zbMATH — the first resource for mathematics

Robustness analysis of elementary flux modes generated by column generation. (English) Zbl 1360.92050
Summary: Elementary flux modes (EFMs) are vectors defined from a metabolic reaction network, giving the connections between substrates and products. EFMs-based metabolic flux analysis (MFA) estimates the flux over each EFM from external flux measurements through least-squares data fitting. The measurements used in the data fitting are subject to errors. A robust optimization problem includes information on errors and gives a way to examine the sensitivity of the solution of the EFMs-based MFA to these errors. In general, formulating a robust optimization problem may make the problem significantly harder. We show that in the case of the EFMs-based MFA, when the errors are only in measurements and bounded by an interval, the robust problem can be stated as a convex quadratic programming (QP) problem. We have previously shown how the data fitting problem may be solved in a column-generation framework. In this paper, we show how column generation may be applied also to the robust problem, thereby avoiding explicit enumeration of EFMs. Furthermore, the option to indicate intervals on metabolites that are not measured is introduced in this column generation framework. The robustness of the data is evaluated in a case-study, which indicates that the solutions of our non-robust problems are in fact near-optimal also when robustness is considered, implying that the errors in measurement do not have a large impact on the optimal solution. Furthermore, we showed that the addition of intervals on unmeasured metabolites resulted in a change in the optimal solution.
92C45 Kinetics in biochemical problems (pharmacokinetics, enzyme kinetics, etc.)
92C40 Biochemistry, molecular biology
90C90 Applications of mathematical programming
EFMEvolver; Metatool
Full Text: DOI
[1] Nemhauser, G. L.; Wolsey, L. A., Integer and Combinatorial Optimization, (1999), John Wiley & Sons, Inc · Zbl 0469.90052
[2] 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, 753904, (2010)
[3] Klamt, S.; Stelling, J., Combinatorial complexity of pathway analysis in metabolic networks., Mol. Biol. Rep., 29, 1-2, 233-236, (2002)
[4] Schilling, C. H.; Schuster, S.; Palsson, B. O.; Heinrich, R., Metabolic pathway analysis: basic concepts and scientific applications in the post-genomic era., Biotechnol. Prog., 15, 3, 296-303, (1999)
[5] Papin, J. A.; Price, N. D.; Wiback, S. J.; Fell, D. A.; Palsson, B. O., Metabolic pathways in the post-genome era., Trends Biochem. Sci., 28, 5, 250-258, (2003)
[6] Gagneur, J.; Klamt, S., Computation of elementary modes: a unifying framework and the new binary approach., BMC Bioinf., 5, 175, (2004)
[7] Urbanczik, R.; Wagner, C., An improved algorithm for stoichiometric network analysis: theory and applications., Bioinformatics (Oxford, England), 21, 7, 1203-1210, (2005)
[8] von Kamp, A.; Schuster, S., Metatool 5.0: fast and flexible elementary modes analysis, Bioinformatics (Oxford, England), 22, 15, 1930-1931, (2006)
[9] de Figueiredo, L. F.; Podhorski, A.; Rubio, A.; Kaleta, C.; Beasley, J. E.; Schuster, S.; Planes, F. J., Computing the shortest elementary flux modes in genome-scale metabolic networks., Bioinformatics (Oxford, England), 25, 23, 3158-3165, (2009)
[10] Kaleta, C.; de Figueiredo, L.; Behre, J.; Schuster, Efmevolver: computing elementary flux modes in genome-scale metabolic networks, (Grosse, I.; Neumann, S.; Posch, S.; Schreiber, F.; Stadler, P., Lecture Notes in Informatics P-157, (2009), Gesellschaft für Informatik Bonn), 179-189
[11] Tabe-Bordbar, S.; Marashi, S.-A., 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, 12, 2039-2044, (2013)
[12] Jungers, R. M.; Zamorano, F.; Blondel, V. D.; Vande Wouwer, A.; Bastin, G., Fast computation of minimal elementary decompositions of metabolic flux vectors, Automatica, 47, 6, 1255-1259, (2011) · Zbl 1235.93267
[13] Oddsdóttir, H.Æ.; Hagrot, E.; Chotteau, V.; Forsgren, A., On dynamically generating relevant elementary flux modes in a metabolic network using optimization, J. Math. Biol., 1-18, (2014)
[14] Lübbecke, M. E.; Desrosiers, J., Selected topics in column generation, Oper. Res., 53, 6, 1007-1023, (2005) · Zbl 1165.90578
[15] Goudar, C. T.; Biener, R.; Konstantinov, K. B.; Piret, J. M., Error propagation from prime variables into specific rates and metabolic fluxes for Mammalian cells in perfusion culture, Biotechnol. Prog., 25, 986-998, (2009)
[16] Mulvey, J. M.; Vanderbei, R. J.; Zenios, S. A.; Vanderbei, R. J.; Mulvey, J. M.; Zenios, S. A., Robust optimization of large-scale systems, Oper. Res., 43, 2, 264-281, (1995) · Zbl 0832.90084
[17] Ben-Tal, A.; El Ghaoui, L.; Nemirovski, A., Robust Optimization, Princeton Series in Applied Mathematics, (2009), Princeton University Press
[18] El Ghaoui, L.; Lebret, H., Robust solutions to least-squares problems with uncertain data, SIAM J. Matrix Anal. Appl., 18, 4, 1035-1064, (1997) · Zbl 0891.65039
[19] Goudar, C. T.; Piret, J. M.; Konstantinov, K. B., Estimating cell specific oxygen uptake and carbon dioxide production rates for Mammalian cells in perfusion culture, Biotechnol. Prog., 27, 5, 1347-1357, (2011)
[20] J.G. Aunins, H.-J. Henzler, Aeration in Cell Culture Bioreactors, Wiley-VCH Verlag GmbH, pp. 219-281.
[21] Zamorano Riveros, F., Metabolic Flux Analysis of CHO Cell Cultures. Ph.D. thesis, (2012), University of Mons
[22] 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, 7, 734-751, (2002)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.