Protocol Update | Published:

Creation and analysis of biochemical constraint-based models using the COBRA Toolbox v.3.0

Nature Protocolsvolume 14pages639702 (2019) | Download Citation


Constraint-based reconstruction and analysis (COBRA) provides a molecular mechanistic framework for integrative analysis of experimental molecular systems biology data and quantitative prediction of physicochemically and biochemically feasible phenotypic states. The COBRA Toolbox is a comprehensive desktop software suite of interoperable COBRA methods. It has found widespread application in biology, biomedicine, and biotechnology because its functions can be flexibly combined to implement tailored COBRA protocols for any biochemical network. This protocol is an update to the COBRA Toolbox v.1.0 and v.2.0. Version 3.0 includes new methods for quality-controlled reconstruction, modeling, topological analysis, strain and experimental design, and network visualization, as well as network integration of chemoinformatic, metabolomic, transcriptomic, proteomic, and thermochemical data. New multi-lingual code integration also enables an expansion in COBRA application scope via high-precision, high-performance, and nonlinear numerical optimization solvers for multi-scale, multi-cellular, and reaction kinetic modeling, respectively. This protocol provides an overview of all these new features and can be adapted to generate and analyze constraint-based models in a wide variety of scenarios. The COBRA Toolbox v.3.0 provides an unparalleled depth of COBRA methods.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Additional information

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Key references using this protocol

Schellenberger, J. et al. Nat. Protocols 6, 1290–1307 (2011):

Becker, S. A. et al. Nat. Protocols 2, 727–738 (2007):

This protocol is an update to Nat. Protoc. 2, 727–738 (2007): and Nat. Protoc. 6, 1290–1307 (2011):


  1. 1.

    Palsson, B. Ø. Systems Biology: Constraint-Based Reconstruction and Analysis (Cambridge University Press, Cambridge, 2015).

  2. 2.

    O’Brien, E. J., Monk, J. M. & Palsson, B. O. Using genome-scale models to predict biological capabilities. Cell 161, 971–987 (2015).

  3. 3.

    Becker, S. A. et al. Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox. Nat. Protoc. 2, 727–738 (2007).

  4. 4.

    Schellenberger, J. et al. Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nat. Protoc. 6, 1290–1307 (2011).

  5. 5.

    Lewis, N. E., Nagarajan, H. & Palsson, B. O. Constraining the metabolic genotype–phenotype relationship using a phylogeny of in silico methods. Nat. Rev. Microbiol. 10, 291–305 (2012).

  6. 6.

    Thiele, I. & Palsson, B. Ø. A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat. Protoc. 5, 93–121 (2010).

  7. 7.

    Kitano, H., Ghosh, S. & Matsuoka, Y. Social engineering for virtual ‘big science’ in systems biology. Nat. Chem. Biol. 7, 323–326 (2011).

  8. 8.

    Bordbar, A., Monk, J. M., King, Z. A. & Palsson, B. O. Constraint-based models predict metabolic and associated cellular functions. Nat. Rev. Genet. 15, 107–120 (2014).

  9. 9.

    Maia, P., Rocha, M. & Rocha, I. In silico constraint-based strain optimization methods: the quest for optimal cell factories. Microbiol. Mol. Biol. Rev. 80, 45–67 (2016).

  10. 10.

    Hefzi, H. et al. A consensus genome-scale reconstruction of Chinese hamster ovary cell metabolism. Cell Syst. 3, 434–443.e8 (2016).

  11. 11.

    Yusufi, F. N. K. et al. Mammalian systems biotechnology reveals global cellular adaptations in a recombinant CHO cell line. Cell Syst. 4, 530–542.e6 (2017).

  12. 12.

    Zhuang, K. et al. Genome-scale dynamic modeling of the competition between Rhodoferax and Geobacter in anoxic subsurface environments. ISME J 5, 305–316 (2011).

  13. 13.

    Jamshidi, N. & Palsson, B. Ø. Systems biology of the human red blood cell. Blood Cells Mol. Dis. 36, 239–247 (2006).

  14. 14.

    Yizhak, K., Gabay, O., Cohen, H. & Ruppin, E. Model-based identification of drug targets that revert disrupted metabolism and its application to ageing. Nat. Commun. 4, 2632 (2013).

  15. 15.

    Shlomi, T., Cabili, M. N. & Ruppin, E. Predicting metabolic biomarkers of human inborn errors of metabolism. Mol. Syst. Biol. 5, 263 (2009).

  16. 16.

    Sahoo, S., Franzson, L., Jonsson, J. J. & Thiele, I. A compendium of inborn errors of metabolism mapped onto the human metabolic network. Mol. Biosyst. 8, 2545–2558 (2012).

  17. 17.

    Thiele, I. et al. A community-driven global reconstruction of human metabolism. Nat. Biotechnol. 31, 419–425 (2013).

  18. 18.

    Pagliarini, R. & di Bernardo, D. A genome-scale modeling approach to study inborn errors of liver metabolism: toward an in silico patient. J. Comput. Biol. 20, 383–397 (2013).

  19. 19.

    Shaked, I., Oberhardt, M. A., Atias, N., Sharan, R. & Ruppin, E. Metabolic network prediction of drug side effects. Cell Syst. 2, 209–213 (2016).

  20. 20.

    Chang, R. L., Xie, L., Xie, L., Bourne, P. E. & Palsson, B. Drug off-target effects predicted using structural analysis in the context of a metabolic network model. PLoS Comput. Biol. 6, e1000938 (2010).

  21. 21.

    Kell, D. B. Systems biology, metabolic modelling and metabolomics in drug discovery and development. Drug Discov. Today 11, 1085–1092 (2006).

  22. 22.

    Duarte, N. C. et al. Global reconstruction of the human metabolic network based on genomic and bibliomic data. Proc. Natl. Acad. Sci. USA 104, 1777–1782 (2007).

  23. 23.

    Swainston, N. et al. Recon 2.2: from reconstruction to model of human metabolism. Metabolomics 12, 109 (2016).

  24. 24.

    Pornputtapong, N., Nookaew, I. & Nielsen, J. Human metabolic atlas: an online resource for human metabolism. Database 2015, bav068 (2015).

  25. 25.

    Zielinski, D. C. et al. Systems biology analysis of drivers underlying hallmarks of cancer cell metabolism. Sci. Rep. 7, 41241 (2017).

  26. 26.

    Mardinoglu, A. et al. Genome-scale metabolic modelling of hepatocytes reveals serine deficiency in patients with non-alcoholic fatty liver disease. Nat. Commun. 5, 3083 (2014).

  27. 27.

    Karlstädt, A. et al. CardioNet: a human metabolic network suited for the study of cardiomyocyte metabolism. BMC Syst. Biol. 6, 114 (2012).

  28. 28.

    Gille, C. et al. HepatoNet1: a comprehensive metabolic reconstruction of the human hepatocyte for the analysis of liver physiology. Mol. Syst. Biol. 6, 411 (2010).

  29. 29.

    Martins Conde Pdo, R., Sauter, T. & Pfau, T. Constraint based modeling going multicellular. Front. Mol. Biosci. 3, 3 (2016).

  30. 30.

    Bordbar, A. et al. A multi-tissue type genome-scale metabolic network for analysis of whole-body systems physiology. BMC Syst. Biol. 5, 180 (2011).

  31. 31.

    Yizhak, K. et al. Phenotype-based cell-specific metabolic modeling reveals metabolic liabilities of cancer. Elife 3, e03641 (2014).

  32. 32.

    Mardinoglu, A. et al. Integration of clinical data with a genome-scale metabolic model of the human adipocyte. Mol. Syst. Biol. 9, 649 (2013).

  33. 33.

    Bordbar, A. et al. Personalized whole-cell kinetic models of metabolism for discovery in genomics and pharmacodynamics. Cell Syst. 1, 283–292 (2015).

  34. 34.

    Shoaie, S. et al. Quantifying diet-induced metabolic changes of the human gut microbiome. Cell Metab. 22, 320–331 (2015).

  35. 35.

    Nogiec, C. D. & Kasif, S. To supplement or not to supplement: a metabolic network framework for human nutritional supplements. PLoS ONE 8, e68751 (2013).

  36. 36.

    Heinken, A., Sahoo, S., Fleming, R. M. T. & Thiele, I. Systems-level characterization of a host-microbe metabolic symbiosis in the mammalian gut. Gut Microbes 4, 28–40 (2013).

  37. 37.

    Heinken, A. et al. Functional metabolic map of Faecalibacterium prausnitzii, a beneficial human gut microbe. J. Bacteriol. 196, 3289–3302 (2014).

  38. 38.

    Magnúsdóttir, S. et al. Generation of genome-scale metabolic reconstructions for 773 members of the human gut microbiota. Nat. Biotechnol. 35, 81–89 (2017).

  39. 39.

    Lakshmanan, M., Koh, G., Chung, B. K. S. & Lee, D.-Y. Software applications for flux balance analysis. Brief Bioinform. 15, 108–122 (2014).

  40. 40.

    Ebrahim, A., Lerman, J. A., Palsson, B. O. & Hyduke, D. R. COBRApy: constraints-based reconstruction and analysis for Python. BMC Syst. Biol. 7, 74 (2013).

  41. 41.

    Arkin, A. P. et al. The United States Department of Energy Systems Biology Knowledgebase. Nat. Biotechnol. 36, 566–569 (2018).

  42. 42.

    Heirendt, L., Thiele, I. & Fleming, R. M. T. DistributedFBA.jl: high-level, high-performance flux balance analysis in Julia. Bioinformatics 33, 1421–1423 (2017).

  43. 43.

    Latendresse, M., Krummenacker, M., Trupp, M. & Karp, P. D. Construction and completion of flux balance models from pathway databases. Bioinformatics 28, 388–396 (2012).

  44. 44.

    Karp, P. D. et al. Pathway Tools version 19.0 update: software for pathway/genome informatics and systems biology. Brief Bioinform. 17, 877–890 (2016).

  45. 45.

    Sandve, G. K., Nekrutenko, A., Taylor, J. & Hovig, E. Ten simple rules for reproducible computational research. PLoS Comput. Biol. 9, e1003285 (2013).

  46. 46.

    Ince, D. C., Hatton, L. & Graham-Cumming, J. The case for open computer programs. Nature 482, 485–488 (2012).

  47. 47.

    Gevorgyan, A., Bushell, M. E., Avignone-Rossa, C. & Kierzek, A. M. SurreyFBA: a command line tool and graphics user interface for constraint-based modeling of genome-scale metabolic reaction networks. Bioinformatics 27, 433–434 (2011).

  48. 48.

    Thorleifsson, S. G. & Thiele, I. rBioNet: a COBRA toolbox extension for reconstructing high-quality biochemical networks. Bioinformatics 27, 2009–2010 (2011).

  49. 49.

    Sauls, J. T. & Buescher, J. M. Assimilating genome-scale metabolic reconstructions with modelBorgifier. Bioinformatics 30, 1036–1038 (2014).

  50. 50.

    Noronha, A. et al. ReconMap: an interactive visualization of human metabolism. Bioinformatics 33, 605–607 (2017).

  51. 51.

    Gawron, P. et al. MINERVA—a platform for visualization and curation of molecular interaction networks. npj Syst. Biol. Appl. 2, 16020 (2016).

  52. 52.

    Olivier, B. G., Rohwer, J. M. & Hofmeyr, J.-H. S. Modelling cellular systems with PySCeS. Bioinformatics 21, 560–561 (2005).

  53. 53.

    Gelius-Dietrich, G., Desouki, A. A., Fritzemeier, C. J. & Lercher, M. J. Sybil—efficient constraint-based modelling in R. BMC Syst. Biol. 7, 125 (2013).

  54. 54.

    Ma, D. et al. Reliable and efficient solution of genome-scale models of metabolism and macromolecular expression. Sci. Rep. 7, 40863 (2017).

  55. 55.

    Klamt, S., Saez-Rodriguez, J. & Gilles, E. D. Structural and functional analysis of cellular networks with CellNetAnalyzer. BMC Syst. Biol. 1, 2 (2007).

  56. 56.

    Klamt, S. & von Kamp, A. An application programming interface for CellNetAnalyzer. Biosystems 105, 162–168 (2011).

  57. 57.

    Apaolaza, I. et al. An in-silico approach to predict and exploit synthetic lethality in cancer metabolism. Nat. Commun. 8, 459 (2017).

  58. 58.

    Maranas, C. D. & Zomorrodi, A. R. Optimization Methods in Metabolic Networks (Wiley, New York, 2016).

  59. 59.

    Chowdhury, A., Zomorrodi, A. R. & Maranas, C. D. Bilevel optimization techniques in computational strain design. Comp. Chem. Eng. 72, 363–372 (2015).

  60. 60.

    Thiele, I. et al. Multiscale modeling of metabolism and macromolecular synthesis in E. coli and its application to the evolution of codon usage. PLoS ONE 7, e45635 (2012).

  61. 61.

    Feist, A. M. et al. A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Mol. Syst. Biol. 3, 121 (2007).

  62. 62.

    Thiele, I., Jamshidi, N., Fleming, R. M. T. & Palsson, B. Ø. Genome-scale reconstruction of Escherichia coli’s transcriptional and translational machinery: a knowledge base, its mathematical formulation, and its functional characterization. PLoS Comput. Biol. 5, e1000312 (2009).

  63. 63.

    Yang, L. et al. Systems biology definition of the core proteome of metabolism and expression is consistent with high-throughput data. Proc. Natl. Acad. Sci. USA 112, 10810–10815 (2015).

  64. 64.

    Bornstein, B. J., Keating, S. M., Jouraku, A. & Hucka, M. LibSBML: an API library for SBML. Bioinformatics 24, 880–881 (2008).

  65. 65.

    Aurich, M. K., Fleming, R. M. T. & Thiele, I. MetaboTools: a comprehensive toolbox for analysis of genome-scale metabolic models. Front. Physiol. 7, 327 (2016).

  66. 66.

    Brunk, E. et al. Recon 3D: a resource enabling a three-dimensional view of gene variation in human metabolism. Nat. Biotechnol. 36, 272–281 (2018).

  67. 67.

    Ma, D. & Saunders, M. A. Solving multiscale linear programs using the simplex method in quadruple precision. in Numerical Analysis and Optimization, Vol. 134 (eds. Al-Baali, M., Grandinetti, L. & Purnama, A.) 223–235 (Springer International Publishing, Cham, Switzerland, 2015).

  68. 68.

    Fleming, R. M. T. & Thiele, I. Mass conserved elementary kinetics is sufficient for the existence of a non-equilibrium steady state concentration. J. Theor. Biol. 314, 173–181 (2012).

  69. 69.

    Gevorgyan, A., Poolman, M. G. & Fell, D. A. Detection of stoichiometric inconsistencies in biomolecular models. Bioinformatics 24, 2245–2251 (2008).

  70. 70.

    Orth, J. D., Thiele, I. & Palsson, B. Ø. What is flux balance analysis? Nat. Biotechnol. 28, 245–248 (2010).

  71. 71.

    Feist, A. M. & Palsson, B. O. The biomass objective function. Curr. Opin. Microbiol. 13, 344–349 (2010).

  72. 72.

    Meléndez-Hevia, E. & Isidoro, A. The game of the pentose phosphate cycle. J. Theor. Biol. 117, 251–263 (1985).

  73. 73.

    Orth, J. D. & Palsson, B. Ø. Systematizing the generation of missing metabolic knowledge. Biotechnol. Bioeng. 107, 403–412 (2010).

  74. 74.

    Yamada, T. et al. Prediction and identification of sequences coding for orphan enzymes using genomic and metagenomic neighbours. Mol. Syst. Biol. 8, 581 (2012).

  75. 75.

    Liberal, R. & Pinney, J. W. Simple topological properties predict functional misannotations in a metabolic network. Bioinformatics 29, i154–i161 (2013).

  76. 76.

    Reed, J. L. et al. Systems approach to refining genome annotation. Proc. Natl. Acad. Sci. USA 103, 17480–17484 (2006).

  77. 77.

    Orth, J. D. & Palsson, B. Gap-filling analysis of the iJO1366 Escherichia coli metabolic network reconstruction for discovery of metabolic functions. BMC Syst. Biol. 6, 30 (2012).

  78. 78.

    Chang, R. L. et al. Metabolic network reconstruction of Chlamydomonas offers insight into light-driven algal metabolism. Mol. Syst. Biol. 7, 518 (2011).

  79. 79.

    Rolfsson, O., Palsson, B. Ø. & Thiele, I. The human metabolic reconstruction Recon 1 directs hypotheses of novel human metabolic functions. BMC Syst. Biol. 5, 155 (2011).

  80. 80.

    Rolfsson, Ó., Paglia, G., Magnusdóttir, M., Palsson, B. Ø. & Thiele, I. Inferring the metabolism of human orphan metabolites from their metabolic network context affirms human gluconokinase activity. Biochem. J. 449, 427–435 (2013).

  81. 81.

    Satish Kumar, V., Dasika, M. S. & Maranas, C. D. Optimization based automated curation of metabolic reconstructions. BMC Bioinformatics 8, 212 (2007).

  82. 82.

    Thiele, I., Vlassis, N. & Fleming, R. M. T. fastGapFill: efficient gap filling in metabolic networks. Bioinformatics 30, 2529–2531 (2014).

  83. 83.

    Willemsen, A. M. et al. MetDFBA: incorporating time-resolved metabolomics measurements into dynamic flux balance analysis. Mol. Biosyst. 11, 137–145 (2014).

  84. 84.

    Kleessen, S., Irgang, S., Klie, S., Giavalisco, P. & Nikoloski, Z. Integration of transcriptomics and metabolomics data specifies the metabolic response of Chlamydomonas to rapamycin treatment. Plant J. 81, 822–835 (2015).

  85. 85.

    Bordbar, A. et al. Elucidating dynamic metabolic physiology through network integration of quantitative time-course metabolomics. Sci. Rep. 7, 46249 (2017).

  86. 86.

    Blazier, A. S. & Papin, J. A. Integration of expression data in genome-scale metabolic network reconstructions. Front. Physiol. 3, 299 (2012).

  87. 87.

    Opdam, S. et al. A systematic evaluation of methods for tailoring genome-scale metabolic models. Cell Syst. 4, 318–329.e6 (2017).

  88. 88.

    Estévez, S. R. & Nikoloski, Z. Generalized framework for context-specific metabolic model extraction methods. Front. Plant Sci. 5, 491 (2014).

  89. 89.

    Vlassis, N., Pacheco, M. P. & Sauter, T. Fast reconstruction of compact context-specific metabolic network models. PLoS Comput. Biol. 10, e1003424 (2014).

  90. 90.

    Becker, S. A. & Palsson, B. O. Context-specific metabolic networks are consistent with experiments. PLoS Comput. Biol. 4, e1000082 (2008).

  91. 91.

    Zur, H., Ruppin, E. & Shlomi, T. iMAT: an integrative metabolic analysis tool. Bioinformatics 26, 3140–3142 (2010).

  92. 92.

    Agren, R. et al. Reconstruction of genome-scale active metabolic networks for 69 human cell types and 16 cancer types using INIT. PLoS Comp. Biol. 8, e1002518 (2012).

  93. 93.

    Jerby, L., Shlomi, T. & Ruppin, E. Computational reconstruction of tissue-specific metabolic models: application to human liver metabolism. Mol. Syst. Biol. 6, 401 (2010).

  94. 94.

    Wang, Y., Eddy, J. A. & Price, N. D. Reconstruction of genome-scale metabolic models for 126 human tissues using mCADRE. BMC Syst. Biol. 6, 153 (2012).

  95. 95.

    Kuhar, M. J. On the use of protein turnover and half-lives. Neuropsychopharmacology 34, 1172–1173 (2008).

  96. 96.

    Lajtha, A. & Sylvester, V. Handbook of Neurochemistry and Molecular Neurobiology (Springer, Boston, 2008).

  97. 97.

    Schuster, S. & Hilgetag, C. On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Syst. 02, 165–182 (1994).

  98. 98.

    Schilling, C. H., Letscher, D. & Palsson, B. Ø. 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).

  99. 99.

    Klamt, S. et al. From elementary flux modes to elementary flux vectors: metabolic pathway analysis with arbitrary linear flux constraints. PLoS Comput. Biol. 13, e1005409 (2017).

  100. 100.

    Bordbar, A. et al. Minimal metabolic pathway structure is consistent with associated biomolecular interactions. Mol. Syst. Biol. 10, 737 (2014).

  101. 101.

    Gudmundsson, S. & Thiele, I. Computationally efficient flux variability analysis. BMC Bioinformatics 11, 489 (2010).

  102. 102.

    Haraldsdóttir, H. S., Cousins, B., Thiele, I., Fleming, R. M. T. & Vempala, S. CHRR: coordinate hit-and-run with rounding for uniform sampling of constraint-based models. Bioinformatics 33, 1741–1743 (2017).

  103. 103.

    Cousins, B. & Vempala, S. Gaussian cooling and algorithms for volume and Gaussian volume. SIAM J. Comput. 47, 1237–1273 (2018).

  104. 104.

    Cousins, B. & Vempala, S. A practical volume algorithm. Math. Prog. Comp. 8, 1–28 (2015).

  105. 105.

    Burgard, A. P., Pharkya, P. & Maranas, C. D. Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol. Bioeng. 84, 647–657 (2003).

  106. 106.

    Patil, K. R., Rocha, I., Förster, J. & Nielsen, J. Evolutionary programming as a platform for in silico metabolic engineering. BMC Bioinformatics 6, 308 (2005).

  107. 107.

    Lun, D. S. et al. Large-scale identification of genetic design strategies using local search. Mol. Syst. Biol. 5, 296 (2009).

  108. 108.

    Ranganathan, S., Suthers, P. F. & Maranas, C. D. OptForce: an optimization procedure for identifying all genetic manipulations leading to targeted overproductions. PLoS Comput. Biol. 6, e1000744 (2010).

  109. 109.

    Antoniewicz, M. R. et al. Metabolic flux analysis in a nonstationary system: fed-batch fermentation of a high yielding strain of E. coli producing 1,3-propanediol. Metab. Eng. 9, 277–292 (2007).

  110. 110.

    Haraldsdóttir, H. S., Thiele, I. & Fleming, R. M. T. Comparative evaluation of open source software for mapping between metabolite identifiers in metabolic network reconstructions: application to Recon 2. J. Cheminform. 6, 2 (2014).

  111. 111.

    Preciat Gonzalez, G. A. et al. Comparative evaluation of atom mapping algorithms for balanced metabolic reactions: application to Recon 3D. J. Cheminform. 9, 39 (2017).

  112. 112.

    Kim, S. et al. PubChem substance and compound databases. Nucleic Acids Res. 44, D1202–D1213 (2016).

  113. 113.

    Kanehisa, M. & Goto, S. KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res. 28, 27–30 (2000).

  114. 114.

    Hastings, J. et al. The ChEBI reference database and ontology for biologically relevant chemistry: enhancements for 2013. Nucleic Acids Res. 41, D456–D463 (2013).

  115. 115.

    Sud, M. et al. LMSD: LIPID MAPS structure database. Nucleic Acids Res. 35, D527–D532 (2007).

  116. 116.

    Forster, M., Pick, A., Raitner, M., Schreiber, F. & Brandenburg, F. J. The system architecture of the BioPath system. In Silico Biol. 2, 415–426 (2002).

  117. 117.

    Williams, A. J., Tkachenko, V., Golotvin, S., Kidd, R. & McCann, G. ChemSpider—building a foundation for the semantic web by hosting a crowd sourced databasing platform for chemistry. J. Cheminform. 2, O16 (2010).

  118. 118.

    Wishart, D. S. et al. HMDB: the Human Metabolome Database. Nucleic Acids Res. 35, D521–D526 (2007).

  119. 119.

    Rahman, S. A. et al. Reaction Decoder Tool (RDT): extracting features from chemical reactions. Bioinformatics 32, 2065–2066 (2016).

  120. 120.

    Kumar, A. & Maranas, C. D. CLCA: maximum common molecular substructure queries within the MetRxn Database. J. Chem. Inf. Model. 54, 3417–3438 (2014).

  121. 121.

    Shimizu, Y., Hattori, M., Goto, S. & Kanehisa, M. Generalized reaction patterns for prediction of unknown enzymatic reactions. Genome Inform. 20, 149–158 (2008).

  122. 122.

    Haraldsdóttir, H. S. & Fleming, R. M. T. Identification of conserved moieties in metabolic networks by graph theoretical analysis of atom transition networks. PLoS Comput. Biol. 12, e1004999 (2016).

  123. 123.

    Klamt, S., Haus, U.-U. & Theis, F. Hypergraphs and cellular networks. PLoS Comput. Biol. 5, e1000385 (2009).

  124. 124.

    Fleming, R. M. T. & Thiele, I. von Bertalanffy 1.0: a COBRA toolbox extension to thermodynamically constrain metabolic models. Bioinformatics 27, 142–143 (2011).

  125. 125.

    Fleming, R. M. T., Thiele, I. & Nasheuer, H. P. Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli. Biophys. Chem. 145, 47–56 (2009).

  126. 126.

    Haraldsdóttir, H. S., Thiele, I. & Fleming, R. M. T. Quantitative assignment of reaction directionality in a multicompartmental human metabolic reconstruction. Biophys. J. 102, 1703–1711 (2012).

  127. 127.

    Noor, E., Haraldsdóttir, H. S., Milo, R. & Fleming, R. M. T. Consistent estimation of Gibbs energy using component contributions. PLoS Comput. Biol. 9, e1003098 (2013).

  128. 128.

    Fleming, R. M. T., Maes, C. M., Saunders, M. A., Ye, Y. & Palsson, B. Ø. A variational principle for computing nonequilibrium fluxes and potentials in genome-scale biochemical networks. J. Theor. Biol. 292, 71–77 (2012).

  129. 129.

    Beard, D. A., Liang, S.-D. & Qian, H. Energy balance for analysis of complex metabolic networks. Biophys. J. 83, 79–86 (2002).

  130. 130.

    Qian, H. & Beard, D. A. Thermodynamics of stoichiometric biochemical networks in living systems far from equilibrium. Biophys. Chem. 114, 213–220 (2005).

  131. 131.

    Fleming, R. M. T., Thiele, I., Provan, G. & Nasheuer, H. P. Integrated stoichiometric, thermo- dynamic and kinetic modelling of steady state metabolism. J. Theor. Biol. 264, 683–692 (2010).

  132. 132.

    Schellenberger, J., Lewis, N. E. & Palsson, B. Ø. Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys. J. 100, 544–553 (2011).

  133. 133.

    Soh, K. C. & Hatzimanikatis, V. Network thermodynamics in the post-genomic era. Curr. Opin. Microbiol. 13, 350–357 (2010).

  134. 134.

    Fleming, R. M. T., Vlassis, N., Thiele, I. & Saunders, M. A. Conditions for duality between fluxes and concentrations in biochemical networks. J. Theor. Biol. 409, 1–10 (2016).

  135. 135.

    ​Aragón Artacho, F.J., Fleming, R. M. T. & Vuong, P. T. Accelerating the DC algorithm for smooth functions. Math. Program. 169, 95–118 (2018).

  136. 136.

    Artacho, F. J. A. & Fleming, R. M. T. Globally convergent algorithms for finding zeros of duplomonotone mappings. Optim. Lett. 9, 1–16 (2014).

  137. 137.

    Ahookhosh, M., Aragón, F. J., Fleming, R. M. T. & Vuong, P. T. Local convergence of Levenberg-Marquardt methods under Hölder metric subregularity. Preprint at (2017).

  138. 138.

    Shannon, P. et al. Cytoscape: a software environment for integrated models of biomolecular interaction networks. Genome Res. 13, 2498–2504 (2003).

  139. 139.

    King, Z. A. et al. Escher: a web application for building, sharing, and embedding data-rich visualizations of biological pathways. PLoS Comput. Biol. 11, e1004321 (2015).

  140. 140.

    Kuperstein, I. et al. NaviCell: a web-based environment for navigation, curation and maintenance of large molecular interaction maps. BMC Syst. Biol. 7, 100 (2013).

  141. 141.

    Kostromins, A. & Stalidzans, E. Paint4net: COBRA Toolbox extension for visualization of stoichiometric models of metabolism. Biosystems 109, 233–239 (2012).

  142. 142.

    Aurich, M. K. et al. Prediction of intracellular metabolic states from extracellular metabolomic data. Metabolomics 11, 603–619 (2014).

  143. 143.

    Guebila, M. B. & Thiele, I. Model-based dietary optimization for late-stage, levodopa-treated, Parkinson’s disease patients. npj Syst. Biol. Appl. 2, 16013 (2016).

  144. 144.

    Sun, Y., Fleming, R. M. T., Thiele, I. & Saunders, M. A. Robust flux balance analysis of multiscale biochemical reaction networks. BMC Bioinformatics 14, 240 (2013).

  145. 145.

    Lewis, N. E. et al. Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models. Mol. Syst. Biol. 6, 390 (2010).

  146. 146.

    Thiele, I., Fleming, R. M. T., Bordbar, A., Schellenberger, J. & Palsson, B. Ø. Functional characterization of alternate optimal solutions of Escherichia coli’s transcriptional and translational machinery. Biophys. J. 98, 2072–2081 (2010).

  147. 147.

    Ballerstein, K., von Kamp, A., Klamt, S. & Haus, U.-U. Minimal cut sets in a metabolic network are elementary modes in a dual network. Bioinformatics 28, 381–387 (2012).

  148. 148.

    von Kamp, A. & Klamt, S. Enumeration of smallest intervention strategies in genome-scale metabolic networks. PLoS Comput. Biol. 10, e1003378 (2014).

  149. 149.

    Fujita, K. A. et al. Integrating pathways of Parkinson’s disease in a molecular interaction map. Mol. Neurobiol. 49, 88–102 (2014).

  150. 150.

    Agren, R. et al. The RAVEN Toolbox and its use for generating a genome-scale metabolic model for Penicillium chrysogenum. PLoS Comput. Biol. 9, e1002980 (2013).

  151. 151.

    Grafahrend-Belau, E., Klukas, C., Junker, B. H. & Schreiber, F. FBA-SimVis: interactive visualization of constraint-based metabolic models. Bioinformatics 25, 2755–2757 (2009).

  152. 152.

    Rocha, I. et al. OptFlux: an open-source software platform for in silico metabolic engineering. BMC Syst. Biol. 4, 45 (2010).

  153. 153.

    Poolman, M. G. ScrumPy: metabolic modelling with Python. Syst. Biol. 153, 375–378 (2006).

  154. 154.

    Hoppe, A., Hoffmann, S., Gerasch, A., Gille, C. & Holzhütter, H.-G. FASIMU: flexible software for flux-balance computation series in large metabolic networks. BMC Bioinformatics 12, 28 (2011).

  155. 155.

    Boele, J., Olivier, B. G. & Teusink, B. FAME, the flux analysis and modeling environment. BMC Syst. Biol. 6, 8 (2012).

Download references


The Reproducible Research Results (R3) team, in particular, C. Trefois and Y. Jarosz, of the Luxembourg Centre for Systems Biomedicine, is acknowledged for their help in setting up the virtual machine and the Jenkins server. This study was funded by the National Centre of Excellence in Research (NCER) on Parkinson’s disease, the U.S. Department of Energy, Offices of Advanced Scientific Computing Research and the Biological and Environmental Research as part of the Scientific Discovery Through Advanced Computing program, grant no. DE-SC0010429. This project also received funding from the European Union’s HORIZON 2020 Research and Innovation Programme under grant agreement no. 668738 and the Luxembourg National Research Fund (FNR) ATTRACT program (FNR/A12/01) and OPEN (FNR/O16/11402054) grants. N.E.L. was supported by NIGMS (R35 GM119850) and the Novo Nordisk Foundation (NNF10CC1016517). M.A.P.O. was supported by the Luxembourg National Research Fund (FNR) grant AFR/6669348. A.R. was supported by the Lilly Innovation Fellows Award. F.J.P. was supported by the Minister of Economy and Competitiveness of Spain (BIO2016-77998-R) and the ELKARTEK Programme of the Basque Government (KK-2016/00026). I.A. was supported by a Basque Government predoctoral grant (PRE_2016_2_0044). B.Ø.P. was supported by the Novo Nordisk Foundation through the Center for Biosustainability at the Technical University of Denmark (NNF10CC1016517).

Author information

Author notes

  1. These authors contributed equally: Laurent Heirendt, Sylvain Arreckx.


  1. Luxembourg Centre for Systems Biomedicine, University of Luxembourg, Belvaux, Luxembourg

    • Laurent Heirendt
    • , Sylvain Arreckx
    • , Almut Heinken
    • , Hulda S. Haraldsdóttir
    • , Jacek Wachowiak
    • , Vanja Vlasov
    • , Stefania Magnusdóttir
    • , German Preciat
    • , Alise Žagare
    • , Maike K. Aurich
    • , Catherine M. Clancy
    • , Jennifer Modamio
    • , Alberto Noronha
    • , Diana C. El Assal
    • , Susan Ghaderi
    • , Masoud Ahookhosh
    • , Marouen Ben Guebila
    • , Hoai M. Le
    • , Miguel A. P. Oliveira
    • , Phan T. Vuong
    • , Lemmer P. El Assal
    • , Ines Thiele
    •  & Ronan M. T. Fleming
  2. Life Sciences Research Unit, University of Luxembourg, Belvaux, Luxembourg

    • Thomas Pfau
    •  & Thomas Sauter
  3. Center for Genome Regulation (Fondap 15090007), University of Chile, Santiago, Chile

    • Sebastián N. Mendoza
    •  & Alejandro Maass
  4. Mathomics, Center for Mathematical Modeling, University of Chile, Santiago, Chile

    • Sebastián N. Mendoza
    •  & Alejandro Maass
  5. Department of Pediatrics, University of California, San Diego, School of Medicine, La Jolla, CA, USA

    • Anne Richelle
    •  & Nathan E. Lewis
  6. European Molecular Biology Laboratory, European Bioinformatics Institute (EMBL-EBI), Hinxton, Cambridge, UK

    • Sarah M. Keating
  7. Department of Chemical Engineering, The Pennsylvania State University, State College, PA, USA

    • Chiam Yu Ng
    • , Siu H. J. Chan
    • , Lin Wang
    •  & Costas D. Maranas
  8. Department of Physics, and Bioinformatics and Systems Biology Program, University of California, San Diego, La Jolla, CA, USA

    • John T. Sauls
  9. Sinopia Biosciences, San Diego, CA, USA

    • Aarash Bordbar
  10. Algorithms and Randomness Center, School of Computer Science, Georgia Institute of Technology, Atlanta, GA, USA

    • Benjamin Cousins
    •  & Santosh Vempala
  11. Biomedical Engineering and Sciences Department, TECNUN, University of Navarra, San Sebastián, Spain

    • Luis V. Valcarcel
    • , Iñigo Apaolaza
    •  & Francisco J. Planes
  12. Institute of Microbiology and Biotechnology, University of Latvia, Riga, Latvia

    • Andrejs Kostromins
    •  & Egils Stalidzans
  13. Institut Curie, PSL Research University, Mines Paris Tech, Inserm, U900, Paris, France

    • Nicolas Sompairac
    • , Inna Kuperstein
    •  & Andrei Zinovyev
  14. Department of Management Science and Engineering, Stanford University, Stanford, CA, USA

    • Ding Ma
    •  & Michael A. Saunders
  15. Department of Statistics, University of Michigan, Ann Arbor, MI, USA

    • Yuekai Sun
  16. Department of Bioengineering, University of California, San Diego, La Jolla, CA, USA

    • James T. Yurkovich
    •  & Bernhard Ø. Palsson
  17. Utah State University Research Foundation, North Logan, UT, USA

    • H. Scott Hinton
  18. Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, London, UK

    • William A. Bryant
  19. Department of Mathematics, University of Alicante, Alicante, Spain

    • Francisco J. Aragón Artacho
  20. Department of Computing and Mathematical Sciences, California Institute of Technology, Pasadena, CA, USA

    • Michael Hucka
  21. Novo Nordisk Foundation Center for Biosustainability, University of California, San Diego, La Jolla, CA, USA

    • Nathan E. Lewis
  22. Novo Nordisk Foundation Center for Biosustainability, Technical University of Denmark, Kemitorvet, Lyngby, Denmark

    • Bernhard Ø. Palsson
  23. Division of Systems Biomedicine and Pharmacology, Leiden Academic Centre for Drug Research, Faculty of Science, Leiden University, Leiden, The Netherlands

    • Ronan M. T. Fleming


  1. Search for Laurent Heirendt in:

  2. Search for Sylvain Arreckx in:

  3. Search for Thomas Pfau in:

  4. Search for Sebastián N. Mendoza in:

  5. Search for Anne Richelle in:

  6. Search for Almut Heinken in:

  7. Search for Hulda S. Haraldsdóttir in:

  8. Search for Jacek Wachowiak in:

  9. Search for Sarah M. Keating in:

  10. Search for Vanja Vlasov in:

  11. Search for Stefania Magnusdóttir in:

  12. Search for Chiam Yu Ng in:

  13. Search for German Preciat in:

  14. Search for Alise Žagare in:

  15. Search for Siu H. J. Chan in:

  16. Search for Maike K. Aurich in:

  17. Search for Catherine M. Clancy in:

  18. Search for Jennifer Modamio in:

  19. Search for John T. Sauls in:

  20. Search for Alberto Noronha in:

  21. Search for Aarash Bordbar in:

  22. Search for Benjamin Cousins in:

  23. Search for Diana C. El Assal in:

  24. Search for Luis V. Valcarcel in:

  25. Search for Iñigo Apaolaza in:

  26. Search for Susan Ghaderi in:

  27. Search for Masoud Ahookhosh in:

  28. Search for Marouen Ben Guebila in:

  29. Search for Andrejs Kostromins in:

  30. Search for Nicolas Sompairac in:

  31. Search for Hoai M. Le in:

  32. Search for Ding Ma in:

  33. Search for Yuekai Sun in:

  34. Search for Lin Wang in:

  35. Search for James T. Yurkovich in:

  36. Search for Miguel A. P. Oliveira in:

  37. Search for Phan T. Vuong in:

  38. Search for Lemmer P. El Assal in:

  39. Search for Inna Kuperstein in:

  40. Search for Andrei Zinovyev in:

  41. Search for H. Scott Hinton in:

  42. Search for William A. Bryant in:

  43. Search for Francisco J. Aragón Artacho in:

  44. Search for Francisco J. Planes in:

  45. Search for Egils Stalidzans in:

  46. Search for Alejandro Maass in:

  47. Search for Santosh Vempala in:

  48. Search for Michael Hucka in:

  49. Search for Michael A. Saunders in:

  50. Search for Costas D. Maranas in:

  51. Search for Nathan E. Lewis in:

  52. Search for Thomas Sauter in:

  53. Search for Bernhard Ø. Palsson in:

  54. Search for Ines Thiele in:

  55. Search for Ronan M. T. Fleming in:


S.A.: continuous integration, code review,, Jenkins,, changeCobraSolver, pull request support, tutorials, tests, coordination, manuscript, and initCobraToolbox. L.H.: continuous integration, code review, fastFVA (new version, test, and integration), MATLAB.devTools,, tutorials, tests, pull request support, coordination, manuscript, initCobraToolbox, and forum support. T.P.: input–output and transcriptomic integration, tutorials, tutorial reviews, input–output and transcriptomic integration sections of manuscript, forum support, pull request support, and code review. S.N.M.: development and update of strain design algorithms, GAMS and MATLAB integration, and tutorials. A.R.: transcriptomic data integration methods, tutorials, transcriptomic integration section of manuscript, RuMBA, pFBA, metabolic tasks, and tutorial review. A.H.: multispecies modeling code contribution, tutorial review, and testing. H.S. Haraldsdóttir: thermodynamics, conserved moiety, and sampling methods. J.W.: documentation. S.M.K.: SBML input–output support. V.V.: tutorials. S.M.: multispecies modeling, tutorial review, and testing. C.Y.N.: strain design code review, tutorial review, and manuscript (OptForce/biotech introduction). G.P.: tutorials and chemoinformatics for metabolite structures and atom mapping data. A.Ž.: metabolic cartography. S.H.J.C.: solution navigation, multispecies modeling code, and tutorial review. M.K.A.: metabolomic data integration. C.M.C.: tutorials and testing. J.M.: metabolic cartography and human metabolic network visualization tutorials. J.T.S.: modelBorgifier code and tutorial. A.N.: virtual metabolic human interoperability. A.B.: MinSpan method and tutorial, supervision on uFBA method and tutorial. B.C.: CHRR uniform sampling. D.C.E.A.: tutorials. L.V.V.: tutorials and genetic MCS implementation. I.A.: tutorials and genetic MCS implementation. S.G.: interoperability with CellNetAnalyzer. M.A.: adaptive Levenberg–Marquardt solver. M.B.G.: tutorial reviews. A.K.: Paint4Net code and tutorial. N.S.: development of metabolomic cartography tool and tutorial. H.M.L.: cardinality optimization solver. D.M.: quadruple-precision solvers. Y.S.: multiscale FBA reformulation. L.W.: strain design code review, tutorial review, and manuscript (OptForce). J.T.Y.: uFBA method and tutorial. M.A.P.O.: tutorial. P.T.V.: adaptive Levenberg–Marquardt solvers and boosted difference of convex optimization solver. L.P.E.A.: chemoinformatic data integration and documentation. I.K.: development of metabolomic cartography tool and tutorial. A.Z.: development of metabolomic cartography tool and tutorial. H.S. Hinton: E. coli core tutorials. W.A.B.: code refinement. F.J.A.A.: duplomonotone equation solver, boosted difference of convex optimization solver, and adaptive Levenberg–Marquardt solvers. F.J.P.: academic supervision, tutorials, and genetic MCS implementation. E.S.: academic supervision, Paint4Net, and tutorial. A.M.: academic supervision. S.V.: academic supervision and CHRR uniform sampling algorithm. M.H.: academic supervision and SBML input–output support. M.A.S.: academic supervision, quadruple-precision solvers, nullspace computation, and convex optimization. C.D.M.: academic supervision and strain design algorithms. N.E.L.: academic supervision and coding, and transcriptomic data integration, RuMBA, pFBA, metabolic tasks, and tutorial review. T.S.: academic supervision and FASTCORE algorithm. B.Ø.P.: academic supervision and openCOBRA stewardship. I.T.: academic supervision, tutorials, code contribution, and manuscript. R.M.T.F.: conceptualization, lead developer, academic supervision, software architecture, code review, sparse optimization, nullspace computation, thermodynamics, variational kinetics, fastGapFill, sampling, conserved moieties, network visualization, forum support, tutorials, and manuscript.

Competing interests

The authors declare no competing interests.

Corresponding author

Correspondence to Ronan M. T. Fleming.

Supplementary information

  1. Supplementary Data 1

  2. Supplementary Manual 1

    MATLAB basics

  3. Supplementary Manual 2

    Shell or Terminal basics

  4. Supplementary Manual 3

    Contributing to the COBRA Toolbox using git

About this article

Publication history


Issue Date



By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.