Genome-Scale Models of Metabolic and Regulatory Networks - Systems Biology: Networks, Models, and Applications - page 251

The representation of network structure is another major difference
between regulatory and metabolic network reconstruction as the latter
are naturally described through the reaction stoichiometry, whereas
for the former there is no single widely accepted description. Clearly,
more detailed descriptions of regulatory networks require increasingly
large amounts of parameters [104].
Because the role of transcriptional regulation is to modulate other
cellular processes, integrating the reconstructed regulatory networks
with models of these other processes is central to understanding
regulatory network function in the context of the whole organism.
Currently, there are major challenges for achieving this integration
relating both to obtaining the relevant data, and to the modeling frame-
works that are able to support the required large-scale integration.
Possibilities for a suitable modeling framework include discrete net-
work models, such as Boolean and Bayesian networks, which allow
representing key combinatorial interactions between regulators
acting on the same gene either deterministically or probabilistically
[105,106]. These qualitative network models, unlike graph-based
models, allow simulating the network behavior but require signifi-
cantly fewer parameters than linear or nonlinear kinetic models.
Boolean regulatory network models can be readily integrated with
genome-scale metabolic models to formulate integrated models of
cellular function [107]. In the regulated flux balance analysis (rFBA)
approach [107], each of the N reactions in the metabolic model is given
a binary variable y i describing whether the reaction is active or not.
The variables y i are evaluated through a series of Boolean rules that
encode how the activity of a reaction depends on the expression of
the genes related to this reaction, and how the expression of all the
metabolic genes in turn depends on the activities of transcription
factors. Finally, the activities of transcription factors are determined
from extracellular metabolite concentrations X ext so that the reactions

states y i are given by

y i = f i ( X ext ) (6)

where f i are the composite Boolean functions describing the overall
relationship between the reaction states y i

and the concentration

vector X ext .
The reaction states y i are then used to determine the constraints
for an FBA calculation in the following form:

v i max y i max c T v subject to Sv = 0, 0 ≤ v i ≤ (7)

where y i {0,1} as determined by eq. (6). In order to then calculate

extracellular concentrations X ext , it is assumed that the production or

=