VARIATION OF ENZYME ACTIVITY WITH pH 659 



by pH changes, K„, will change in a more complex fashion than indicated 

 here. However, it is iii,,, which is usually determined experimentally. 



We may now turn to a somewhat more general system in which the en- 

 zyme ionizes: 



^■2 E + P 



A-, ES aA- 



-^ ^:^H'' 3/-, (14-31) 



E ^ HES -> HE + P 



'^ -^ 



A'„ HE ^A's 



where both complexes, ES and HES. can occur and break down into prod- 

 ucts. The constants a and /? represent the effects of the association of the 

 enzyme with a proton on K, and ko respectively. This scheme is actually 

 identical with that previously formulated for generalized inhibition (Eq. 

 3-2), with K^ replacing K^ and a proton replacing the inhibitor. The re- 

 lationships between S and H may be competitive, noncompetitive, mixed, 

 or coupling. For the competitive situation {a = cc): 



(14-32) 



which means that H is essentially a competitive inhibitor, since HE is 

 incapable of binding the substrate. A noncompetitive situation {a = 1 

 and /? = 0) leads to: 



F™ (S) 



// (S) + K, 



(14-33) 



in which case K, is not altered but the maximal rate is. In the same manner 

 as with K^, one may designate an apparent maximal rate, VJ, which in 

 this case is equal to VJf^. Thus the effect of pH may be to change either 

 K^ of F„; or both. If the substrate also ionizes and only one form of the sub- 

 strate combines with the enzyme, the appropriate pH functions for the 

 substrate should also be included as described above. When more than one 

 form of the substrate combines with the enzyme and the resulting complexes 

 can break down at different rates to form the product, the situation is con- 

 siderably more complex. 



Finally, an extension to enzymes containing two ionizing groups will be 

 outlined according to the following scheme: 



K' H2E aPA:, 



k: he oK^ ^ H^ES 



J^ 1^ ^, (14-34) 



K, ES «A';' ^ HE + P 



