94 



3. KINETICS OF ENZYME INHIBITION 



The most common values for a probably lie between 1 and 10, since bind- 

 ing of one molecule usually decreases binding of a second, if there is any 

 effect, and if a is much higher than 10 the inhibition generally behaves as 

 if there were only one inhibitor molecule combining. The most likely val- 

 ues for /? are probably or slightly above, since it is logical that binding 

 of one molecule of inhibitor would decrease the enzymic rate, if it didn't 

 abolish it entirely. 



Noncompetitive inhibition with 



1 leads to (I)r 



K, and this 



concentration is often experimentally determined to calculate K^. If n = 2 

 or more, this no longer holds and (I)o.5 varies over a wide range as can be 

 observed in Fig. 3-19. It is of some interest to compare the values of (lOo.s 

 for various combinations of a and /?, since this concentration is a good in- 

 dication of the average degree of inhibition produced (see tabulation). 



Uncritical equating of (I)o.5 with K^ is therefore apt to lead to error, even 

 when the inhibition is of the pure noncompetitive type. The general equa- 

 tion for the inhibitor concentration to produce 50% inhibition is: 



(Do.s = 



- a(l - 2^) + V«'(l - 2iS)2 -j- 2a 



(3-90) 



If n is greater than 2, the inhibition equation is of the general form: 



(!')" (I')' (I')" 



(1 - m') + (1 - n -— -f (1 - ^") ^ + ... + (1 - K) ^- 



a a an 



(IT (IT (IT 



1 + (I') + -L^ + -^- + ... + ^^ 

 Of a a„ 



(3-91) 



where a, a' ... «„ are the interaction constants for successive bindings and 

 /?, /?'... /5,j represent the effects of successive inhibitor molecules on k. 



