VARIATION OF ENZYME ACTIVITY WITH pH 657 



The formation of water from H+ and 0H~ is very rapid, k^ being 1.3 x lO^i 

 liters mole-^ sec"^. Since most of these rates are very rapid, one would 

 not expect them to be limiting in ordinary enzyme reactions. 



Let us consider initially the simple situation in which the enzyme does 

 not ionize over the pH range studied; the -pK,, of a monobasic substrate, 

 however, lies within this range. It may be assumed that either S or HS 

 combines with the enzyme. The former case is represented by the reactions: 



(14-20) 



(14-21) 

 (14-22) 



The term lES) has been omitted in the expression for (S,) because this is 

 not a mutual depletion system. The rate is given by v = A'2(ES). Solving 

 Eqs. 14-21 and 14-22 for (ES) and substituting this in the rate equation: 



^^'^ (14-23) 



" (s,) + K,[i + miKa] 



or in terms of the functions described earlier: 



V = V^ ^^— (14-24) 



'" (S,) +fs'K, 



Thus one may say in this case that the experimentally determined sub- 

 strate constant, KJ, is equal to fJK,, where K, is the true substrate con- 

 stant expressing the association of the active form of the substrate, S, 

 with the enzyme. This relationship can be derived more directly. The ap- 

 parent substrate constant is given by: 



K,' = (E)(S,)/(ES) (14-25) 



where (S,) is the total substrate concentration, i.e., (S) -[- (HS). If a mu- 

 tual depletion system is being dealt with. (ES) must be included and a more 

 complex quadratic expression results. From Eq. 14-3. (S,) =//(S), and 

 thus: 



K ' =f' J5115L = f'K, (14-26) 



