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Fast Flux Module Detection Using Matroid Theory

  • Arne C. Müller
  • Frank J. Bruggeman
  • Brett G. Olivier
  • Leen Stougie
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8394)

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.

Keywords

metabolic networks FBA flux modules matroid theory 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Arne C. Müller
    • 1
    • 2
    • 3
  • Frank J. Bruggeman
    • 8
  • Brett G. Olivier
    • 4
    • 5
    • 7
  • Leen Stougie
    • 4
    • 6
  1. 1.Department of Mathematics and Computer ScienceFreie Universität BerlinBerlinGermany
  2. 2.International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC)Max Planck Institute for Molecular GeneticsBerlinGermany
  3. 3.Berlin Mathematical School (BMS)BerlinGermany
  4. 4.Centre for Mathematics and Computer Science (CWI)AmsterdamThe Netherlands
  5. 5.Molecular Cell PhysiologyVU UniversityAmsterdamThe Netherlands
  6. 6.Operations ResearchVU UniversityAmsterdamThe Netherlands
  7. 7.Netherlands Institute for Systems BiologyAmsterdamThe Netherlands
  8. 8.Systems BioinformaticsVU UniversityAmsterdamThe Netherlands

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