564 12. RATES OF INHIBITION 



and the variation in enzyme rate with time by: 



F,„(S)e-'=' 

 "" (S) + K, 



(12-50) 



We must now consider how such inactivation may modify the development 

 of true inhibition. It is important to remember that inhibition may be 

 measured in two basically different ways: the decrease in enzymic rate 

 may be based on the initial activity or it may be based at a particular time 

 on the activity of a control enzyme preparation that has not been treated 

 with the inhibitor. In the first case, one is measuring the development of 

 both inhibition and inactivation, whereas in the second case, one attempts 

 as far as i^ossible to separate inhibition from inactivation. Although the 

 second i^rocedure may seem valid as a means of eliminating inactivation, 

 it is not necessarily so. If the EI complex is inactivated at a rate either slow- 

 er or faster than that for the free enzyme E, the concentration of inactivat- 

 ed enzyme (X) will be different in the presence of the inhibitor than in the 

 control. Such a simple correction is valid only when the inhibitor does not 

 affect the inactivation rate (case HA above). 



A very cursory treatment of the kinetics of inhibition accompanied by 

 inactivation will now be presented with the aim of illustrating some of the 

 basic characteristics of such systems and the complexities encountered in 

 their analysis. 



(I) Free enzyme is stable but the EI complex is unstable. When the binding 

 of the inhibitor to the enzyme is very tight and the dissociation of EI can 

 be neglected, the following simple reaction may be written: 



E 4- I ^ EI ^ X (12-51) 



The fractional inhibition is given by: 



(EI) + (X) 



E(,) 



(12-52) 



since the inhibited (EI) and inactivated (X) enzyme forms both contribute 

 to the loss in activity. Since: 



- ''[•ED + (X)I ^ ,_,E„„ ,12-53) 



dt 



and from Eq. 12-52: 



<i[(EI)+(X)] |j,_j^ ,j2-54) 



dt dt 



we can write the differential equation for the inhibition as: 



dildt = A:.(I)(1 - i) (12-55) 



