VARIATION OF ENZYME INHIBITION WITH pH 



681 



If K^ is calculated from the slope of a type A plot, it will now be given by: 



Ki = 



(H) sV^ - fne'K, 



(14-98) 



which may be compared with 14-84 and 14-85. The slope of a type D plot 

 is also altered by the factor K,J(E.). The type F plot gives fJK, as the in- 

 tercept and the slope again depends on the pH. 



(/) Noncompetitive inhibition on the inactive form HE {scheme 14-68) 



1/., - 1/(S): — 



IM - (I): 



(I)(l - i)li - (S): 



1 



F, 



K. 



F„,(S) 



1 +fe' 



'f: + ™-^ 



(S) 



+ -. 



A%(H)(I) 



(I)(l - i) 



= fne'Ki + 



A%(H) 



(14-99) 



(14-100) 



(14-101) 



These equations are similar again to those in the i)revioiis section {e) with 

 the pH dependence changed. 



These examples well show that the calculation of K^ for inhibitions on 

 ionizing enzymes will sometimes be straightforward (i.e., as in the non- 

 ionizing cases), but in others it will be more complex and will involve terms 

 in (H) or (S). If we define the apparent inhibitor constant, K- , as that which 

 would be derived in the graphical methods based on the assumption that 

 no ionization occurs, the relationship between K,' and K^ will vary with 

 the type of inhibition and the method of plotting. In the literature it has 

 been generally assumed that K- = f/K^ or K/ = f/./K, when the enzyme 

 ionizes monobasically, but this is not necessarily true, or will be true only 

 over a certain range of pH or (S). 



Case V: enzyme ami inhibitor andjor substrate ionize. It can be easily 

 seen, by inspection of the equations given above for the different iDlots, 

 that in every case in which the inhibitor ionizes, one needs only to mul- 

 tiply Ki by the proper pH function for the inhibitor. Thus, if one wishes 

 to calculate K^ for a competitive inhibition on the active form HE from 

 the intercept of a type F plot, and only the I form of the inhibitor is effective, 

 K, = K/lffy/fi'. If the substrate ionizes and its concentration enters into 

 the expression for K/, then the pH functions for the substrate must also 

 be included. For example, the slope of a type D plot of competitive inhibition 

 is KJV,,,K,{S), but if only one ionization form of the substrate is active, 

 its concentration is not (S) but (S)//,, so that K/ = f,K,, or, if the inhibitor 



