Systems Biology and Metabolic Engineering in Bacteria - Systems Biology of Metabolic and Signaling Networks - page 344

13.3 Steady State Models
Steady state models attempt to predict the flux distribution during balanced growth,
a condition reached in chemostats and at certain phases of a batch culture. Histori-
cally, most experiments have striven to reach balanced growth, since the constancy
of the composition of the bacterial cell greatly facilitates the interpretation of the
results. However, the constancy of composition is also the major experimental
drawback of balanced growth. In order to obtain the large amount of data necessary
to constrain a mathematical model, the experimental measurements have to be
repeated under many different growth conditions.
A steady state model is a mathematical representation of the intracellular
metabolic flows that can, or cannot, be observed directly. The basis on which all
these models are built is the stoichiometry matrix (equivalent to the connectivity of
the metabolic network, describing all possible reactions and their reaction
stoichiometries) and a set of measured fluxes. These fluxes can be intracellular
fluxes, which need tracer experiments, or uptake fluxes. In general, the combination
of experimental datasets and topological models of the biological network leads to
an under-determined system. Additional constraints have to be imposed in order to
uniquely calculate the (steady state) behavior of the network. These constraints
come from experimental monitoring of flux distribution, usually using 13C-labeling
techniques, or predicting the flux distribution based on an objective function. The
former method is called “metabolic flux analysis” (MFA), the latter “flux balance
analysis” (FBA). Powerful tools for both approaches have been developed. Toya
et al. ( 2011 ) have described the principles and available software tools for using
MFA and FBA [see also (Dandekar et al. 2012 )]. An excellent review of tools for
constraint-based reconstruction and analysis methods can be found in Lewis
et al. ( 2012 ).
Metabolic Flux Analysis (MFA) can be applied to metabolic networks of any
complexity, e.g., cycles, parallel and reversible reactions. Labeling patterns provide
very useful information, directly about the intracellular flux distribution. The
procedure is normally initiated by adding the labeled compound (typically
13 C-glucose for central metabolism) to a steadily growing culture. The flux distri-
bution is then derived by comparing the observed labeling pattern of metabolites
with the predictions from an assumed flux distribution. The result is optimized in an
iterative process of model adjustment and comparison to the experimental data. A
limitation of this approach is it requires measuring fluxes under different experi-
mental conditions. This constraint can be somewhat alleviated by parallel labeling
experiments, where the same substrate carries multiple labels, or differently labeled
substrates are added to the culture simultaneously (Crown and Antoniewicz 2012 ).
With this approach specific fluxes can be measured precisely and efficiently to
validate the proposed structure of a biochemical network. One disadvantage of
multiple labeling is the higher cost of the experiment.
The other, commonly used technique for calculating metabolic fluxes is “flux
balance analysis” (FBA). The principle is well described in Orth et al. ( 2010 ) and