170
Chapter 5
Figure 5.10 A procedure for estimating metabolic fluxes using
13
C-labeled data. The procedure starts with a
guess of the free fluxes, and then all the fluxes are calculated using matrix inversion (in analogy with eq. (
2
)
in Example 5.10). The calculated fluxes can be compared directly with measured rates and they can be used
to calculate the fractional labeling of all the intracellular metabolites. The calculated fractional labeling can
then be compared with experimental data on the fractional labeling, and a total deviation between calculated
fluxes and fractional labeling of metabolites can be found. Through the use of an optimization algorithm it
is possible to propose a new set of fluxes, and hereby iterate until the total deviation is minimized, resulting
in a good estimate of the fluxes.
When a proper model has been identified it is possible to estimate the fluxes through the different
branches of the central carbon metabolism. In the literature one may find several examples of the
use of l
3
C-labeled data to estimate the metabolic fluxes (see e.g. Pedersen
et al.
(2000); Christensen
and Nielsen (2000); Dauner
et al.
(2001)). Thus Fig. 5.11 shows a flux map for the central carbon
metabolism in 5.
cerevisiae
during aerobic growth. Metabolic flux maps of the type shown in Fig.
5.11 contain useful information about the
contribution
of various pathways to the overall
metabolic processes o f substrate utilization and product formation. However, the real value of
such metabolic flux maps lies in the
flux differences
that are observed when flux maps obtained
with different strains or under different conditions are compared with one another. In Fig. 5.11
the fluxes are compared for growth at glucose repressed conditions (batch culture) and at glucose
de-repressed conditions (chemostat culture at low dilution rate). Through such comparisons the
impact of genetic and environmental perturbations can be fully assessed, and the importance of
specific pathways, or reactions within a given pathway can be accurately described. Hereby new
insight into the function of the different pathways may be obtained and this can be used to guide
metabolic engineering (Vallino and Stephanopoulos, 1991).
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