Elementary Flux Modes

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Metabolic pathway analysis is a key method to study a metabolism in its steady state, and the concept of elementary fluxes (EFs) plays a major role in the analysis of a network in terms of non-decomposable pathways. The supports of the EFs contain in particular those of the elementary flux modes (EFMs), which are the support-minimal pathways, and EFs coincide with EFMs when the only flux constraints are given by the irreversibility of certain reactions. Practical use of both EFMs and EFs has been hampered by the combinatorial explosion of their number in large, genomescale systems. The EFs give the possible pathways in a steady state but the real pathways are limited by biological constraints, such as thermodynamic or, more generally, kinetic constraints and regulatory constraints from the genetic network. We provide results on the mathematical structure and geometrical characterization of the solution space in the presence of such biological constraints (which is no longer a convex polyhedral cone or a convex polyhedron) and revisit the concept of EFMs and EFs in this framework. We show that most of the results depend only on very general properties of compatibility of constraints with vector signs: either sign-invariance, satisfied by regulatory constraints, or sign-monotonicity (a stronger property), satisfied by thermodynamic and kinetic constraints. We show in particular that the solution space for sign-monotone constraints is a union of particular faces of the original polyhedral cone or polyhedron and that EFs still coincide with EFMs and are just those of the original EFs that satisfy the constraint, and we show how to integrate their computation efficiently in the double description method, the most widely used method in the tools dedicated to EFs computation. We show that, for sign-invariant constraints, the situation is more complex: the solution space is a disjoint union of particular semi-open faces (i.e., without some of their own faces of lesser dimension) of the original polyhedral cone or polyhedron and, if EFs are still those of the original EFs that satisfy the constraint, their computation cannot be incrementally integrated into the double description method, and the result is not true for EFMs, that are in general strictly more numerous than those of the original EFMs that satisfy the constraint.

In this work we study the optimization of a polyhydroxyalkanoates (PHA) production process by mixed cultures based on a detailed hybrid metabolic model. The metabolic network under consideration was first decomposed into its fundamental pathways using the elementary flux modes (EFM) technique. Then, a dynamical hybrid semi-parametric model was formulated, which allowed to identify the EFM kinetics from experimental data of 7 batch runs. The EFM fluxes were interpreted in terms of metabolic consistency. The final model allowed to characterize the metabolism dynamics, namely of how the relative weight of pathways evolves in time in a typical batch or fed-batch run. The present technique is a step forward for the integration of systems biology and bioprocess control.

Elementary Flux Modes (EFMs) have been claimed as one of the most promising approaches for pathway analysis. These are a set of vectors that emerge from the stoichiometric matrix of a biochemical network through the use of convex analysis. The computation of all EFMs of a given network is an NP-hard problem and existing algorithms do not scale well. Moreover, the analysis of results is difficult given the thousands or millions of possible modes generated. In this work, we propose a new plug-in, running on top of the OptFlux Metabolic Engineering workbench (Rocha et al., 2010), whose aims are to ease the analysis of these results and explore synergies among EFM analysis, phenotype simulation and strain optimisation. Two case studies are shown to illustrate the capabilities of the proposed tool.

Background Understanding complex systems through decomposition into simple interacting components is a pervasive paradigm throughout modern science and engineering. For cellular metabolism, complexity can be reduced by decomposition into pathways with particular biochemical functions, and the concept of elementary flux modes provides a systematic way for organizing metabolic networks into such pathways. While decomposition using elementary flux modes has proven to be a powerful tool for understanding and manipulating cellular metabolism, its utility, however, is severely limited since the number of modes in a network increases exponentially with its size. Results Here, we present a new method for decomposition of metabolic flux distributions into elementary flux modes. Our method can easily operate on large, genome-scale networks since it does not require all relevant modes of the metabolic network to be generated. We illustrate the utility of our method for metabolic engineering of...

Constraint-based analysis of genome-scale metabolic networks has become increasingly important for describing and predicting the cellular behavior of living organisms. The steady-state constraints provide a reliable framework without the need for additional kinetic details of the system. As the number of metabolic network reconstructions and their level of detail continually increases, many computational tools for their analysis become unpractical to use. This invites for more efficient algorithms and tools for the analysis of metabolic networks. We have a two-fold aim with this work: first, to design new algorithms that improve the efficiency of some of the existing methods, secondly to create additional tools that fill in gaps in our toolbox for metabolic network analysis. These methods will provide additional insight into the structure of metabolic networks and ultimately broaden our understanding of cellular systems. In the first part of the thesis we focus on improving flux cou...