148 



4. SUBSTRATE INHIBITION AND PRODUCT INHIBITION 



^^^-T 



K. 



1 + 



(S) (S)F„ 





(S) , (S)F, 



+ 



4Z,Z/(S)F. 

 iiT.F™' 



(4-49) 



1 + 



K. 



+ 



/CT, 



where F,„ is the maximal rate for E^ and F,„' for E,. The quantity 

 4i5CpiCp'(S)F„;/^,F„/ determines the level of (P). If the inhibition is on 

 El, either K^ is increased or F,„ is decreased; in either case (P) is seen to 

 decrease. If E^ is inhibited, either K^ is increased or F„/ is decreased, 

 resulting in increase in (P). For noncompetitive inhibition, KJ{S) is re- 

 placed by 1 + KJ{^). If the product diffuses away at a rate proportional 

 to k'(P), the corresponding quantity in the quadratic equation is 4(S)F,„/ 

 k'Kg, from which a similar decrease in (P) is seen to occur upon inhibition 

 of the enzyme. 



An example of such a mechanism occurs in the early stages of glycolysis: 



El Ea 



Glucose ;z± glucose— 6 — P ;=± 



fructose -6 -P ^ fructose- 1,6 -diP (4-50) 



where E^ is hexokinase. Eg is phosphoglucose isomerase, and Eg is 6-phos- 

 phofructokinase. The second reaction is very rapid and the free energy 

 change for it is very small (glucose-6-P/fructose-6-P = 2.3); fructose-6-P 

 also inhibits hexokinase but about half as potently as glucose-6-P. Thus 

 this second reaction is relatively unimportant and the third reaction may 

 be considered as the principal step for the removal of inhibitory products. 

 Crane and Sols (1953) found that addition of 6-phosphofructokinase did 

 reduce the inhibition on hexokinase. Thus in the cell it is possible that 

 these enzymes may form a steady-state system regulated in part by the 

 level of hexose monophosphates. Both stimulation and inhibition of hexo- 

 kinase will therefore be less effective than expected on the basis of studies 

 of the purified enzyme. It is likely that many similar situations occur in 

 the metabolic sequences and cycles within the cell. 



