612 13. REVERSAL OF INHIBITION 



COMPETITIVE DISPLACEMENT OF THE INHIBITOR BY 



SUBSTRATE 



If an enzyme and a competitive inhibitor are incubated so that a con- 

 stant equilibrium inhibition is reached and substrate is then added, the in- 

 hibition will fall to a new level. The initial inhibition will be given by the 

 usual noncompetitive equation, Iq = (r)/[(r) + 1], since no substrate is 

 present. The final inhibition after the substrate is added will be given by 

 the equation for competitive inhibition, if= (r)/[(r) + 1 + (S')]. In the 

 over-all reaction, inhibitor has been displaced from the enzyme. However, 

 this displacement should not be conceived as involving an active partici- 

 pation of the substrate. The substrate molecules do not force the inhibitor 

 from the enzyme but only combine with enzyme molecules that are not 

 reacted with inhibitor. The displacement thus comprises two separate reac- 

 tions, the dissociation of the EI complex and the formation of the ES com- 

 plex: 



k_, 

 EI ;^ E +1 (13-12) 



E + S ^ ES (13-13) 



where the numerical subscripts of the rate constants conform to the con- 

 ventions of this and the last chapter. Since the reaction of the substrate 

 with the enzyme is usually much faster than the dissociation of the EI 

 complex, at least in those cases that can be dealt with experimentally, the 

 rate of the displacement and the time required to achieve the new equi- 

 librium are ordinarily dependent only on the dissociation rate constant k_^. 

 A simple approximate treatment of the displacement rate can be based 

 on the expression for the rate of change of (EI): 



"^^^^^ ^-' [(E,) - (ES) - (EI)](I) - k^,m) (13-14) 



dt Ki 



Assum.ing that the equilibrium of the enzyme with substrate is very rapidly 

 achieved and that the rate of breakdown of the ES complex into the pro- 

 duct is relatively slow (i.e., when the enzyme conforms to the Michaelis 

 formulation), this equation may be integrated with the boundary condi- 

 tions defined by the values of i^ and if given above for the beginning and 

 end of the displacement. 



. . (, , (S') r k_,t {!') 



(13-15) 



