GENERALIZED KINETICS OF REVERSIBLE INHIBITION 59 



Because it is frequently stated that in competitive inlubition the Michaelis 

 constant is increased in the presence of the inhibitor, and because in re- 

 ciprocal plotting the determined Michaelis constant can assume theoretically 

 any value from Kg to infinity, one must beware of assuming that the ex- 

 perimentally determined Michaelis constant bears any relation to this effect 

 of the inhibitor on substrate affinity. To illustrate this, let us consider com- 

 pletely competitive inhibition: if (I) is kept constant and (S) is varied, the 

 plotted results will provide a value for K„^. which from Eq. 3-12 is equal to 

 Kf. multiplied by the factor l-}-(I);ii; — however, this does not mean that 

 the inhibitor has increased the dissociation constant K, by this amount, 

 since actually the presence of the inhibitor on the enzyme raises Kg to in- 

 finit}^ the substrate being entirely prevented from binding. The factor 

 l + [(I)/^i] is a statistical term indicating the number of enzyme molecules 

 combined with inhibitor. In order to find the true effect of an inhibitor on 

 substrate binding, the value of a must be determined. 



Coupling or Uncompetitive Inhibition 



There is another possible type of inhibition that may be derived from the 

 generalized equations above. This occurs if a < 1, the inhibitor increasing 

 the affinity of the enzyme for the substrate. If the breakdown of the sub- 

 strate complex is unaffected (/? = 1) or accelerated (/? > 1), this would 

 result in activation rather than inhibition. However, if /5 < 1, the over-all 

 effect may be inhibition. If the situation where the EIS complex does not 

 break down to products is considered (/5 = 0), increased binding of the 

 substrate to form the inactive EIS complex will result in inhibition; if a 

 is very low, approaching zero, the inhibition may be essentially complete 

 since aU of the enzyme will be in the inactive EIS form, inasmuch as in the 

 present treatment it is assumed that (S) and (I) are greater than (E^). 

 Equations 3-20 and 3-21 express the kinetics for this situation, from which 

 it may be seen that as a falls below one, the inhibition will increase, becom- 

 ing complete when a is zero. This type of inhibition is really a special form 

 of mixed inhibition. It was given the unsatisfactory name of uncompetitive 

 inhibition by Ebersole et al. (1944), coupling inhibition (because the inhibitor 

 increases the coupling of enzyme and substrate) by Friedenwald and Maeng- 

 wyn-Davies (1954, p. 154), and anticompetitive inhibitioyi by Dodgson, 

 et al. (1956). Friedenwald and Maengwyn-Davies developed the kinetic 

 equations of coupling inhibition for the special case in which a = 0, assum- 

 ing that the inhibitor combined only with the ES complex and not with 

 the free enzyme. 



E+S^ES^E-P (3-22) 



ES + I — EIS K,' = -^^^ (3-23) 



(EIS) 



