RATES OF INHIBITION OF PURE ENZYMES 567 



allow the following expression for the rate of change of i to be derived: 



dijdt = A-i(I) - [^-1(1) + k^Ki + ks] i + k^i- (12-63] 



This may be integi'ated readily but the general expression is complex and 

 it is more convenient to select values for the constants and (I), which has 

 been done to give curve 4 of Fig. 12-20. This curve may be compared with 

 curve 3 which represents the course of the inhibition when no enzyme 

 inactivation occurs. When EI is unstable, the level of inhibition reached is 

 lower than that for the case when EI is stable (Eq. 12-11). It is impossible, 

 of course, to determine experimentally the true inhibition, unless the inac- 

 tivation of the enzyme can be followed independently by some means. 

 An interesting extension of this form of inactivation is provided by 

 the inhibition of yeast alcohol dehydrogenase by the zinc chelator, ortho- 

 phenanthroline (Williams et al., 1958). This enzyme is immediately in- 

 hibited by o-phenanthroline when the inhibitor is added with all the com- 

 ponents of the reaction present, but if the enzyme is preincubated with the 

 inhibitor, a time-dependent inhibition is observed. This second inhibition 

 is either irreversible or only partly reversible and thus may be considered 

 an inactivation as in scheme 12-57. The inactivation occurs-rather slowly: 

 with 1 milf o-phenanthroline an inhibition of 15% was reached in about 

 15 mill, while at 5 mAI it required about 60 min to reach an inhibition of 

 80%. First-order kinetics were followed. The results conform to the theory 

 that the inactivated enzyme is Elg so that the following reaction series 

 can be written: 



E + I ^ EI -i EI2 (12-64) 



From d{m2)!dt = A-3(EI)(I) and (E,) = (E) + (EI) + (EI,), and assum- 

 ing that i = (El2)/(E;), considering only the inactivation, the inhibition 

 is given by: 



kJdr 



i = 1 ~ exp 



(I) + K, 



(12-65) 



so that: 



2.3 log (1 -I) = ~ -Tj^^^- (12-66) 



A plot of log (1 — i)it against 0.434(I)2/[(I) + K^] will give a straight line 

 with a slope of — k^. The linearity of this plot will provide some confir- 

 mation for the mechanism whereby the inactivation is associated with the 

 binding of a second molecule of inhibitor. 



(II) Free enzyme and the EI complex are both unstable. We may first 

 consider the case in which the presence of the inhibitor on the enzyme does 



