Biochemical Reaction Networks
149
Pyruvate obviously is a pathway branch point metabolite, and therefore a balance can be set up around
this metabolite. In the conversion of pyruvate to metabolic products, three other pathway intermediates
are involved: acetyl-CoA, acetyl-P, and acetaldehyde. Of these, only acetyl-CoA is located at a branch
point and needs to be considered. Finally, conservation of the redox equivalents in the catabolic pathway
yields an additional balance for NADH. One could also set up a balance for NAD+, but this balance
would be linearly dependent on the NADH balance and give no additional information, and would result
in appearance of singularity in the stoichiometric matrix. Note that a balance for ATP could be set up,
but because only catabolic metabolism is considered, there is no consumption of ATP and this balance
therefore would not close. In summary, three pathway metabolites: pyruvate, acetyl-CoA, and NADH;
one substrate: glucose (g); and five metabolic products: lactate (/), carbon dioxide (c), formate (/), acetate
(a), and ethanol (e) are included in the model. Thus, Eq. (5.1) becomes:
'-0 .5
0
rl
0
1
P
0
0
P
0
0
P
=
0
0
P
0
0
PYR
0
1
-1
AcCoA
0
0
0
NADH
,
1
-1
0
0
0
0 '
0
0
0
0
( v \
1
0
0
0
vl
V2
0
1
0
0
P
0
0
1
0
0
0
0
1
v5
-1
-1
0
0
1
1
-1
-1
1
0
0
- 2 ,
(
1
)
Here the stoichiometry is written on a mole basis, and the flux V
| is taken to be in mole pyruvate formed,
and the stoichiometric coefficient for glucose in the first reaction is therefore -0.5. From the balance
equation it is seen that all six fluxes can be directly measured from measurement of the glucose uptake
rate and the formation rate of the five products,
i.e.
'- 0 .5 v, n
rl
V2
p
P
rf
V 4
P
V 5
P j
,
V 6
j
(
2
)
In the balance equation (1) there are three constraints given by the pseudo-steady state assumption to the
three intracellular compounds, pyruvate, AcCoA, and NADH, and with six fluxes the degrees of freedom
F=
3. Thus, if we choose three measured rates then we can calculate the three other rates in the system
(and all the fluxes). If we choose rate measurements of glucose, lactate, and formate, we find by using
Eq. (5.25):
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