Biochemical Reaction Networks
161
Table 5.3 Fluxes through key reactions in the metabolic network during anaerobic growth of
S. cerevisiae
and using different models.1
Reaction
Reference model
Model
Including IDP2
Excluding ADH3
Glucose-6P dehydrogenase
7.5
-80
7.9
IDH
1.7
-117
1.3
IDP2
0
176
0
2-Oxoglutarate dehydrogenase
0
22
-0.3
ADH32
1.0
-12
0
1
All fluxes are normalized with respect to the glucose uptake rate that is set to 100, and the fluxes are given as C-mole
(C-mole glucose)'1. All fluxes are for a dilution rate of 0.3 h'1.
2 The flux for Adh3 is given for the direction from acetaldehyde to ethanol in which NADH is consumed.
The approach of combining a metabolic model and measurement of a few rates is attractive due to
its simplicity. The approach does, however, have some pitfalls. Among these are:
Linearly dependent reaction stoichiometries.
This was discussed in Note 5.3, and it was
indicated how the problem could be solved. However, in some cases there is no information
available on regulation of the different pathways, and in fact it may be interesting to
evaluate the relative activity of two different pathways that have the same overall
stoichiometry. As discussed in Note 5.3 one may use enzyme activity measurements as
additional constraints, but
in vitro
determined enzyme activities do rarely represent
in vivo
fluxes.
High sensitivity o f certain fluxes to certain measured rates.
In some cases the matrix
equation is ill-conditioned and this can result in very high sensitivities in the flux estimation
to the measured rates. Whether the matrix equation is ill-conditioned can be checked by the
condition number
(see Note 5.4), which typically has to be less than 100. Alternatively one
may check the sensitivity matrix for the model (see also Note 5.4).
The fluxes are determined by balances fo r specific co-factors.
As illustrated for the simple
metabolic network models in Section 5.3 balances for the co-factors NADH, NADPH and
ATP may be very useful for estimation of the fluxes, particularly as these co-factors link
different parts of the metabolism together. Basically it is not a problem to include balances
for co-factors in metabolic models, but a requirement for proper use of these balances is that
all
reactions involving these co-factors are included in the model. This may be problematic,
since not all parts of the metabolism may be known, and one may inadvertently leave out
important reactions that involve these co-factors. This may result in substantial errors in the
flux estimation. Thus, particularly estimation of the flux through the pentose phosphate
pathway is sensitive to whether
all
reactions involving NADPH are included in the model
when the fluxes are estimated from measurable rates alone.
Introducing
additional
constraints
on
individual
carbon
atom
transitions
combined
with
measurements of the labeling patterns of the some metabolites when the cells are growing on
specifically labeled substrates can circumvent most of the above-mentioned problems as discussed
in Section 5.4.2.
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