 

 coupled with diazotized arsanilic acid ) . The reaction studied by these 

 workers was 



A' ; + AG ^ AC- 

 and their bovine serum albumin contained thirteen introduced 

 benzenearsonic acid azo groups per molecule. They calculated a AF° 

 of — 5.2 kcal. per mole. From the above this is equivalent to a bond 

 free energy change AFi° of 



-5.2 -\- 7?rin(13/2) 

 or 



-5.2 + 1.1 = -4.1 kcal. /bond 

 Contrary to expectations, this value is less (i.e., more positive) than 



