638 13. REVERSAL OF INHIBITION 



bition data cannot be interpreted in the usual manner and any calculations 

 of inhibition constants from the results will be incorrect. 



Spontaneous Monomolecular Destruction of an Unstable Inhibitor 



The nonenzymic inactivation of an inhibitor is the simplest case of 

 inhibition reversal due to the destruction of the inhibitor and simple ex- 

 pressions for the decline in inhibition with time may be obtained in some 

 instances. The following two reactions proceed simultaneously: 



k_ 



EI ;=^' E + I (13-59) 



k 

 I -> Q 



where Q is the inactive form to which the inhibitor is altered. There are 

 three possible situations: the rate of dissociation of the EI complex may 

 limit the rate of reversal, the destruction of the inhibitor may limit the 

 rate, or the rates may be comparable. When k ^ ^•_i, the concentration of 

 free inhibitor may be kept essentially at zero and the decrease in inhibition 

 will be determined by the EI dissociation rate (Eq. 13-4). When k_^ ^ k, 

 an approximate equilibrium will be maintained between the enzyme and 

 the free inhibitor so that the inhibition at any time may be calculated from 

 the concentration of free inhibitor. In this case: 



dt 



and upon integrating, setting (I) = (Iq) when t = 0, and replacing (I) by 

 iKJl — i, the inhibition is found to be: 



^ (13-60) 



1 + [(l/io) - l]e 



where ?'q is the initial inhibition. This equation is plotted in Fig. 13-13 for 

 different levels of the initial inhibition. It is characteristic of such curves 

 that at high inhibitions, the inhibition does not change greatly with time, 

 despite the fact that the rate of destruction of the inhibitor is highest 

 then. This results from the nature of the inhibition equation, i =■ (I') 

 [(I') + 1], in that at high values of (I'), when reduction of {!') decreases 

 both numerator and denominator comparably, the inhibition is rather in- 

 sensitive to {!'). Actually each curve in Fig. 13-13 has the same configura- 

 tion and they are merely shifted along the time axis. This means that at 



