Chapter 5
Constraints imposed on the
metabolic network
Figure 5.12 Illustration of the concept behind the use of linear programming to constrain the operation
of metabolic networks. A given network model allows an infinite number of solutions represented by the
null space at the bottom. When an optimization criterion is applied, it is possible to identify a flux vector
that specifies how the network should operate to fulfill the optimization criterion. [Adapted from I.
Famili, J. Forster, J. Nielsen and B. 0. Palsson (2002) Systems properties of a reconstructed genome-
scale metabolic network for
Saccharomyces cerevisiae.].
Another possibility to constrain the flux vector is to impose an objective function on the system
and apply linear programming to find the optimal solution within the underdetermined system
(see Fig. 5.12). The solution to the optimization problem will give a flux vector that represents
the set o f fluxes that leads to the optimum. A typical optimality criterion is to optimize the
specific growth rate, but clearly the concept can also be used to identify the operation of the
network that gives the maximum yield of a given metabolite (see discussion later). The
optimality criterion may not always give a unique solution for the flux vector, as there may be
several modes of operation of the network that result in the same overall optimal operation. Thus,
one may not necessarily obtain robust estimates of the fluxes in the network using linear
programming, but clearly the advantage is that one may use metabolic models for prediction of
how a metabolic network may operate whereas the approaches discussed earlier only allows
analysis based on a given set of experimental data. In Note 5.6 we will discuss the concepts of
linear programming and in Example 5.11 it is illustrated how a simple model for
E. coli
can be
analyzed using linear programming.
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