VARIATION OF ENZYME INHIBITION WITH pH 



669 



If both ionization forms of the inhibitor can bind to the enzyme: 



K, ES -> E + P 



MKi E K 



EI 



^ ^ 



EHI 



(14-48) 



I + H — HI 



the difference in the dissociation constants being exi^ressed by //, the inhi- 

 bition is given by: 



{It) 



HJi + Jhi 



1 + 



{^ 



(14-49) 



If /^ = 00 and EI is not formed, the equation reduces to 14-47; if // = 1 

 and both I and HI combine with the enzyme equally, K- = [f/fhi'lifi + 

 //j/)] K, = K^, and the apparent and true inhibition constants are identical. 



Case II: only the substrate ionizes. When the substrate concentration is a 

 factor in the inhibition (as in competitive inhibition) and (S) occurs in the 

 expression for the inhibition, the ionization of the substrate may be taken 

 into account by multiplying the true substrate constant by the appropriate 

 pH function for that form of the substrate that is active. Thus if the sub- 

 strate is dibasic and only HS reacts with the enzyme: 



(I) 



(I) + K, 



1 + 



(S, 



As I^s 



(14-50) 



Case III. both the inhibitor and substrate ionize. In this case both the 

 substrate and inhibitor constants are simply multiplied by the proper pH 

 functions. Indeed, one may write for all the ordinary types of inhibition 

 general equations derivable from Eq. 3-11. from which all special cases 

 may be obtained. Thus, in general: 



K, 



C^fsKs 



ih) +LK, 



/?(!,) + af,K, 



(14-51) 



Case IV: only the enzyme (active center) ionizes. Up to this point the re- 

 sults have been simple and expected. However, the ionization of the enzyme 

 introduces some complications which have previously not been realized; 

 in fact most of the interpretations for ionizing groups on the enzyme from 

 work with inhibitors are incorrect. Let us consider a typical enzyme reac- 

 tion in which the enzyme is active in only one ionization state, either as 



