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stoichiometric coecients of the metabolites in the respective reactions (the
rows of the matrix correspond to the metabolites, the columns correspond
to the reactions). Together with the flux vector v , composed of the reaction
rates of the unknown internal reactions rates r and the partially experimen-
tally determined exchange reactions b, and the assumption of a steady state,
the computational task remains to find a solution for S ∗ v =0.Thistask
can be achieved by the tools that linear algebra provides (details would be
beyond the scope of this topic, the interested reader is referred to [230] for
further information). For most reaction networks, the system is underdeter-
mined if only constrained by extracellular uptake and secretion rates and the
growth rate of the cell, meaning that often not all fluxes, especially those of
parallel pathways and cycle fluxes of the network, can be resolved.
Additional constraints are gained from growth experiments with stable iso-
tope tracers like 13 C (cf. Section 5.1.1). The data can be used to estimate
the flux distribution inside the cell of interest. The rationale behind these
13 C tracer experiments is that the carbon backbones of the metabolites often
are manipulated differently by alternative pathways, leading to different 13 C
labeling patterns of the metabolites. Thus, constraints to fluxes complemen-
tary to the basic stoichiometric constraints can be derived by measuring the
mass isotope distribution of metabolites, that is, the relative abundances of
molecules only differing in the number of heavy isotopes, which render the
system fully resolvable.
Currently, two main approaches exist for such interpretation of the deter-
mined 13 C labeling patterns and the inference of intracellular fluxes. In the
global isotopomer balancing approach [275, 339, 345, 259], the problem of es-
timating metabolic fluxes from the isotopomer measurements are formulated
as a nonlinear optimization problem, where candidate flux distributions are
iteratively generated until they fit well enough to the experimental 13 Cla-
beling patterns. The second method is metabolic flux ratio analysis ,coined
as METAFoR [269], which relies on the local interpretation of labeling data
using probabilistic equations, which constrain the ratios of fluxes producing
the same metabolite. The approach is mainly independent of the global flux
distribution in the entire metabolic network [269, 43, 94] meaning that flux
ratios can be calculated without knowing the uptake and production rates
of external metabolites and the biomass composition of the cell. If enough
independent flux ratios can be identified, it is possible to use them to con-
strain the metabolic network equation system and to calculate the full flux
distribution of the network [95].
5.1.3 FiatFlux
FiatFlux [353], developed to facilitate 13 C-based metabolic flux analysis, is a
MatLab-based software that provides a user interface and interactive work-
flow for the analysis of GC-MS-detected 13 C patterns of proteinogenic amino
acids. It allows for the calculation of flux partitioning ratios (METAFoR
 
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