Genome-Scale Models of Metabolic and Regulatory Networks - Systems Biology: Networks, Models, and Applications - page 235

substrate uptake rates and byproduct secretion rates and use these
values as the maximum allowed rates in constraint-based analysis [27].
Further constraints, including restrictions on allowed flux distribu-
tions due to free energy balancing in loops in metabolic networks, can
be applied to further reduce the size of the solution space [28-30].
Additionally, regulatory constraints due to transcriptional regulation
acting on metabolic enzyme expression can be imposed on the network
resulting in time- and condition-dependent changes in the solution
space. These regulatory constraints will be discussed in more detail in
the section focusing on regulatory networks below.
Constraints (2)-(4) together with any additional constraints form the
basis for the analysis of allowable flux distributions in a reconstructed
metabolic network. A number of different mathematical methods
described below can be applied to analyzing these allowable flux
distributions (figure 8.2). The methods can be roughly classified into
two categories: (1) methods that assume an objective for the network
(e.g., biomass production) and result in prediction of a single optimal
flux distribution or a set of optimal distributions; and (2) methods
that do not assume a particular objective and aim to characterize all
the allowed flux distributions. Methods in the former class are com-
putationally more efficient, and result in experimentally verifiable
predictions, whereas the methods in the latter class tend to be more
computationally demanding, and can be used to analyze general
network properties.

Finding Optimal Network States
Flux balance analysis . The most commonly used constraint-based
analysis method is flux balance analysis (FBA), which allows identify-
ing a particular point (corresponding to a particular flux distribution
in the network) in the subspace defined by constraints (2)-(4), based on
optimizing a specific objective function. The objective usually assumed
for metabolic physiology of microbial cells is cellular growth, which
can be mathematically represented by the biomass composition c of
the cell. In vector c the production flux for each biomass component
is represented by a coefficient equivalent to the experimentally meas-
ured fraction of the cell biomass. While the biomass composition varies
depending on growth conditions, for practical purposes a constant
biomass composition is usually assumed. In addition to the biomass
components, this objective function typically also includes the ATP
maintenance requirements of the cell for cellular processes outside
metabolism. Given a biomass composition represented by the nonzero
components of the vector c , we can predict flux distributions using
FBA as the solution of the following linear program:

v i max max c T v subject to Sv = 0, 0 ≤ v i ≤ (5)