Biochemical Reaction Networks
137
In the follow ing w e are going to consider a sim plified m odel o f C hristiansen and N ielsen (2002) w here
enzyme production is not considered (only a sm all am o u n t o f free energy is going to this anyw ay). In the
model N A D H , N A D P H and F A D H : are lum ped into one com pound (N A D H ). In the original m odel both
NADH and FA D H
2
w ere considered as substantial am ounts o f FA D FF are form ed during grow th on
citrate, and the P/O ratio for this com pound is different from that for N A D H . H ere w e intend prim arily to
illustrate the concept o f how data from grow th on tw o different substrates can be used to estim ate all
three energetic param eters, and w e therefore apply a less com plex m odel.
In the m odel the overall stoichiom etry for biom ass synthesis for grow th on glucose and citrate are:
b io m a ss+ 0.148 C O , + 0.176 N A D H - 1.148 C H 20 - (0.43 + A',) A TP = 0
(1)
biom ass + 1.025 C 0
2
+ 0.917 N A D H - 2.025 C H
8
i
6
0
7/6
- (0.73 + ATX
) A TP = 0
(2)
The glucose catabolism is:
0.667 A T P + 2 N A D H + C O , - C H 20 = 0
(3)
and citrate catabolism is:
4/18 A T P + 1.5 N A D H + C 0
2
- C H
8
,
6
0„„ = 0
(4)
For growth on both substrates respiration is described by:
P/O A TP - N A D H - 0.50 0
2
= 0
(5)
Finally a m aintenance reaction eq. (5.11) w as considered in the m odel.
From the balances o f co-factors and the balances for glucose and citrate in the tw o m odels the follow ing
equations can be derived in analogy w ith eq. (5.18):
-rsk
= | 1-148-
(0 .4 3 + A / J - 0 . 1 7 6 P / 0
2 P / 0 + 0 .6 6 7
M +
2 P / 0 + 0 .6 6 7
= O
+
(6)
=
2 .0 2 5
(0 .7 3 + Ä / J - 0 . 9 1 7 P / 0
1 .5 P /0 + 4 /1 8
1 .5 P /0 + 4 /1 8
=
0
+
"3
(7)
From chem ostat cultures C hristiansen and N ielsen (2002) found the follow ing yield coefficients and
maintenance coefficient":
2
The true yield coefficient for citrate is not reported by Christiansen and Nielsen (2002) as they only give data for a
single chemostat experiment. Their approach is therefore somewhat more complicated, and to reduce the complexity
we will here use a true yield coefficient that has been calculated from their data.
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