74 3. KINETICS OF ENZYME INHIBITION 



when used in the sense of Goldstein. He used this fractional activity because 

 it is this value that is actually measured in enzyme experiments but, as 

 stated above, here we are more concerned with the reduction in rate brought 

 about by the inhibitor and hence shall express the equations in terms of i. 



It will be convenient to designate the zone behavior with subscripts to 

 indicate whether the substrate or inhibitor is referred to. Thus zone A^. 

 refers to a system which is in zone A with respect to substrate and zone Bj 

 to one that is in zone B with respect to inhibitor. A complete characteriza- 

 tion of the system may be made by combining these designations: thus 

 zone AgB^ implies a system which is in zone A with respect to substrate and 

 simultaneously in zone B with respect to inhibitor. There are therefore nine 

 possible states in which a competitive inhibition system may exist. 



Most enzyme systems will be in zone A, where (E,') is small (it must be 

 less than 0.1) and this simplification leads to the following zone equations: 



Zone A,A^: substrate and inhibitor mainly free 



(I/) = Y-^ [(S') + 1] (3-48) 



(I/) 



(3-49) 



(I/) + (S') + 1 

 Zone A^Br substrate mainly free, inhibitor free and combined 



(I/) = T-^— [(S') + 1] + i(E/) (3-50) 



1 — I 



_ [(I/) + (S') -f (E,') -f- 1] - V[(I/) + (S') + (E/) -t- If - 4(I/)(E/) 



2(E,') 



Zone AjCj: substrate mainly free, inhibitor mainly combined 



(hi = i(E,') (3-52) 



(I/) (I.) 



(E/) (E,) 



(3-53) 



Equation 3-49 is the expected classic expression for competitive inhibition 

 in systems uncomplicated by depletion of free inhibitor concentration; Eq. 

 3-51 is identical with 3-35 with the addition of (S'); and Eq. 3-53 is identical 

 with 3-36 for noncompetitive inhibition. The last equivalence forces one 

 to conclude, as did Goldstein, that competitive inhibition cannot occur in 

 zone C(. When (S') becomes large enough so that competition can occur, it 

 displaces the inhibitor from the enzyme, increasing the concentration of 

 free inhibitor, and putting the system into zone B,. 



