158
Chapter 5
With 15 fluxes and 8 balance equations, there are 7 degrees of freedom. Thus, if 7 reaction rates are
specified, the other rates can be calculated. In their analysis Aiba and Matsuoka measured six reaction
rates in the network: the glucose uptake rate (rg|C
= - v,); the carbon dioxide production rate (rc); the citric
acid production rate (rc„); the isocitrate production rate (r,cl); the protein synthesis rate (грт0|); and the
carbohydrate synthesis rate (rcar). The rates rplol and
raa
were found from measurements of the protein and
carbohydrate contents of the biomass (in a steady state chemostat). In addition to the six measurements,
Aiba and Matsuoka imposed an extra constraint by setting one of the rates in the network equal to zero.
Three different cases were examined, reflecting three different modes of operation of the network:
Model 1:
The glyoxylate shunt is inactive,
i.e.,
vn = 0.
Model 2:
Pyruvate carboxylase is inactive,
i.e.,
v4 = 0.
Model 3:
The TCA cycle is incomplete,
i.e.,
v8 = 0.
Setting a flux to zero corresponds to removing the corresponding reaction from the model. The number
of fluxes is therefore reduced to 14 and the degrees of freedom to 6. With the listed six measured rates,
the system of equations is therefore exactly determined for each of the three models and can be solved to
determine all the fluxes using eq. (5.25) and the unknown exchange rates using eq. (5.26). If we consider
Model 1 we find:
'-1
0
0
0
0
0
0
0
0
0
0
0
0
0 ^
-1
( r
r gkc
V
,
0
1
1
-1
0
0
1
1
0
0
0
0
0
0
Гс
V3
0
0
0
0
1
-1
0
0
0
0
0
0
0
0
r ,
V4
0
0
0
1
0
1
-1
0
0
0
0
0
0
0
r,d
V5
0
0
0
0
0
0
0
0
0
0
0
0
0
1
*
pro!
V6
0
0
0
0
0
0
0
0
0
0
0
1
0
0
rcar
v
7
1
-1
0
0
0
0
0
0
0
0
0
-1
0
0
0
V8
0
2
-1
-1
0
0
0
0
0
0
0
0
0
0
0
v .
0
0
1
0
- 1
0
0
0
0
0
- 1
0
- 1
0
0
v m
0
0
0
0
0
0
1
- 1
0
0
0
0
0
- 1
0
V12
0
0
0
0
0
0
0
1
- 1
0
0
0
0
0
0
V13
0
0
0
0
0
0
0
0
1
- 1
1
0
0
0
0
V14
0
0
0
1
- 1
0
0
0
0
1
0
0
0
0
0
VVI5.
, 0
0
0
0
0
0
0
0
0
0
- 1
0
0
0
J
3 0
or
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