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  Section: Molecular Biology of Plant Pathways » Metabolic Organization in Plants
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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.

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