Biochemical Reaction Networks
147
-0 .3 3 3
rs
=3.093
rx
and
Ysx
=0.108
;
Yse = YxeYsx
=5.14-0.108 = 0.554
Ysg
= 0.5 —
4.19
Ysx
= 0.0484
;
= 0.167 + 1.1
43Ysx
= 0.290
Thus, the black box model becomes:
-
CH 20 +
0.554
CH ,O 05 +
0.290
C 0 2 +
0.108* + 0.0484C//g
,0 = 0
(
6
)
Just as in Example 3.1 the stoichiometry of Eq. (6) satisfies a carbon and a redox balance, but although the
same biomass composition CH| 74O06N0
was used the stoichiometry is not quite the same. A little less
biomass and glycerol is produced while the ethanol and carbon yields are higher. It is reasonable that
Yig
and
Tsx decrease together since conversion of glucose to ethanol is redox neutral and therefore
\ fg = a rx
where a is the stoichiometric coefficient for NADH production in the first reaction. We see from the overall
carbon balance that Ysg = 0.0484/0.108 = 0.45, which is the ratio between a = 0.15 and
in our example.
In Eq. (3.23)
Ysg =
0.077/0.137 = 0.56, which means that a portion of the glycerol formed is used as a sink
for NADH produced in reactions which are not accounted for in the simple metabolic model that we use
here.
Since (in the absence of acetaldehyde) the pathway to ethanol is the only one which provides ATP for
glycerol production and especially for biomass formation a relatively higher yield of ethanol in Eq. (6)
compared to Eq. (3.23) indicates that the ATP demand for biomass production is lower than 2.42 mol ATP
(C-mol DW)'1
assumed in the model. If the ATP coefficient in the first reaction is reduced to 1.80 the result
is:
r
ac
-
j r - 2.473
rx
;
for
rac= 0 : Ysx
= 0.1348;
and consequently
r =3.90 r
e
X
rc = - \ r s
+ 0.8335
rx
8
The stoichiometry for
r„ =
0 is:
-
C H 20 + 0.526CH,O05
+0.279
C 0 2
+0.135X
+ 0.0606CH, , 0
= 0
(7)
The stoichiometric coefficients for ethanol, C02 and biomass are now close to the experimental values in
Eq. (3.23). The glycerol to biomass ratio is still too low, but it is beyond the capability of the model to
correct t
h
i
s
.
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