682 14. EFFECTS OF pH ON ENZYME INHIBITION 



also ionizes, K^ = fjfi^. In most methods of plotting, however, the pH 

 functions for the substrate need not be considered. 



These illustrations emphasize that the calculation of K^ is not as simple 

 as has often been assumed when the active center possesses one or more 

 ionizing groups, and that the apj^arent inhibitor constant is not always di- 

 rectly related to the true constant through simple pH functions. 



Ionization of Enzynne-lnhibitor Complexes 



It has been assumed in most of the inhibitions previously discussed that 

 only one form of the enzyme binds the inhibitor and therefore that only one 

 enzyme-inhibitor complex occurs. The ionization of this complex in such 

 cases does not enter into the formulations. Before applying the Dixon 

 treatment to inhibition it will be necessary to determine under what con- 

 ditions ionization of the enzyme-inhibitor complex is imi)ortant and how 

 it may modify the expressions for rates and inhibitions in the preceding 

 sections. When two substances form a complex, ionizing groups on either 

 substance may be modified and this will be expressed as a shift in the 

 Ip/iC^'s of these groups. Most of these effects arise from changes in the elec- 

 tric field surrounding the ionizing group as a result of the binding of the 

 other substance. Thus the binding of an ionic inhibitor to the active cen- 

 ter will superimpose the electric field of the inhibitor onto that of the en- 

 zyme; any ionizing groups at the active center or in the vicinity will be 

 modified as a consequence. Thus the piiT^/s of the enzyme-inhibitor com- 

 plexes are often different from the pK^'s of the free enzyme or the inhi- 

 bitor. If the inhibitor is uncharged, the effect upon the pJ?^^ of an enzyme 

 group may be very small, but if the inhibitor is an ion, the enzyme p^^ 

 may be shifted as much as one pH unit or more. 



The two types of competitive inhibition on a monobasic enzyme will be 

 treated to illustrate how the ionization of the enzyme-inhibitor complex 

 may be incorporated into the inhibition equations. If HE is the catalyt- 

 ically active form of the enzyme: 



A, HES -> HE -K P 



K„ HE- aA- 



-^ kN;' (14-102) 



E HEX 



A', EI «A„ 



where a indicates the change in K^, when the inhibitor is bound to the en- 

 zyme. The inhibition is now given by: 



(14-103) 



