566 



12. RATES OF INHIBITION 



The solution of these simultaneous equations may be obtained by classical 

 methods or by the Laplace transform (see Salvadori and Schwarz, 1954, 

 p. 236) but is very cumbersome unless absolute values are known for the 

 constants and (I). Figure 12-21 shows the variations in the enzyme frac- 

 tions with time for a typical case. It may be noted that reaction 12-57 is 

 identical in form with the substrate reaction: 



E + S: 



ES 



and the transient-state kinetics for this system have been treated by Chance 

 (1943) and Yang (1954). 



TIME ^ 



Fig. 12-21. Variations in the concentrations of 

 the enzyme fractions with time (scheme 12-57). 



In these cases, the loss of enzyme activity proceeds to completion, but 

 the actual inhibition, exclusive of inactivation, reaches a level which 

 is not necessarily the equilibrium inhibition. The true inhibition is related 

 to (EI) and the amount of enzyme that is not inactivated as follows: 



(EI) 



(E,) - (X) 

 The usual differential equation for EI: 



d(EI)ldt = A-,(E)(1) - m)ikj{, + k,) 

 and the expression for d{¥il)ldt obtained from Eq. 12-60: 



dm) 

 dt 



[(E<) - (X)] 



di 

 dt 



d{X) 

 dt 



(12-60) 



(12-61) 



(12-62) 



