96 3. KINETICS OF ENZYME INHIBITION 



are really intrinsic or microscopic constants, although we designate them 

 by K^ rather than k, so that they will not be confused with rate constants. 

 An excellent treatment of polyvalent molecules and the dissociation be- 

 havior of both independent and interactive groups is given by Edsall and 

 Wyman (1958, p. 477). 



The binding of one inhibitor molecule is assumed to change the dissocia- 

 tion constant of the second site to aK^. The situation is similar to that 

 discussed above where there are two independent sites with constants K^ 

 and aK^. The inhibition is thus given by: 



(3-94) 



The reactions involved may be represented as follows: 



R.I ^ «= ^«. R. ^ '^^ ^. R, 



E A' E 



E^ E^ E^ +P (3.95) 



"A, E A, E 



^R,I ^R,S 



The complexes ERjIS and ERglS can, of course, be formed since non- 

 competitive inhibition is assumed but, inasmuch as they are inactive, they 

 will not alter the kinetics. Furthermore, any interaction between the sub- 

 strate sites, altering K^., will not influence this type of inhibition. If the 

 inhibition is competitive the situation is expressed by Eq. 3-95, but when 

 substrate site interaction occurs, an additional constant is introduced. When 

 there are more than two sites an equation of the type 3-93 may be used. 



The variation in inhibition with a in plotted in Fig. 3-20. Whatever the 

 inhibition produced by a certain inhibitor concentration when the sites 

 are independent {a = 1), increasing the repulsion interaction (a > 1) 

 will reduce the inhibition progressively to one-half the initial value. The 

 inhibitor concentration for 50% inhibition is given by (I)o.5 = K^\ a so 

 that this interaction factor can also lead to significant deviation of (I)o.5 

 from K^. 



THE INHIBITOR IS ALSO A SUBSTRATE FOR THE ENZYME 



In certain inhibitions, usually competitive and with an inhibitor related 

 structurally to the substrate, the inhibitor may be acted upon by the en- 

 zyme. If only one of these reactions is determined, Eqs. 3-12 and 3-13 for 

 competitive inhibition are applicable since the inhibitor slows down the 



