56 3. KINETICS OF ENZYME INHIBITION 



by making the appropriate assumptions. The procedure is an extension of 

 that presented by Friedenwald and Maengwyn-Davies (1954, p. 154). A 

 discussion of the plotting of the resultant equations and the practical de- 

 termination of the kinetic constants will be reserved for Chapter 5. It is 

 convenient to use the equilibrium approach inasmuch as the steady-state 

 treatment of generalized inhibition leads to equations and constants so 

 complex that the basic concepts are obscured. Thus it will be assumed that 

 all complexes with the enzyme are in equilibrium with their components 

 and Kg will be used instead of K^,;, in the simplified equations, iC, can gen- 

 erally be replaced by K,„ == {k_i-\rk2)lki. This limitation will be discussed 

 in more detail later. Initially it will be assumed that no coenzymes or acti- 

 vators are present and they will be introduced subsequently. It is assumed 

 that the presence of the inhibitor can either alter the affinity of the enzyme 

 for the substrate or affect the rate at which the substrate complex breaks 

 down to products, according to the following equations: 



Pk (3-2) 



EIS -EI + P 



E + I ^ EI X, . ^f 



(ik (EI)(S) 



EI + S — EIS ^ El + P aK, = ^— ^ (3-5) 



pk (ES)(1) 



ES -fl — EIS ^ El + P uK, = ^jf- (3-6) 



(EIS) 



where a represents the change in affinity and /? the change in rate of complex 

 decomposition induced by the inhibitor. It may be noted that this situation 

 is similar to that discussed for activators and formulated in Eq. 2-73; it 

 will not be surprising that the resulting kinetic equations are similar. In 

 fact, it may be assumed that I above is a modifier; the values of a and /? 

 will determine whether it is an activator or inhibitor. The following relation- 

 ships may be written: 



(E,) = (E) + (ES) -T- (El) + (EIS) (3-7) 



t\ = A-(ES) + /3A'(E1S) (3-8) 



