168
S
00
Chapter 5
For this network we have the metabolite balance equation:
o
f - 1
0
0
0
0
0 '
' v , ]
0
0
0
0
0
1
V2
rP2
0
0
0
0
1
0
V3
0
1
- 1
- 1
0
0
0
V4
0
0
0
1
1
0
- 1
V5
O y
, 0
1
0
- 1
- 1
0 .
, v 6 y
Clearly three fluxes can be measured directly and with three degrees of freedom we can in principle
estimate the fluxes using matrix inversion. However, the matrix does not have full rank (addition of the
second and fourth column gives the third column), and we therefore need additional information. We
now set v, to
100
and then express the other fluxes as function of two of the fluxes (v
3
and v4), i.e.
o
©
o
V 2
o0
1
V 3
V 3
V 4
V4
w
o0
1
r:
1
v 6
)
l
v 3 + v 4
)
(
2
)
The two fluxes v
3
and v
4
will be termed free fluxes, and if we can obtain information about these from
balances around the individual carbon atoms then we can calculate all the fluxes in the network using eq.
(2). With the carbon transitions specified in the network we can set up balances for the individual carbon
atoms. Thus, for the first reaction we have:
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