REACTION WITH COENZYME OR ACTIVATOR SITES 83 



presence of inhibitor on the enzyme reduces activity to zero. If the rate 

 equation with respect to substrate is written in the Michaehs-Menten form: 



(A') + (D + (1/y) (A')(r) + 1 



' HIP) (A') -^ aia) {!') + ai^/i) (A')(r) + i ^ ' 



Noncompetitive Inhibition with Respect to Activator 



When the inhibition is completely noncompetitive with the activator 

 and the substrate, we may set a = y = u = I and obtain the equation: 



(S')(A' ) 1 



"■ - '^" (S') [(.V) + 1] - «A') ^ 1 (vm ''-'''' 



and for the situation where activator doesn't influence substrate binding 

 (/5 = 1): 



V V (S') (A') 1 



In the latter case one obtains the usual noncompetitive equation for the 

 inhibition: i = (r)/[(r) + l]. However, in the more general case where 

 /? 7^ 1, the inhibition will involve this factor; from Eqs. 2-71 and 3-60 one 

 obtains: 



. (!') + [(S') + 1] [1 - iS]/[(S')(A') + (S') + ig(A') + 1] 



^ = ^j;p^3 (3-62) 



Competitive Inhibition with Respect to Activator 



If the inhibitor competes with the activator for the activator site but 

 does not affect substrate binding, we must set a = 1 and / = // = go. 

 The general rate equation is: 



_ y (S')(A') 



'''■ '" (S') [(A') + ^(D + p] + [(A') + ^(D +1] 

 and for the special case where /? = 1: 



'' - ^'" i^Wl (A-) + (D + 1 ^'-''^ 



From the latter we obtain an expression for the inhibition (relative to the 

 rate in Eq. 2-72 for the uninhibited reaction): 



i = ~ (3-65) 



d') -i- (A') +1 



