608 13. REVERSAL OF INHIBITION 



the former reaction may be sufficiently slow as to be susceptible to the ex- 

 perimental techniques available. The rate of inhibition reversal depends 

 on the energy of activation for the dissociation of the inhibitor from the 

 enzyme, and since this energy is greater than the association activation 

 energy by an amount equivalent to the over-all free energy change, gener- 

 ally ki > k_i, the ratio of the rate constants being given by: 



k_,lk, = e'^''"'^ (13-5) 



For example, if the free energy of binding is — 4 kcal/mole, it is easily 

 calculated that k^^ is only 1/645 of k^. Since most inhibitions involve 

 free energy changes of several kcal/mole, such relations between the rate 

 constants are usual. 



It is perhaps worth noting that, rigorously speaking, it is technically 

 impossible to maintain the free inhibitor concentration at zero throughout 

 the enzyme preparation during the reversal of inhibition. If dialysis is 

 used to remove the inhibitor, the concentration of free inhibitor within the 

 dialysis bag is usually significant in case the dissociation rate of the EI 

 complex is relatively fast, and with any technique it is impossible to pre- 

 vent some reassociation of released inhibitor molecules. When a substance 

 that binds the free inhibitor is added, the inhibitor concentration cannot, 

 of course, be reduced to zero. Thus reversal experiments invariably involve 

 some assumptions if the simple interpretation outlined above is followed, 

 but frequently these deviations from ideal behavior are quite insignificant 

 and may be ignored. Nevertheless, it is well in studies of this type to 

 consider such factors and determine if they are or are not significant. 



Dissociation of the El Complex When Free Inhibitor Concentration Is 



Not Zero 



When the free inhibitor concentration is suddenly decreased to a lower 

 value, as by dilution of the enzyme solution, the inhibition will drop to a 

 new equilibrium level, providing the inhibition is reversible. In this case, 

 the reverse reaction of association (Eq. 13-1) must be taken into account 

 and the following rate equations may be written: 



^ A',(E)(I) (13-6) 



I + k_, ^^- (13-7) 



A, 



where (ly) designates the final concentration to which the inhibitor has been 

 reduced. Equation 13-7 may be integrated to give: 



i = if + {i^ - if) e-*-,«/(i-.7) (13-8) 



