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Flux modules in metabolic networks

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Abstract

The huge number of elementary flux modes in genome-scale metabolic networks makes analysis based on elementary flux modes intrinsically difficult. However, it has been shown that the elementary flux modes with optimal yield often contain highly redundant information. The set of optimal-yield elementary flux modes can be compressed using modules. Up to now, this compression was only possible by first enumerating the whole set of all optimal-yield elementary flux modes. We present a direct method for computing modules of the thermodynamically constrained optimal flux space of a metabolic network. This method can be used to decompose the set of optimal-yield elementary flux modes in a modular way and to speed up their computation. In addition, it provides a new form of coupling information that is not obtained by classical flux coupling analysis. We illustrate our approach on a set of model organisms.

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References

  • Beard DA, Babson E, Curtis E, Qian H (2004) Thermodynamic constraints for biochemical networks. J Theoret Biol 228:327–333

    Google Scholar 

  • Burgard AP, Vaidyaraman S, Maranas CD (2001) Minimal reaction sets for Escherichia coli metabolism under different growth requirements and uptake environments. Biotechnol Progr 17:791–797

    Google Scholar 

  • Burgard AP, Nikolaev EV, Schilling CH, Maranas CD (2004) Flux coupling analysis of genome-scale metabolic network reconstructions. Genome Res 14(2):301–312

    Article  Google Scholar 

  • de Figueiredo LF, Podhorski A, Rubio A, Kaleta C, Beasley JE, Schuster S, Planes FJ (2009) Computing the shortest elementary flux modes in genome-scale metabolic networks. Bioinformatics 25(23):3158–3165

    Article  Google Scholar 

  • Durot M, Bourguignon P-Y, Schachter V (2009) Genome-scale models of bacterial metabolism: reconstruction and applications. FEMS Microbiol Rev 33:164–90

    Article  Google Scholar 

  • Feist AM, Palsson BO (2010) The biomass objective function. Curr Opin Microbiol 13:344–349

    Article  Google Scholar 

  • Fleming RM, Maes CM, Saunders MA, Ye Y, Palsson BO (2012) A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks. J Theoret Biol 292:71–77

    Article  MathSciNet  Google Scholar 

  • Grünbaum B (2003) Convex polytopes. In: Graduate texts in mathematics, 2nd edn. Springer, Berlin

  • Kelk SM, Olivier BG, Stougie L, Bruggeman FJ (2012) Optimal flux spaces of genome-scale stoichiometric models are determined by a few subnetworks. Sci Rep 2:580

    Article  Google Scholar 

  • Khannapho C, Zhao H, Bonde BL, Kierzek AM, Avignone-Rossa CA, Bushell ME (2008) Selection of objective function in genome scale flux balance analysis for process feed development in antibiotic production. Metab Eng 10(5):227–233

    Article  Google Scholar 

  • Larhlimi A, Bockmayr A (2009) A new constraint-based description of the steady-state flux cone of metabolic networks. Discr Appl Math 157(10):2257–2266

    Article  MathSciNet  MATH  Google Scholar 

  • Larhlimi A, David L, Selbig J, Bockmayr A (2012) F2c2: a fast tool for the computation of flux coupling in genome-scale metabolic networks. BMC Bioinf 13:57

    Article  Google Scholar 

  • Mahadevan R, Schilling C (2003) The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab Eng 5:264–276

    Article  Google Scholar 

  • Müller A (2012) Thermodynamic Constraints in Metabolic Networks. Master’s thesis, Freie Universität Berlin, Fachbereich Mathematik und Informatik. http://page.mi.fu-berlin.de/arnem/theses/master.pdf

  • Müller A, Bockmayr A (2013) Fast thermodynamically constrainted flux variability analysis. Bioinformatics 29(7):903–909

    Article  Google Scholar 

  • Noor E, Lewis NE, Milo R (2012) A proof for loop-law constraints in stoichiometric metabolic networks. BMC Syst Biol 6:140

    Article  Google Scholar 

  • Orth JD, Thiele I, Palsson BO (2010) What is flux balance analysis. Nat Biotechnol 28:245–248

    Article  Google Scholar 

  • Papin AJ, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO (2004) Comparison of network-based pathway analysis methods. TRENDS Biotechnol 22(8):400–405

    Article  Google Scholar 

  • Papin Jason A, Reed JL, Palsson BO (2004) Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. TRENDS Biochem Sci 29(12):641–647

    Article  Google Scholar 

  • Price ND, Reed JL, Palsson BØ (2004) Genome-scale models of microbial cells: evaluating the consequences of constraints. Nat Rev Microbiol 2:886–897

    Article  Google Scholar 

  • Sarıyar B, Perk S, Akman U, Hortaçsu A (2006) Monte carlo sampling and principal component analysis of flux distributions yield topological and modular information on metabolic networks. J Theoret Biol 242:389–400

    Article  MathSciNet  Google Scholar 

  • Schellenberger J, Lewis NE, Palsson BØ (2011) Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys J 100:544–553

    Article  Google Scholar 

  • Schilling CH, Letscher D, Palsson BO (2000) Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function form a pathway-oriented perspective. J Theoret Biol 203:229–248

    Article  Google Scholar 

  • Schuster S, Hilgetag C (1994) On elementary flux modes in biochemical systems at steady state. J Biol Syst 2:165–182

    Article  Google Scholar 

  • Schuster S, Schuster R (1991) Detecting strictly detailed balanced subnetworks in open chemical reaction networks. J Math Chem 6(1):17–40

    Article  MathSciNet  Google Scholar 

  • Schuster S, Fell DA, Dandekar T (2000) A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat Biotechnol 18:326–332

    Article  Google Scholar 

  • Schuster S, Pfeiffer T, Fell DA (2007) Is maximization of molar yield in metabolic networks favoured by evolution? J Theoret Biol 252(3):497–504

    Article  MathSciNet  Google Scholar 

  • Terzer M, Stelling J (2008) Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics 24(19):2229–2235

    Article  Google Scholar 

  • Terzer M, Maynard ND, Covert MW, Stelling J (2009) Genome-scale metabolic networks. Wiley interdisciplinary reviews. Syst Biol Med 1(3):285–297

    Google Scholar 

  • Teusink B, Wiersma A, Jacobs L, Notebaart R, Smid E (2009) Understanding the adaptive growth strategy of Lactobacillus plantarum by in silico optimisation. PLoS Comput Biol 5(6):e1000410

    Google Scholar 

  • Varma A, Palsson BO (1994) Metabolic flux balancing: basic concepts, scientific and practical use. Nat Biotechnol 12:994–998

    Article  Google Scholar 

  • von Kamp A, Schuster S (2006) Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22(15):1930–1931

    Article  Google Scholar 

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Acknowledgments

We thank Leen Stougie, who presented this problem on the ENUMEX Summerschool (Enumeration Algorithms & Exact Methods For Exponential Problems in Computational Biology).

Funding:This work was funded by the Berlin Mathematical School in terms of a PhD stipend.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 , Berlin, Germany

    Arne C. Müller & Alexander Bockmayr

  2. International Max Planck Research School for Computational Biology and Scientific Computing (IMPRS-CBSC), Max Planck Institute for Molecular Genetics, Ihnestr 63-73, 14195 , Berlin, Germany

    Arne C. Müller

  3. Berlin Mathematical School (BMS), Berlin, Germany

    Arne C. Müller

  4. DFG-Research Center Matheon, Berlin, Germany

    Alexander Bockmayr

Authors
  1. Arne C. Müller
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  2. Alexander Bockmayr
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Correspondence to Arne C. Müller.

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Müller, A.C., Bockmayr, A. Flux modules in metabolic networks. J. Math. Biol. 69, 1151–1179 (2014). https://doi.org/10.1007/s00285-013-0731-1

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  • DOI: https://doi.org/10.1007/s00285-013-0731-1

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