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Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism

Abstract

Elementary modes (EMs) are steady-state metabolic flux vectors with minimal set of active reactions. Each EM corresponds to a metabolic pathway. Therefore, studying EMs is helpful for analyzing the production of biotechnologically important metabolites. However, memory requirements for computing EMs may hamper their applicability as, in most genome-scale metabolic models, no EM can be computed due to running out of memory. In this study, we present a method for computing randomly sampled EMs. In this approach, a network reduction algorithm is used for EM computation, which is based on flux balance-based methods. We show that this approach can be used to recover the EMs in the medium- and genome-scale metabolic network models, while the EMs are sampled in an unbiased way. The applicability of such results is shown by computing “estimated” control-effective flux values in Escherichia coli metabolic network.

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References

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

    Article  PubMed  CAS  Google Scholar 

  • Çakir T, Kirdar B, Ülgen KÖ (2004) Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks. Biotechnol Bioeng 86:251–260

    Article  PubMed  Google Scholar 

  • Çakir T, Kirdar B, Önsan ZI, Ülgen KÖ, Nielsen J (2007) Effect of carbon source perturbations on transcriptional regulation of metabolic fluxes in Saccharomyces cerevisiae. BMC Syst Biol 1:18

    Article  PubMed  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 25:3158–3165

    Article  PubMed  Google Scholar 

  • Fukuda K, Prodon A (1996) Double description method revisited. In: Deza M et al (eds) Combinatorics and computer science, vol 1120. Springer, Berlin, Heidelberg, pp 91–111

    Chapter  Google Scholar 

  • Gagneur J, Klamt S (2004) Computation of elementary modes: a unifying framework and the new binary approach. BMC Bioinformatics 5:175

    Article  PubMed  Google Scholar 

  • Hädicke O, Klamt S (2010) CASOP: a computational approach for strain optimization aiming at high productivity. J Biotechnol 147:88–101

    Article  PubMed  Google Scholar 

  • Kaleta C, De Figueiredo LF, Schuster S (2009) Can the whole be less than the sum of its parts? Pathway analysis in genome-scale metabolic networks using elementary flux patterns. Genome Res 19:1872–1883

    Article  PubMed  CAS  Google Scholar 

  • Larhlimi A, Bockmayr A (2006) A new approach to flux coupling analysis of metabolic networks. Lect Notes Comput Sci 4216:205–215

    Article  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 Bioinformatics 13:57

    Article  PubMed  Google Scholar 

  • Lewis NE, Nagarajan H, Palsson BØ (2012) Constraining the metabolic genotype–phenotype relationship using a phylogeny of in silico methods. Nature Rev Microbiol 10:291–305

    CAS  Google Scholar 

  • Machado D, Soons Z, Patil KR, Ferreira EC, Rocha I (2012) Random sampling of elementary flux modes in large-scale metabolic networks. Bioinformatics 28:i515–i521

    Article  PubMed  CAS  Google Scholar 

  • Marashi S-A (2011), Constraint-based analysis of substructures of metabolic networks, Ph.D. Thesis, Freie Universität Berlin, Berlin, Germany

  • Marashi S-A, David L, Bockmayr A (2012) Analysis of metabolic subnetworks by flux cone projection. Algorithms Mol Biol 7:17

    Article  PubMed  Google Scholar 

  • Pál C, Papp B, Lercher MJ, Csermely P, Oliver SG, Hurst LD (2006) Chance and necessity in the evolution of minimal metabolic networks. Nature 440:667–670

    Article  PubMed  Google Scholar 

  • Papin JA, Price ND, Edwards JS, Palsson BØ (2002) The genome-scale metabolic extreme pathway structure in Haemophilus influenzae shows significant network redundancy. J Theor Biol 215:67–82

    Article  PubMed  CAS  Google Scholar 

  • Price ND, Papin JA, Schilling CH, Palsson BØ (2003) Genome-scale microbial in silico models: the constraints-based approach. Trends Biotechnol 21:162–169

    Article  PubMed  CAS  Google Scholar 

  • Reed JL, Vo TD, Schilling CH, Palsson BO (2003) An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR). Genome Biol 4:R54

    Article  PubMed  Google Scholar 

  • Schellenberger J, Que R, Fleming RMT, Thiele I, Orth JD, Feist AM, Zielinski DC, Bordbar A, Lewis NE, Rahmanian S, Kang J, Hyduke DR, Palsson BØ (2011) Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nat Protoc 6:1290–1307

    Article  PubMed  CAS  Google Scholar 

  • Schilling CH, Palsson BØ (2000) Assessment of the metabolic capabilities of Haemophilus influenzae Rd through a genome-scale pathway analysis. J Theor Biol 203:249–283

    Article  PubMed  CAS  Google Scholar 

  • Schuster S, Dandekar T, Fell DA (1999) Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol 17:53–60

    Article  PubMed  CAS  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. Nature Biotechnol 18:326–332

    Article  CAS  Google Scholar 

  • Schuster S, Pfeiffer T, Moldenhauer F, Koch I, Dandekar T (2002) Exploring the pathway structure of metabolism: decomposition into subnetworks and application to Mycoplasma pneumoniae. Bioinformatics 18:351–361

    Article  PubMed  CAS  Google Scholar 

  • Schwartz JM, Gaugain C, Nacher JC, de Daruvar A, Kanehisa M (2007) Observing metabolic functions at the genome scale. Genome Biol 8:R123

    Article  PubMed  Google Scholar 

  • Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED (2002) Metabolic network structure determines key aspects of functionality and regulation. Nature 420:190–193

    Article  PubMed  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  • Trinh CT, Unrean P, Srienc F (2008) Minimal Eschenchia coli cell for the most efficient production of ethanol from hexoses and pentoses. Appl Environ Microbiol 74:3634–3643

    Article  PubMed  CAS  Google Scholar 

  • Wlaschin AP, Trinh CT, Carlson R, Srienc F (2006) The fractional contributions of elementary modes to the metabolism of Escherichia coli and their estimation from reaction entropies. Metab Eng 8:338–352

    Article  PubMed  CAS  Google Scholar 

  • Yizhak K, Tuller T, Papp B, Ruppin E (2011) Metabolic modeling of endosymbiont genome reduction on a temporal scale. Mol Syst Biol 7:479

    Article  PubMed  Google Scholar 

  • Zhang Q, Wang W, Xiao H, Xiu Z (2010) Effect of oxygen level on efficiencies of metabolic fluxes in Klebsiella pneumoniae, 4th International Conference on Bioinformatics and Biomedical Engineering (iCBBE), Chengdu, China, article number 5517846

  • Zomorrodi AR, Suthers PF, Ranganathan S, Maranas CD (2012) Mathematical optimization applications in metabolic networks. Metab Eng 14:672–686

    Article  PubMed  CAS  Google Scholar 

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Correspondence to Sayed-Amir Marashi.

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Tabe-Bordbar, S., Marashi, SA. Finding elementary flux modes in metabolic networks based on flux balance analysis and flux coupling analysis: application to the analysis of Escherichia coli metabolism. Biotechnol Lett 35, 2039–2044 (2013). https://doi.org/10.1007/s10529-013-1328-x

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  • DOI: https://doi.org/10.1007/s10529-013-1328-x

Keywords

  • Constraint-based modeling
  • Elementary flux modes
  • Flux balancing analysis
  • Flux coupling analysis
  • Metabolic networks
  • Metabolic pathways
  • Random sampling