Constraints-Based Network Analysis
Constraints-based network analysis aims to reveal the function and capacity of
metabolic networks without recourse to kinetic parameters (Bailey, 2001). The
development and scope of the method has been reviewed (Covert
et al., 2001;
Papin
et al., 2003; Price
et al., 2003, 2004), and its current importance as a modeling
strategy owes much to the successful completion of numerous microbial genome
sequencing projects. The analysis follows a three-step procedure: construction of a
network, application of the constraints to limit the solution space of the network,
and extraction of physiologically relevant information about network performance.
The first step draws heavily on genome annotation, but biochemical and
physiological data can provide complementary information that helps to improve
the accuracy of the deduced network (Covert
et al., 2001). Ideally, the reconstructed
network should also include regulatory elements at the level of gene
expression to allow the model to be applicable under non–steady-state conditions
(Covert and Palsson, 2002). The next step is to use reaction stoichiometry, directionality,
and enzyme level to constrain the network and to work out the full set of
allowed flux distributions (Price
et al., 2004). Finally, these solutions are analyzed
to identify the flux distribution that optimizes a particular outcome, for example,
growth rate (Price
et al., 2003).
Constraints-based genome-scale models have been constructed for several
microorganisms and their utility for probing the relationship between genotype
and phenotype is now well established (Price
et al., 2003). Assessing the impact of
gene additions and deletions on predicted growth rate turns out to be a powerful
test of the validity of the model as well as an effective way of identifying useful
targets for genetic manipulation (Edwards and Palsson, 2000a; Price
et al., 2003).Moreover, network robustness can be modeled by constraining the maximum flux
through particular reactions, and this has demonstrated how effectively the network
can sustain growth despite quite severe restrictions on central carbon
metabolism (Edwards and Palsson, 2000b). The response to genetic modification
and pathway robustness can also be assessed in terms of elementary flux modes—
the set of nondecomposable fluxes that make up the steady-state flux distributions
in the network (Klamt and Stelling, 2003; Schuster
et al., 1999). Thus, changes in
network topology brought about by the addition or deletion of genes have an
immediate effect on the set of elementary flux modes, and the impact on the
synthesis of a particular metabolite and the efficiency with which it can be
produced can be predicted (Schuster
et al., 1999). For example, an analysis of a
metabolic network linking 89 metabolites via 110 reactions in
E. coli revealed over
43,000 elementary flux modes, and from an in
silico exploration of the consequences
of gene deletion, it was concluded that the relative number of elementary
flux modes was a reliable indicator of network function in mutant phenotypes
(Stelling
et al., 2002), suggesting that elementary mode analysis could be a major
asset in identifying targets for metabolic engineering (Cornish-Bowden and
Cardenas, 2002).
The extent to which constraints-based network analysis succeeds in generating
realistic and useful models of metabolism can be assessed directly from work on
red blood cells. Much effort has been put into developing a comprehensive kinetic
model of red blood cell metabolism (Jamshidi
et al., 2001; Mulquiney and Kuchel,
2003), and the question arises as to whether network analysis can make accurate
predictions about the performance of the network. In fact, the complete set of
the so-called extreme pathways (essentially a subset of the elementary modes for
the network) has been worked out for the red blood cell network and after suitable
classification it was shown that these pathways could be used to make physiologically
sensible predictions about ATP:NADPH yield ratios (Wiback and Palsson,
2002). Thus, it has been concluded that network analysis can indeed generate
metabolically important insights without the need for the labor-intensive measurement
of a multitude of kinetic parameters (Papin
et al., 2003). Interestingly,
network analysis has recently been combined with
in vivo measurements of
concentrations and a simplified representation of enzyme kinetics to calculate
the allowable values of these kinetic parameters, and this novel approach
may well facilitate the construction of kinetic models in the absence of the full
characterization of the enzymes in the network (Famili
et al., 2005).
In the light of this conclusion, and particularly given the utility of network
analysis in guiding metabolic engineering (Papin
et al., 2003; Price
et al., 2003;
Schuster
et al., 1999), there would appear to be a strong case for extending the
constraints-based approach to the analysis of plant metabolic networks. However,
there appear to have been few attempts to do so, and the only substantial contribution
is a paper describing an elementary modes analysis of metabolism in the
chloroplast (Poolman
et al., 2003). This analysis highlighted the interaction
between the Calvin cycle and the plastidic oxidative pentose phosphate pathway,
and the potential involvement of the latter in sustaining a flux from starch to triose
phosphate in the dark.
