Yet cells switch specific pathways ‘on’ and ‘off’ to sustain their energetic budget in different environments. 8, 16 In addition, current graph constructions are usually derived from the whole set of metabolic reactions in an organism, and thus correspond to a generic metabolic ‘blueprint’ of the cell. Many of these constructions, however, lead to graphs that do not include directional information that is central to metabolic function. 1 Existing graph constructions have been useful for developing an intuitive understanding of metabolic complexity. 23Ī key feature of metabolic reactions is the directionality of flows: metabolic networks contain both irreversible and reversible reactions, and reversible reactions can change their direction depending on cellular and environmental contexts. 22 Importantly, the conclusions of graph-theoretical analyses are highly dependent on the chosen graph construction. 16 For example, one can create a graph with metabolites as nodes and edges representing the reactions that transform one metabolite into another 7, 8, 17, 18 a graph with reactions as nodes and edges corresponding to the metabolites shared among them 19, 20, 21 or even a bipartite graph with both reactions and metabolites as nodes. 12, 13, 14, 15 A central challenge, however, is that there are multiple ways to construct a network from a metabolic model. Tools from graph theory 6 have previously been applied to the analysis of structural properties of metabolic networks, including their degree distribution, 7, 8, 9, 10 the presence of metabolic roles, 11 and their community structure. This enmeshed web of reactions is thus naturally amenable to network analysis, an approach that has been successfully applied to different aspects of cellular and molecular biology, e.g., protein-protein interactions, 2 transcriptional regulation, 3 or protein structure. Yet metabolic reactions are highly interconnected: enzymes convert multiple reactants into products with other metabolites acting as co-factors enzymes can catalyse several reactions, and some reactions are catalysed by multiple enzymes, and so on. 1 Cellular metabolism is usually thought of as a collection of pathways comprising enzymatic reactions associated with broad functional categories. Metabolic reactions enable cellular function by converting nutrients into energy, and by assembling macromolecules that sustain the cellular machinery. By integrating constraint-based models and tools from network science, our framework allows the study of context-specific metabolic responses at a system level beyond standard pathway descriptions. The flux-dependent graphs under various environmental conditions and genetic perturbations exhibit systemic changes in their topological and community structure, which capture the re-routing of metabolic flows and the varying importance of specific reactions and pathways. We illustrate our approach on the central carbon metabolism of Escherichia coli and on a metabolic model of human hepatocytes. The methodology can be applied in the absence of a specific biological context by modelling fluxes probabilistically, or can be tailored to different environmental conditions by incorporating flux distributions computed through constraint-based approaches such as Flux Balance Analysis. Our graphs encode the directionality of metabolic flows via edges that represent the flow of metabolites from source to target reactions. We present a framework for the systematic construction of flux-based graphs derived from organism-wide metabolic networks. Cells adapt their metabolic fluxes in response to changes in the environment.
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