model with J fluxes v and K constraints will in practice have several degrees o f freedom F=J-K,
and there is an infinite number of solutions v to the model. In order to identify a unique solution
v it is necessary to add more information or impose further constraints on the system. This can be
done in three different ways:
Use o f directly measurable non-zero rates.
This approach is the same as that discussed
for the simple metabolic network models in Section 5.3, and when exactly
measured the fluxes in the network can be calculated using eq. (5.1) - or eq. (5.25). This
approach is discussed further in Section 5.4.1.
Use o f labeled substrates.
When cells are fed with labeled substrates, e.g., glucose that is
enriched for l3C in the first position, then there will be a specific labeling of the
intracellular metabolites. As there are different carbon transitions in the different cellular
pathways, the labeling pattern of the intracellular metabolites is a function of the activity
o f the different pathways. Through measurements of the labeling pattern of intracellular
metabolites and application o f balances for the individual carbon atoms in the different
biochemical reactions, additional constraints are added to the system. As discussed in
Section 5.4.2 this is used to quantify the fluxes, even when only a few rates are measured.
Use o f linear programming.
It is possible using linear programming to identify a solution
(or a set of solutions) for the flux vector v that fulfills a specific optimization criterion,
e.g., the flux vector that gives maximum growth yield. This approach is the subject of
Section 5.4.3. *
Note 5.3 Biomass equation in metabolic network models
Biomass formation is the result of a large number of different biochemical reactions. In Chapters 2 and 3
we looked at some of the many different reactions that are involved. Biomass synthesis starts with the
formation of precursor metabolites (see Table 2.4), which are converted into building blocks (amino
acids, nucleotides, lipids etc.). The building blocks are the monomers in macromolecules, which are the
major constituents of biomass (see Table 2.5). The macromolecular composition of a given cell depends
on the growth conditions, and on the composition, e.g. the amino acids in the proteins, of the different
macromolecules. It is therefore not possible to specify a single reaction converting precursor metabolites
into biomass. If this is still done one must make an assumption that the macromolecular composition is
constant. There are three different ways of setting up an equation for formation of biomass with constant
Direct synthesis from precursor metabolites
Direct synthesis from building blocks
Synthesis from macromolecules
In some cases one may use a combination of three approaches.
In the first approach an overall reaction is specified for conversion of precursor metabolites into biomass.
Here information compiled in Table 2.4 is used together with information about the costs of ATP,
NADPH and NADH to make biomass from the precursor metabolites. This identifies the stoichiometric
coefficients for the different precursor metabolites involved in biomass formation. Reactions leading
from the individual precursor metabolites to building blocks are not considered in this model, except
perhaps for reactions leading to building blocks that are used for product formation, e.g. the synthesis of
valine, cysteine and a -aminoadipic acid may have to be considered in a model for penicillin production.
The synthesis of all other amino acids can be lumped into the overall biomass equation describing