Interplay between Constraints, Objectives, and Optimality for Genome-Scale Stoichiometric Models

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.Author Summary: Organisms depend on huge networks of molecular reactions for environmental sensing, information integration, gene expression, and metabolism. The discovery of general principles of network behavior is a major ambition of systems biology and of great interest to biotechnology and medicine. We present a computational tool that calculates all optimal states of metabolism in terms of pathways, which is arguably the most intuitive and preferred approach to characterize whole-cell metabolism. We show how the space of all feasible flux distributions can be compactly described in terms of a unique set of minimal and feasible pathways, given realistic stoichiometric, thermodynamic, and optimization-objective constraints. This description clarifies the interplay between flux constraints and optimization objectives. We explain why some fluxes are variable and cross-correlate within the solution space while others do not and how multi-objective optimization shrinks the solution space. We illustrate our findings with a toy metabolic model to explain the main insights and apply it to a genome-scale stoichiometric model of Escherichia coli metabolism.