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On dynamically generating relevant elementary flux modes in a metabolic network using optimization. (English) Zbl 1330.90122
Summary: Elementary flux modes (EFMs) are pathways through a metabolic reaction network that connect external substrates to products. Using EFMs, a metabolic network can be transformed into its macroscopic counterpart, in which the internal metabolites have been eliminated and only external metabolites remain. In EFMs-based metabolic flux analysis (MFA) experimentally determined external fluxes are used to estimate the flux of each EFM. It is in general prohibitive to enumerate all EFMs for complex networks, since the number of EFMs increases rapidly with network complexity. In this work we present an optimization-based method that dynamically generates a subset of EFMs and solves the EFMs-based MFA problem simultaneously. The obtained subset contains EFMs that contribute to the optimal solution of the EFMs-based MFA problem. The usefulness of our method was examined in a case-study using data from a Chinese hamster ovary cell culture and two networks of varied complexity. It was demonstrated that the EFMs-based MFA problem could be solved at a low computational cost, even for the more complex network. Additionally, only a fraction of the total number of EFMs was needed to compute the optimal solution.

MSC:
90C35 Programming involving graphs or networks
90C20 Quadratic programming
90C90 Applications of mathematical programming
92C42 Systems biology, networks
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[1] Acuña, V; Chierichetti, F; Lacroix, V; Marchetti-Spaccamela, A; Sagot, MF; Stougie, L, Modes and cuts in metabolic networks: complexity and algorithms, Biosystems, 95, 51-60, (2009)
[2] Ahn, WS; Antoniewicz, MR, Metabolic flux analysis of CHO cells at growth and non-growth phases using isotopic tracers and mass spectrometry, Metab Eng, 13, 598-609, (2011)
[3] Altamirano, C; Illanes, A; Casablancas, A; Gmez, X; Cair, JJ; Gdia, C, Analysis of cho cells metabolic redistribution in a glutamate-based defined medium in continuous culture, Biotechnol Prog, 17, 1032-1041, (2001)
[4] Bonarius, HPJ; Schmid, G, Flux analysis of underdetermined metabolic networks : the quest for the missing constraints, Trends Biotechnol, 15, 308-314, (1997)
[5] Clarke BL (1980) Stability of complex reaction networks, vol 43. Advances in chemical physics
[6] 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
[7] Gagneur, J; Klamt, S, Computation of elementary modes: a unifying framework and the new binary approach, BMC Bioinform, 5, 175, (2004)
[8] Goudar, C; Biener, R; Boisart, C; Heidemann, R; Piret, J; Graaf, A; Konstantinov, K, Metabolic flux analysis of CHO cells in perfusion culture by metabolite balancing and 2d [13c, 1h] COSY NMR spectroscopy, Metab Eng, 12, 138-149, (2010)
[9] Griva I, Nash SG, Sofer A (2009) Linear and nonlinear optimization, 2nd edn. Society for Industrial Mathematics, Philadelphia, PA, USA · Zbl 1159.90002
[10] Jungers, RM; Zamorano, F; Blondel, VD; Vande Wouwer, A; Bastin, G, Fast computation of minimal elementary decompositions of metabolic flux vectors, Automatica, 47, 1255-1259, (2011) · Zbl 1235.93267
[11] Kaleta, C; Figueiredo, L; Schuster, Behre J; Grosse, I (ed.); Neumann, S (ed.); Posch, S (ed.); Schreiber, F (ed.); Stadler, P (ed.), Efmevolver: computing elementary flux modes in genome-scale metabolic networks, 179-189, (2009), Bonn
[12] Kanehisa, M; Goto, S, KEGG: Kyoto encyclopedia of genes and genomes, Nucleic Acids Res, 28, 27-30, (2000)
[13] Kanehisa, M; Goto, S; Sato, Y; Furumichi, M; Tanabe, M, KEGG for integration and interpretation of large-scale molecular data sets, Nucleic Acids Res, 40, d109-d114, (2012)
[14] Klamt, S; Schuster, S, Calculability analysis in underdetermined metabolic networks illustrated by a model of the central metabolism in purple nonsulfur bacteria, Biotechnol Bioeng, 77, 734-751, (2002)
[15] Klamt, S; Stelling, J, Combinatorial complexity of pathway analysis in metabolic networks, Mol Biol Rep, 29, 233-236, (2002)
[16] Klamt, S; Stelling, J, Two approaches for metabolic pathway analysis?, Trends Biotechnol, 21, 64-69, (2003)
[17] Llaneras, F; Picó, J, Stoichiometric modelling of cell metabolism, J Biosci Bioeng, 105, 1-11, (2008)
[18] Llaneras, F; Picó, J, Which metabolic pathways generate and characterize the flux space? A comparison among elementary modes, extreme pathways and minimal generators, J Biomed Biotechnol, 2010, 753,904, (2010)
[19] Lübbecke, ME; Desrosiers, J, Selected topics in column generation, Op Res, 53, 1007-1023, (2005) · Zbl 1165.90578
[20] Nelson DL, Cox MM (2004) Lehninger principles of biochemistry, 4th edn. W. H. Freeman, New York, NY, USA
[21] Nemhauser GL, Wolsey LA (1999) Integer and combinatorial optimization, 1st edn. Wiley, New York, NY, USA
[22] Papin JA, Price ND, Wiback SJ, Palsson BO (2003) Metabolic pathways in the post-genome era. Trends Biochem Sci 28(5):250-258
[23] Papin JA, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO (2004) Comparison of network-based pathway analysis methods. Trends Biotechnol 22(8):400-405
[24] Planes, FJ; Beasley, JE, A critical examination of stoichiometric and path-finding approaches to metabolic pathways, Brief Bioinform, 9, 422-436, (2008)
[25] Price, ND; Reed, JL; Papin, JA; Famili, I; Palsson, BO, Analysis of metabolic capabilities using singular value decomposition of extreme pathway matrices, Biophys J, 84, 794-804, (2003)
[26] Provost A (2006) Metabolic design of dynamic bioreaction models. PhD thesis, Université catholique de Louvain
[27] Provost, A; Bastin, G; Agathos, SN; Schneider, YJ, Metabolic design of macroscopic bioreaction models: application to Chinese hamster ovary cells, Bioprocess Biosyst Eng, 29, 349-366, (2006)
[28] Rezola, A; Figueiredo, LF; Brock, M; Pey, J; Podhorski, A; Wittmann, C; Schuster, S; Bockmayr, A; Planes, FJ, Exploring metabolic pathways in genome-scale networks via generating flux modes, Bioinformatics, 27, 534-540, (2011)
[29] Schilling, CH; Schuster, S; Palsson, BO; Heinrich, R, Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era, Biotechnol Prog, 15, 296-303, (1999)
[30] Schilling, CH; Letscher, D; Palsson, BO, Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective, J Theor Biol, 203, 229-248, (2000)
[31] Schuster, S; Hilgetag, C, On elementary flux modes in biochemical reaction systems at steady state, J Biol Syst, 2, 165-182, (1994)
[32] 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)
[33] Terzer, M; Stelling, J, Large-scale computation of elementary flux modes with bit pattern trees, Bioinformatics, 24, 2229-2235, (2008)
[34] Urbanczik R, Wagner C (2005) An improved algorithm for stoichiometric network analysis: theory and applications. Bioinformatics 21(7):1203-1210
[35] von Kamp A, Schuster S (2006) Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22(15):1930-1931
[36] Zamorano Riveros F (2012) Metabolic flux analysis of CHO cell cultures. PhD thesis, University of Mons
[37] Zamorano, F; Vande Wouwer, A, A detailed metabolic flux analysis of an underdetermined network of CHO cells, J Biotechnol, 150, 497-508, (2010)
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