178
Chapter 5
As discussed in Note 5.6 a problem with linear programming is that the flux vector v may not be
uniquely defined by the optimization process, and consequently there may be many different
pathway routes that lead to the maximum overall yield of the product of interest, and in practice
only a few o f these may be of interest. It is problematic to use linear programming to identify
different solutions for the flux vector v that gives the optimum yield, and alternative approaches
are therefore interesting.
One alternative approach to analyze the capabilities of a metabolic network is
elementary flux
modes
(Schuster
et al.,
2000), which is shortly described in Note 5.7. The elementary flux modes
completely characterize the metabolic network and any operation of the network as a linear
combination of the elementary flux modes. Even though this approach offers the possibility to
obtain all possible modes of operation of the network, and hereby also several different modes
that gives a high yield of the product of interest, its practical limitations lies in the fact that even
for relatively small networks there is a huge number of elementary flux modes, and when more
reactions are added to the network the number of elementary flux modes increases drastically.
Schilling
et al.
(2000) handled the problem using so-called
extreme pathway analysis,
where the
extreme pathways are represented by the edges of the cone in Fig. 5.12 and any mode of
operation o f the network can be expressed as a linear combination o f these extreme pathways.
With the introduction of large (and almost complete) metabolic networks it is of course of
significant interest to evaluate the metabolic capabilities, not only for biotech applications but
also in order to gain further insight into the systemic properties of large networks. Development
of new algorithms for analysis of metabolic networks is therefore a key theme in Systems
Biology, and it is currently a hot topic of research.
Note 5.8
Elementary flux modes
The elementary flux modes of a metabolic network is a unique representation of the system, and it
basically represents a new definition to the concept of metabolic pathways substantially different from
the traditionally classified pathways, such as glycolysis, pentose phosphate pathway, TCA cycle etc.
Schuster and co-workers (Schuster
et al.,
1999; Schuster
et al.,
2000) developed the concept of
elementary flux modes, which allows identification of a unique set of reaction paths that span all possible
modes of operation of the network. Thus, any operation of the network can be represented as a linear
combination of the elementary flux modes. To illustrate, consider the very simple pathway structure
below.
Pathway fluxes
v,=2 and v2=v3=1
B
Pathway 1
fluxes:
v,=1,v2=1
B
Pathway 2
fluxes: v,=1,Vj=1
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