Flux modules in metabolic networks

Müller, Arne C.; Bockmayr, Alexander

doi:10.1007/s00285-013-0731-1

“…Similarly, υ A is the subvector of υ with only entries corresponding to reactions in A. 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].…”

Section: Introductionmentioning

confidence: 99%

Hierarchical decomposition of metabolic networks using k-modules

Reimers

¹

2015

Biochemical Society Transactions

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The optimal solutions obtained by flux balance analysis (FBA) are typically not unique. Flux modules have recently been shown to be a very useful tool to simplify and decompose the space of FBA-optimal solutions. Since yield-maximization is sometimes not the primary objective encountered in vivo, we are also interested in understanding the space of sub-optimal solutions. Unfortunately, the flux modules are too restrictive and not suited for this task. We present a generalization, called k-module, which compensates the limited applicability of flux modules to the space of sub-optimal solutions. Intuitively, a k-module is a sub-network with low connectivity to the rest of the network. Recursive application of k-modules yields a hierarchical decomposition of the metabolic network, which is also known as branch decomposition in matroid theory. In

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“…Here, we also allow b = 0 to simplify notation in the context of modules. Furthermore, the space of optimal-yield fluxes is again a polyhedron and can be written in this form, too [15]. In this paper we will show that we can reduce the analysis of P to the analysis of linear vector spaces, i.e.…”

Section: Definitions and Preliminariesmentioning

confidence: 99%

“…Each such a module has in each optimum specific fixed input and output compounds. Müller and Bockmayr [15] used this property to formalize the notion of flux-module in a mathematically rigorous way. This allowed them to show that every optimal yield elementary flux mode (EFM) [23] is a concatenation of reactions with fixed flux and an elementary mode of each of the flux modules.…”

Section: Introductionmentioning

confidence: 99%

“…While the method by Kelk et al [9] required the enumeration of exponentially many vertices of a flux polyhedron (which are related to the optimal yield EFMs), Müller and Bockmayr [15] showed a way to find the modules without needing to compute all extreme solutions. Their method however relied on many runs of flux variability analysis (FVA) [3,13].…”

Section: Introductionmentioning

confidence: 99%

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Fast Flux Module Detection Using Matroid Theory

Reimers

¹

,

Bruggeman

²

,

Olivier

³

et al. 2015

Journal of Computational Biology

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Abstract. Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. 2012, that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space.Using the mathematical definition of module introduced by Müller and Bockmayr 2013, we discovered that flux modularity is rather a local than a global property which opened connections to matroid theory. Specifically, we show that our modules correspond one-to-one to so-called separators of an appropriate matroid. Employing efficient algorithms developed in matroid theory we are now able to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this paper, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.

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“…We showed that flux modules [9,15] of genome-scale metabolic networks can efficiently be computed using matroids. We confirmed the previous results that the optimal flux space of most genome-scale metabolic networks decomposes into modules.…”

Section: Enumeration Of Optimal-yield Pathwaysmentioning

confidence: 99%

Fast Flux Module Detection Using Matroid Theory

Müller

¹

,

Bruggeman²,

Olivier

³

et al. 2014

Lecture Notes in Computer Science

Self Cite

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Abstract. Flux balance analysis (FBA) is one of the most often applied methods on genome-scale metabolic networks. Although FBA uniquely determines the optimal yield, the pathway that achieves this is usually not unique. The analysis of the optimal-yield flux space has been an open challenge. Flux variability analysis is only capturing some properties of the flux space, while elementary mode analysis is intractable due to the enormous number of elementary modes. However, it has been found by Kelk et al. 2012, that the space of optimal-yield fluxes decomposes into flux modules. These decompositions allow a much easier but still comprehensive analysis of the optimal-yield flux space.Using the mathematical definition of module introduced by Müller and Bockmayr 2013, we discovered that flux modularity is rather a local than a global property which opened connections to matroid theory. Specifically, we show that our modules correspond one-to-one to so-called separators of an appropriate matroid. Employing efficient algorithms developed in matroid theory we are now able to compute the decomposition into modules in a few seconds for genome-scale networks. Using that every module can be represented by one reaction that represents its function, in this paper, we also present a method that uses this decomposition to visualize the interplay of modules. We expect the new method to replace flux variability analysis in the pipelines for metabolic networks.

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Flux modules in metabolic networks

Cited by 22 publications

References 30 publications

Hierarchical decomposition of metabolic networks using k-modules

Hierarchical decomposition of metabolic networks using k-modules

Fast Flux Module Detection Using Matroid Theory

Fast Flux Module Detection Using Matroid Theory

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