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
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
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
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
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
Gagneur J, Klamt S (2004) Computation of elementary modes: a unifying framework and the new binary approach. BMC Bioinformatics 5:175
Hädicke O, Klamt S (2010) CASOP: a computational approach for strain optimization aiming at high productivity. J Biotechnol 147:88–101
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
Larhlimi A, Bockmayr A (2006) A new approach to flux coupling analysis of metabolic networks. Lect Notes Comput Sci 4216:205–215
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
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
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
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
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
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
Price ND, Papin JA, Schilling CH, Palsson BØ (2003) Genome-scale microbial in silico models: the constraints-based approach. Trends Biotechnol 21:162–169
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
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
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
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
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
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
Schwartz JM, Gaugain C, Nacher JC, de Daruvar A, Kanehisa M (2007) Observing metabolic functions at the genome scale. Genome Biol 8:R123
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
Terzer M, Stelling J (2008) Large-scale computation of elementary flux modes with bit pattern trees. Bioinformatics 24:2229–2235
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
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
Yizhak K, Tuller T, Papp B, Ruppin E (2011) Metabolic modeling of endosymbiont genome reduction on a temporal scale. Mol Syst Biol 7:479
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
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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