SUBSTRATE INHIBITION 



135 



Substrate inliibition alone: 

 Presence of competitive inhibitor: 



(So') =VBC (4-22) 



(So'), =V'BC[1 +(!')] (4-23) 



The peak will thus be shifted to higher substrate concentrations. 



The simplest and least general representation of type A substrate inhi- 

 bition as shown in reactions 4-6 may be modified for the presence of an 

 inhibitor as follows: 



R + V 



K 



■y 



ES 



nK 



\A'- ^ RSJ 



(4-24) 



and the general rate equation written as: 



1 



i + ^ii+mi + fl 



1 + 



(D 



+ 



d') 



(4-25) 



from which the special cases of competitive and noncompetitive inhibition 

 may be derived: completely competitive inhibition (/5 = oo), 



V- = V 



1 



1 + [1/(S')] [1 + (I')] + (S')/« 



. _ (T) 



' (I') + 1 -f (S') [1 + (S')/«] 



and completely noncompetitive inhibition (p — 1). 

 V, = V, 



1 



[1 + (I,)] [1 + 1/(S') 



(D 

 d') + 1 



(S')/«] 



(4-26) 



(4-27) 



(4-28) 



(4-29) 



The (So') will be shifted from \/ a to V « [1 + (I')] in the presence of a 

 competitive inhibitor. These equations are, of course, special cases of 

 Eqs. 4-18 to 4-21 and apply specifically to type A inhibition. However, 

 they are the most commonly used and the competitive rate equation was 

 first derived by Murray (1930) in connection with the inhibition of liver 

 esterase by cZ-methyl-n-hexyl carbinol, the shift in (Sq) and the change in 

 the form of the rate-pS curve being demonstrated. 



