88 3. KINETICS OF ENZYME INHIBITION 



may be substituted in the usual equations for competitive inhibition (3-12 

 and 3-13) as the concentration of the active inhibitor. If, in addition to 

 the inhibition produced by SI, there is depletion of free substrate, the 

 value of (S) from Eq. 3-72 must be used instead of (S^). A characteristic 

 of inhibitions exerted by SI is the increase in inhibitor concentration with 

 increasing substrate concentration. Therefore, competition between S and 

 I is not so evident as in those cases where I is itself the inhibitor, at least 

 over a certain range of substrate concentrations. 



An interesting approach to inhibitions involving complexes of inhibitor 

 with substrate has been formulated by Reiner (1959, p. 156). The plotting 

 of (I^) against il{l — i) often helps to distinguish between the different 

 types of inhibition and occasionally allows the calculation of the constants. 

 The equations for the three possible mechanisms may be written as 

 follows: 



(1) inhibition due to depletion of free substrate 



w(S,) 



(I,) = [1 + (S,)//^,] 



iiK.i + 



1 +u[l + {S,)IKsl 



(3-76) 



(2) inhibition due to the combination of SI with the enzyme 



ih) = [(S,) + K,] [(S<) + Z,,] -^ (3-77) 



(3) inhibition due to both mechanisms 



(I,) = KAi + (s,,/A-.] \^s^^-^ + ^ s, + K.^,:Z+^s,|KA} \ <'■'«' 



The inhibition term, ^7(l — i), has been indicated by u for convenience. 

 Plots of (I,) against u for the first and third situations lead to curves which 

 are linear for low and high values of u, the slopes for these regions being 

 easily evaluated by inspection of the equations. For example, for inhibition 

 due to the depletion of substrate, the slope at low vahies of u (i.e., low inhi- 

 bitions) will be [K^j + (SJ] [1 -\- {Si)IK,] and for high values of m the slope 

 will be ^.,,[1 -f (8,)/-^",]. The curves will bend upwards or downwards, 

 depending on the inhibition mechanism. However, the plot for inhibition 

 by the complex SI will be a straight line passing through the origin. The 

 slope will depend on (S,) in a characteristic way: it will be high for both 

 low and high values of (S,) and reach a minimum when (S,) = V K^Kgi. 

 Other features of this method of plotting will be found in the original pres- 

 entation by Reiner. 



