550 



12. RATES OF INHIBITION 



bition will depend only on the inhibitor concentration and not on the con- 

 centration of the enzyme, but it is obvious that if the enzyme concentration 

 is near that of the inhibitor, the later rates of inhibition will be slower due 

 to the fall in inhibitor concentration. An irreversible mutual depletion 

 reaction may represented as: 



E + I — > EI 



that: 



and: 



dm) 

 ^~dt 



= A-,[(E,) - (EI)] [(I,) - (EI)] 



di 

 ~dt 



h,{h) -^^^[(E,) +(I,)] +^■^A•,(E,) 



(12-21) 



(12-22) 



(12-23) 



30 



TIME 



20 150 



MIN 



Fig. 12-13. Inhibition of succinoxidase by iodosobenzoate at 16° 

 and a concentration of 2 n\M. (From Slater, 1949.) 



Integration of this equation leads to: 



\ _ g-fci[(I<)- (Ej)] 



1 



(E, 



(12-24) 



(I.) 



g-fcl[(T()-(Ei)] 



which gives the variation in the inhibition with time for any initial con- 

 centrations of enzyme and inhibitor. It may be noted that when (I,) ^ 

 (E,), this reduces to the simple expression, t = 1 — g-^'i^'i*', which is 

 Eq. 12-16. The changes of inhibition with time for such systems are shown 

 in Fig. 12-14 by plotting Eq. 12-24 for constant concentrations of inhibitor 

 and variable concentrations of enzyme. Curve 1 represents the ordinary 

 logarithmic progression of inhibition when the inhibitor is much in excess 

 of the enzyme and significant depletion of inhibitor does not occur. The 

 other curves show the results of increasing enzyme concentration to levels 



