Biochemical Reaction Networks
177
Table 5.4 Shadow prices at different specific oxygen uptake rates [in mmol (g DW h)'1] calculated using
the metabolic model of Varma
et al.
(1993a)a
Metabolite
Shadow price
[g DW (mmol metabolite)']
0
12
20
Oxygen
0.0399
0.0283
0
ATP
0.0109
0.0106
0.0049
NADH
-0.0054
0
0.0065
Acetate
0
0
0.0242
Ethanol
0
0.0106
0.0422
Lactate
0.0054
0.0106
0.0422
‘The specific glucose uptake rate is 10 mmol (g DW h)'1.
The model was also applied to investigate the potential of
E. coli
to produce specific compounds,
e.g.,
amino acids (Varma
et al.,
1993b). This potential can be determined from the magnitude of the shadow
prices, since these provide a measure of the trade off in biomass growth for the production of a specific
compound. It was found that the shadow prices are low for amino acids like glycine, alanine, and
aspartate, which have simple biosynthetic routes, whereas the shadow prices are high for the aromatic
amino acids phenylalanine, tryptophan, and tyrosine, which have complex biosynthetic routes. Thus, if
the product is the end-result of a long and complex biosynthetic route, the requirement of cell
metabolism is large and the effect on biomass growth is therefore severe. On the contrary, the cells can at
a small cost produce a compound with a simple metabolic route, and the effect on biomass growth is
therefore small.
_____
_______ _____________________________
Application o f linear programming has been used for flux analysis of many cellular systems, and
recently it has been used to analyze genome-scale metabolic models, i.e., metabolic models that
are reconstructed
from
genomic
information,
possibly combined with
information
from
biochemical reaction databases (Covert
et al.,
2001). Genome-scale models contain a large
number of reactions. Using these models the role of specific genes in the overall metabolism can
be evaluated, and operation of the network during growth on different media can be analyzed in
great detail (see e.g. Edwards and Palsson (2000) and Edwards
et al.
(2001)).
The concept of linear programming is well suited to evaluate the potential of a given metabolic
network for producing a specific compound, and the maximum possible yield can easily be
calculated. Calculation of maximum theoretical yields provides a benchmark for real processes.
Furthermore, the influence of the network structure on the overall yield can be analyzed by
inserting or deleting reactions from the network. Burgaard and Maranas (2001) provided a
formalized approach based on
mixed linear integer programming
(MILP) to this type of analysis.
previous page 201 Bioreaction Engineering Principles, Second Edition  read online next page 203 Bioreaction Engineering Principles, Second Edition  read online Home Toggle text on/off