678 14. EFFECTS OF pH ON ENZYME INHIBITION 



interaction of the inhibitors with the enzyme calculated; it is by the re- 

 lationship between K^ and the apparent inhibitor constant, K/, that the 

 pE'^'s of the ionizing groups on the enzyme may be determined with 

 Dixon's treatment. The exi3erimental K/ found by the usual graphical 

 methods will generally not be the true K^ if ionization of any of the 

 involved components occurs. It is therefore particularly important to look 

 critically into the methods for the determination of both K/ and K^. 



In the simplest situation, K^' differs from Kj because only a fraction of 

 the total inhibitor j^resent is active. These fractions are expressed in terms 

 of the pH functions presented earlier in this chapter. If, for example, the 

 inhibitor exists in the forms I and HI, and only I binds to the enzyme, 

 the true inhibitor constant will be given by: 



Ki = K/lf/ (14-79) 



Thus, from the p/C„ of the inhibitor and the pH at which the experiment is 

 run, it is possible to determine K, after K/ has been found. However, when 

 the enzyme also ionizes over the pH range investigated, the calculation 

 of K^ may be more complex. 



The first matter that must be examined is the applicability of the plot- 

 ting methods described in Chapter 5 to situations in which ionizing groups 

 are involved in the inhiljition. For this purpose we may consider some of 

 the cases presented in the preceding section. 



Cases I, II, and HI: only iJie sabstrate or the i»Jdbitor or both ionize. The 

 apparent inhibitor constant determined by every method of graphical anal- 

 ysis will be K j multiplied by the appropriate pH function or functions, as 

 indicated in the expressions for the inhilntion (Eqs. 14-47, 14-49, 14-50, 

 14-51) for each situation. The only complication arises in scheme 14-48 

 where both forms of the inliibitor combine with the enzyme but with 

 different affinities, since here: 



K, = 



1 



fh>' f'f,' 



K/ (14-80) 



If this tyi^e of inhibition is recognized, the value of// may be estimated from 

 data obtained at different pH's, and hence /iT, may be calculated. 



Ca.se IV: only the enzyme ionizes. Six different situations were discussed 

 for an enzyme with a monobasic ionizing group at the active center. Six 

 methods of graphical analysis for the determination of the constants were 

 presented in Chapter 5. It is important to know in each case how the de- 

 termined constant relates to K^. We shall consider here only three methods 

 of plotting: Ijv^ against 1/(S) (type A), l/v, against (I) (type D), and (I) 

 (1 — i)li against (S) (type F). The results obtained by the other methods 



