REVERSAL BY A SUBSTANCE BINDING THE INHIBITOR 621 



Following reduction of the free inhibitor concentration, the dissociation of 

 the EI complex may occur: 



EI ;z± E -- I (13-32) 



If the former reaction is very rapid relative to the EI dissociation, the 

 kinetics are simply those discussed previously. If the affinity of the re- 

 versor for the inhibitor is high and (R^) is greater than (I^), the inhibitor 

 concentration will be reduced to a very low level and dissociation of the 

 EI complex will proceed at a rate dependent only on k_-^ (see preceding 

 section), inasmuch as inhibitor released from the enzyme will be imme- 

 diately bound by the reversor. When the inhibitor concentration is not re- 

 duced to near zero but is appreciable and in equilibrium with the reversor, 

 the inhibition will fall to a new level and the kinetics will follow those for 

 dilution (see preceding section). In most experimental studies of reversal, 

 the reversor is added in definite excess over the inhibitor, and the rate of 

 reaction of the two is reasonably rapid. Therefore situations where the rate 

 of reversal is related only to the dissociation of the EI complex are probably 

 quite common. 



It is also possible to conceive of cases where the dissociation rate is 

 much greater than the rate of combination of the reversor with the free 

 inhibitor. Here the rate of change of the inhibition will depend almost 

 solely on k^. The differential equation for the inhibitor concentration is: 



'^^^^ k.KAh) - A-3[(R.) - K,]a) (13-33) 



dt 



when the reversor is not depleted during the reaction. This may be inte- 

 grated to: 



(I) = -^^ {K, ^ (R,)e-'^3t^^'-V'} (13-34) 



This value of (I) may be substituted in the usual inhibition equations. It 

 may be noted that at « = 0, (I) = (I^) and i^ = (I/)/[(I/) + 1]; when equi- 

 librium has been reached and t = oo, (I) = {I,)KJ[(Ri) + K,] and i/ = 

 (I/)/[(I/) + 1+ (R/)], as expected. If the reversor is depleted during 

 the reaction, the differential equation must be modified to: 



4^ = k,KAh) - A-3[(R,) ^K,- (hr.d) - kAir (13-35) 



at 



which may also be integrated to provide values for (I) at any time. Since 

 very little quantitative work has been done on reversal kinetics, it is im- 

 possible in most instances to relate the changes in inhibition that are meas- 



