Systems Biotechnology: Combined in Silico and Omics Analyses for the Improvement of Microorganisms for Industrial Applications - Systems Biology: Networks, Models, and Applications - page 205

Such biomass composition of metabolites (mmol metabolite/g biomass)
can be experimentally evaluated at a given specific growth rate, or can
be found from the literature [60]. For the maximization/minimization
of the rate of product or byproduct formation, the objective function
corresponds to its net transport flux in eq. (3), which is formulated
by summing all fluxes linked to the product. For example, the maxi-
mization of the rate of succinic acid production can be formulated as
follows:

S jj
jJ

Maximize ∑ (6)

succ,

∈

where S succ, j designates the stoichiometric coefficient of reaction j
involving succinic acid.

Flux Analysis Based on Labeled Substrates
The constraints-based flux analysis can be upgraded with respect to
its accuracy by providing additional material balance equations
through isotope balancing. Thus, more realistic internal fluxes may
be predicted [61]. Using a labeled carbon source such as 13 C-labeled
glucose as a substrate, the labeling states of the metabolites can be
traced. Generally, two approaches are used for the flux interpretation
of 13 C labeling patterns (figure 7.5). One is the identification of the
flux ratio in converging reaction at the branch point using partial
isotopomer data which are generated from the 13 C pattern of proteino-
genic amino acids [62]. This approach is taken by solving the equations
of metabolic reactions and optimizing the solution by error minimization.
The flux ratios can be readily determined through GC/MS data with-
out significant computational burden, but absolute flux values cannot
be obtained [33]. The other iterative approach uses all available 13 C
labeling data, extracellular material fluxes, and biomass composition
for simultaneous interpretation of metabolic models of varying
complexities [63]. The labeling state of metabolic intermediates is
balanced within a model through an iterative fitting procedure on the
isotopomer patterns of network metabolites. These approaches of employ-
ing 13 C data from NMR [64-66] allowed successful determination of
the in vivo internal flux distributions in different microorganisms. It
should be mentioned that isotope balances are bilinear with respect
to its labeling and reaction rate. This is why an iterative approach of
error minimization is used for flux determination. The mathematical
complexity of this approach has been addressed by several researchers,
who introduced concepts like exchange fluxes [67,68], isotopomer
mapping matrices [64] resembling atom mapping matrices [69], cumomer
balances [68], and summed fractional labeling [70].