144 4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



reaction scheme is similar to Eq. 3-2 and the rate and inhibition equations 

 are similar to those from Eqs. 3-9 to 3-30 if one replaces (I) with (P) and 

 K^ with Kp. If the product is added at different concentrations and only 

 initial rates are determined, the kinetics are identical with those for inhi- 

 bition by substances unrelated to the reaction. However, if no product is 

 present initially but is formed during the reaction, i.e., if (S) + (P) is 

 constant, it is interesting to observe, as in Fig. 4-18, that the course of the 

 reaction depends markedly on K^. If K^ is small the rate may drop very 

 rapidly after the reaction has started; e.g., if K^^ 10~^ ilf the inhibition 

 reaches 50% after only 5% of the substrate has been transformed. 



The products may also combine with an activator and inhibit by this 

 mechanism although this situation has not been reported. Carboxylic and 

 amino acids formed in hydrolytic reactions might complex with metal ions, 

 the substrates having little or no affinity for these activators. Reaction 

 of the products with coenzyme or acceptor sites is also possible and in all 

 cases the kinetics will follow the corresponding equations in Chapter 3. 



Examples of Product Inhibition 



The hexokinases of brain and schistosomes are inhibited quite potently 

 by the product glucose-6-phosphate, 50% inhibition occurring at a concen- 

 tration of about 0.6 n\M in both cases (Crane and Sols, 1953; Bueding and 

 MacKinnon, 1955) and this inhibition is noncompetitive with respect 

 to either glucose or adenosine triphosphate (ATP) (Weil-Malherbe and Bone, 

 1951). On the other hand, yeast hexokinase is not inhibited by hexose- 

 monophosphates (Colowick and Kalckar, 1943). The other product aden- 

 osine diphosphate (ADP) inhibits all of these enzymes but is competitive 

 with ATP on the enzyme from brain (Sols and Crane, 1954) and noncom- 

 petitive in the case of hexokinase from yeast (Gamble and Najjar, 1955) and 

 schistosomes (Bueding and MacKinnon, 1955); the inhibition in the latter 

 case actually increases somewhat with increasing ATP concentration. The 

 reaction rate falls off rapidly due to the accumulation of these products 

 in preparations of the purified enzymes. These inhibitions are not due to 

 the occurrence of the reverse reaction but are of type B mechanism, as 

 is evident from the free energy change of the reaction, the fact that either 

 product alone is inhibitory (for the reverse reaction both products must 

 be present), and the absence of glucose-6-phosphate inhibition of the 

 yeast hexokinase. The inhibitions are fairly specific since other hexo3e- 

 phosphates inhibit less than glucose-6-phosphate or not at all, while aden- 

 osine-5-phosphate (AMP), pyrophosphate, and phosphate are inactive 

 (Sols and Crane, 1954). The reverse reaction catalyzed by yeast hexokin- 

 ase, measured by an exchange reaction between labeled glucose or glu- 

 cose-6-phosphate, is inhibited by glucose, another example of product 

 inhibition (Gamble and Najjar, 1955). 



