Cell Metabolism - Bioprocess Engineering: Kinetics, Biosystems, Sustainability and Reactor Design - page 508

P 1

IV

M 4

III

M 1 M 2 M 3

II

I

V

M 5

VI

P 2

FIGURE E10-3.2 Simplified schematic of the sequential feedback control of branched pathways.

Therefore, the fluxes can be written based on simplified pathways as one usually does. The
simplified pathway is shown in Fig. E10-3.2 , which is identical to Fig. 10.15 c, with each path
numbered. The fluxes for each path can be written quite easily based on this example.
From Eqn (E10-3.39) ,

k 1c ½ M

1 ½

E

2 T

J I ¼ (E10-3.47)

K 1 þ K 1 K 1

f1 ½

M 3 þ½ M

1

From Eqn (E10-3.40) ,

J II ¼ k 2c ½

M

2 ½

E

3 T

(E10-3.48)

K 2 þ½

2

M

From Eqn (E10-3.41) ,

k 3c ½ M

3 ½

E

4 T

J III ¼ (E10-3.49)

K 3 þ K 3 K 1

f2 ½

P 1 þ½ M

3

From Eqn (E10-3.42) ,

J IV ¼ k 4 c ½ M

4

(E10-3.50)

From Eqn (E10-3.43) ,

k 5c ½ M

3 ½

E

5 T

J v ¼ (E10-3.51)

K 5 þ K 5 K 1

f3 ½

P 2 þ½ M

3

From Eqn (E10-3.44) ,

J VI ¼ k 6c ½ M

5

(E10-3.52)

This example shows that the fluxes in a complicated pathway can be easily written based
on its starting point, whether enzyme is involved (which is the case for almost all the reac-
tions in the cell) and/or regulated by other products or species in the cell. The fluxes are
not linear in most cases because of the enzyme catalysis. In general, the flux expression is
consistent with the Michaelis e Menten equation (Chapter 8) or any other related form
pending on the type of the reaction involved.