134 4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



Inhibition of Substrate-Inhibited Enzymes by Other Inhibitors 



It might be thought superficially that the inhibition produced by sub- 

 strate and the inhibition produced by another inhibitor might be additive 

 but this is never so. The presence of substrate inhibition will alter the 

 kinetics formulated in the previous chapter in a characteristic manner. It 

 would be expected that noncompetitive inhibition is unaffected by sub- 

 strate inhibition, since the inhibitor does not alter substrate binding nor 

 does substrate binding affect the inhibitor. On the other hand, a competi- 

 tive inhibitor should modify the kinetics of substrate inhibition and be 

 modified by the substrate inhibition in turn. It is easy to visualize this if 

 one pictures the effects of increasing substrate concentration: there will 

 be two simultaneous and opposing effects — the antagonism of the inhi- 

 bition because of displacement of inhibitor from the enzyme and the pro- 

 duction of inhibition by whatever mechanism is involved. 



We have seen that most types of substrate inhibition can be represented 

 by rate equations of the following form: 



V = V (4-17) 



''"A + B/CS) +(S)/C ^ ^ 



It is easy to show that the inhibited rate equations are: 



Completely competitive inhibition 



v- = V (4-18) 



' ''"A+B/(S)[1 +(I)/Z,] +(S)/C 



(!') 



(I') + 1 + [(S)/B] [A + (S)/C] 

 Completely noncompetitive inhibition 



(4-19) 



V- = V (4-20) 



"^ [1 + (I')] [A + B/(S) + (S)/C] 



_a;)_ 

 d') + 1 



(4-21) 



These expressions for the inhibition may be compared to Eqs. 3-28 and 

 3-29 to determine the effect of substrate inhibition. In agreement with ex- 

 pectations, the inhibition in noncompetitive systems is not altered; i.e., 

 the inhibition produced by a noncompetitive inhibitor is neither altered 

 by substrate concentration or substrate inhibition, nor will the presence 

 of a noncompetitive inhibitor alter the rate-pS curves other than to de- 

 press them uniformly. On the other hand, a competitive inhibitor will 

 shift the peak of the substrate inhibition curve: 



