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

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.

Constraint-based stoichiometric modelling from single organisms to microbial communities

“…FVA can be formulated as follows:whereby Z opt is determined, using FBA. More advanced methods exist to study all the alternative optimal flux distributions [63,64]. …”

Hierarchical decomposition of metabolic networks using k-modules

“…The largest value with which an edge of a branchdecomposition is annotated is called the branch width of the branch decomposition. For the example of Figure 1, we see in Figure 2 a branch-decomposition with branch width 4, because A' : = {r 11 , r 12 , r 13 , r 14 } is only a 4-module, i.e. λ(A') = 4.…”

“…With this definition, originally introduced by Müller and Bockmayr [11], the flux modules can be efficiently computed [12]. By computing the pathways through each module, a comprehensive pathway-based description can be obtained efficiently [13]. However, this unfortunately only works for the optimal yield space, because for the full steady-state flux space (without yield-optimality condition) no interesting flux modules can typically be found.…”

The number of active metabolic pathways is bounded by the number of cellular constraints at maximal metabolic rates

“…For these linear models, it is known -similar to what we will 76 derive in the general, nonlinear case in this work-that few minimal pathways constitute 77 the optimal solutions in such models [15]. However, constraints on reaction rates do not 78December 21, 2018 3/25 111 infeasible to find the complete set of EFMs in a genome-scale network [22,23].…”