REACTION WITH SUBSTRATE, COENZYME, OR ACTIVATOR 89 



Reaction of Inhibitor with Other Components of the Reaction 



When reaction of the inhibitor occurs with coenzyme, activator, or a 

 second substrate, the same type of inhibition will result if the rate equa- 

 tions are symmetrical (e.g., Eqs. 2-61 and 2-72). However, if substrate 

 binding is affected by these other components, this factor will com- 

 plicate the inhibition. For the situation in which the activator is essential 

 for the reaction (Eqs. 2-67 and 2-68), an equation similar to 3-72 will be ob- 

 tained with (A,) and K^^ replacing (S^) and K^^, providing that the fraction 

 of activator combined with enzyme is small, which was assumed in deriving 

 the rate Eq. 2-69. The value of (A) can then be substituted in Eq. 2-69. 

 When this is plotted, against either pi or pA, inhibition curves of form and 

 slope much like those of competitive inhibition are obtained. The concen- 

 tration of activator must be reduced below K^ before appreciable inhibition 

 occurs. 



If the activator in the uninhibited system is mainly bound to the en- 

 zyme and (A) is negligible, addition of inhibitor will withdraw some of the 

 activator from the enzyme and one can write (A^) = (EA) + (lA). The 

 degree of inhibition produced will depend on the relative affinities of the 

 enzyme and inhibitor for the activator and on the relative concentrations 

 of enzyme and inhibitor. An expression for (EA) is quadratic: 



{^kY[K - K,i\ + (EA)[ZJ(I,) - (A,)} ^^ 



and may be substituted in / = 1 — [(EA)/(E;)], but it is seldom that the 

 constants and the enzyme concentration are known. However, if the en- 

 zyme were saturated with activator and (E^) = (A,), the enzyme concen- 

 tration can be eliminated from the equations. In the extreme case where 

 Kai<^K^, i.e., the activator is bound much more tightly to the inhibitor 

 than to the enzyme, one may write (EA) = (A,) — (I,) from which the in- 

 hibition is seen to be i = (I^)/(A,), a linear relationship with inhibitor con- 

 centration. This is, of course, a titration type of inhibition and corresponds 

 to zone C behavior with respect to inhibitor and activator. 



The situation in which the activator may combine with both substrate 

 and inhibitor, probably of frequent occurrence when the activator is a heavy 

 metal, has been analyzed by Gryder et al. (1955), and the following rate 

 equation derived: 



.. = F ^^™5 (3-80) 



"" (S)(A)(I) + a[KsK„sa) + K,K,,{S) + {K,K,K,,KJl{k)] 



where Z,, = (A)(S)/(AS), K^, = (A)(I)/(AI), and a is the factor by which 

 K^ is changed by the presence of activator. This may be compared with the 



