Abstract
High-throughput data generation and genome-scale stoichiometric models have greatly facilitated the comprehensive study of metabolic networks. The computation of all feasible metabolic routes with these models, given stoichiometric, thermodynamic, and steady-state constraints, provides important insights into the metabolic capacities of a cell. How the feasible metabolic routes emerge from the interplay between flux constraints, optimality objectives, and the entire metabolic network of a cell is, however, only partially understood. We show how optimal metabolic routes, resulting from flux balance analysis computations, arise out of elementary flux modes, constraints, and optimization objectives. We illustrate our findings with a genome-scale stoichiometric model of Escherichia coli metabolism. In the case of one flux constraint, all feasible optimal flux routes can be derived from elementary flux modes alone. We found up to 120 million of such optimal elementary flux modes. We introduce a new computational method to compute the corner points of the optimal solution space fast and efficiently. Optimal flux routes no longer depend exclusively on elementary flux modes when we impose additional constraints; new optimal metabolic routes arise out of combinations of elementary flux modes. The solution space of feasible metabolic routes shrinks enormously when additional objectives---e.g. those related to pathway expression costs or pathway length---are introduced. In many cases, only a single metabolic route remains that is both feasible and optimal. This paper contributes to reaching a complete topological understanding of the metabolic capacity of organisms in terms of metabolic flux routes, one that is most natural to biochemists and biotechnologists studying and engineering metabolism.
Highlights
Research in biotechnology and medicine benefits from understanding the metabolic capacity of organisms, including their sensitivities to genetic and environmental changes
Organisms depend on huge networks of molecular reactions for environmental sensing, information integration, gene expression, and metabolism
The accuracy of Flux Balance Analysis (FBA) predictions depends on the availability of realistic flux constraints, which can be derived from experimental data
Summary
Research in biotechnology and medicine benefits from understanding the metabolic capacity of organisms, including their sensitivities to genetic and environmental changes. The combined use of high-throughput metabolomics data, comprehensive protocols [3], and (automated) reconstruction tools [4] has resulted in an explosion in the number and size of genome-scale stoichiometric metabolic models [5, 6]. There are insufficient flux constraints to obtain a single unique solution and a large space of optimal flux distributions results [14,15,16]. These alternative flux distributions give an impression of the robustness of a metabolic network [17], but not every alternative is favorable for the organism. The solution space can be analyzed further with secondary objectives [18,19,20,21,22], e.g. minimization of the number of active fluxes [23] or the sum of absolute fluxes [24], which have been used as proxies for maximization of the protein expression efficiency and minimization of the protein burden, respectively
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