BKAXCHED LINEAR CHAINS 341 



and glycogen in a purely glycolytic system, or the impingement of hydrogen 

 atoms from two or more dehydrogenases or substrates on a common elec- 

 tron-transport system, would be obvious examples. For simplicity we may 

 represent such a system as: 



A E, E^ 



^B^C (7-22) 



X E3 



where during the steady state, v^ + v^ = v^ = d{C)ldt. The steady-state 

 level of (B) is given by: 



(B) ^ ^ /'"'- + ^'•' (7-23) 



where v^ and v^ are equal to their ordinary Michaelis expressions. It is 

 evident that inhibition of either E^ or E^ will reduce d{C)ldt, but that the 

 reduction of product formation will be less than the inhibition on the single 

 enzyme, and that the inhibition of d{C)!dt can never be complete. Since the 

 response of the system depends on the relative rates of reaction 1 and reac- 

 tion 3, let us define this bj^ putting i'3 = rv-^, in which case it may be easily 

 shown that: ^ 



it = Y-~- (7-24) 



1 + r 



where if is the inhibition of d{C)ldt and i^ is the inhibition on E^. The max- 

 imum inhibition on the formation of C would thus be 1/(1 -f- r). 



Inhibition of Eo will not affect d{Q)'dt until V^ is reduced below i\ + Ug 

 or until for some reason (B) cannot rise sufficiently to maintain the rate, 

 the system behaving similarly to the unbranched system 7-1. 



Divergent Chains 



Metabolic processes in which a substance formed can react in two or 

 more different pathways are common. The oxidation of pyruvate formed 

 from glycolysis to acetyl-CoA or its condensation with CO2 to form dicar- 

 boxylic acid (Freedman and Graff 1958) and the diversion of glucose-6-phos- 

 phate formed from glucose into glycogen or the glycolytic pathway would 

 be important examples. Such a system may be represented by: 



E, E C 

 A^B( (7-25) 



E>I> 



where the steady state implies that i\ = v^ + 1'3 and the individual rates are: 



F,(A) F,(B) F3(B) 



''~'(A)+^, '' = (B) + K, '^= (B)+Z3 ^'-^'^ 



