VARIATION OF ENZYME INHIBITION WITH pH 



683 



This is identical with Eq. 14-55 except for the new function /'/,(.„ since 

 uK^ is equivalent to the K^ in the former equation. If « = 1 and the binding 

 of the inhibitor has no effect on the enzyme \}K^: 



(I) 



(I) + K, 



1 + 



(S) 1 



(14-104) 



The inhibition is always somewhat greater when HEI can dissociate to 

 form EI because this will reduce further the concentration of the active 

 complex, HES. If E is the catalytically active form of the enzyme: 



A' HE 



P + E 



the inhibition is given by: 



ES 



E 



a A.', 



'^ 



HEI 



EI 



(14-105) 



(14-106) 



so that again the true inhibitor constant is divided by the pH function for 

 the enzyme-inhibitor complex. It should be noted that the inhibitor con- 

 stant that is applicable is that expressing the binding of the inhibitor to 

 the active form of the enzyme. When « = 1. a similar equation to 14-104 

 is obtained with // replacing fj. In both of the cases given, when « = 1 

 the ionization of HEI is not apparent in the inhibition equations as a pH 

 function for this complex, but nevertheless it increases the inhibition or 

 reduces the apparent inhibitor constant. If the enzyme is dibasic, the 

 proper /" functions can be used. 



Application of Dixon's Treatment to the Variation of K,' with pH 



Dixon (1953 a) implies that the binding of the inhibitor may be treated 

 analogously to the binding of the substrate and. therefore, that one can 

 write for the general case: 



K,= 



(E,)(I, 



/e(E)/,(I) /J, 



K, 



(EI,) /e,(EI) A, 



in conformity with Eq. 14-41. Likewise, we may write: 



pZ/ = vK-i - log/e - log fi + \og fei 

 or 



pZ,' = pZ, + p/e + p/i - pAi 



(14-107) 



(14-108) 

 (14-109) 



