Integration of a constraint-based metabolic model of Brassica napus developing seeds with 13C-metabolic flux analysis

Frontiers in Plant Science

Volumn 5, Issue DEC, 2014, Pages

  Hay, Jordan O ^a   Shi, Hai ^a   Heinzel, Nicolas ^b   Hebbelmann, Inga ^a   Rolletschek, Hardy ^b   Schwender, Jorg ^a  

^a BROOKHAVEN NATIONAL LABORATORY   (United States)

^b LEIBNIZ INSTITUTE OF PLANT GENETICS AND CROP PLANT RESEARCH IPK   (Germany)

Author keywords

13C metabolic flux analysis; Carbon partitioning; Central metabolism; Constraint based reconstruction and analysis; Loopless flux balance analysis

Indexed keywords

ARABIDOPSIS THALIANA; BRASSICA NAPUS; BRASSICACEAE;

EID: 84919415304     PISSN: None     EISSN: 1664462X     Source Type: Journal    
DOI: 10.3389/fpls.2014.00724     Document Type: Article

References (91)

1. Akesson, M., Forster, J., and Nielsen, J. (2004). Integration of gene expression data into genome-scale metabolic models. Metab. Eng. 6, 285-293. doi: 10.1016/j.ymben.2003.12.002
2. Al-Shehbaz, I., Beilstein, M., and Kellogg, E. (2006). Systematics and phylogeny of the Brassicaceae (Cruciferae): an overview. Plant Syst. Evol. 259, 89-120. doi: 10.1007/s00606-006-0415-z
3. Altschul, S. F., Madden, T. L., Schaffer, A. A., Zhang, J., Zhang, Z., Miller, W., et al. (1997). Gapped BLAST and PSI-BLAST: a new generation of protein database search programs. Nucleic Acids Res. 25, 3389-3402. doi: 10.1093/nar/25.17.3389
4. Arnold, A., and Nikoloski, Z. (2014). Bottom-up metabolic reconstruction of Arabidopsis and its application to determining the metabolic costs of enzyme production. Plant Physiol. 165, 1380-1391. doi: 10.1104/pp.114.235358
5. Beeler, S., Liu, H. C., Stadler, M., Schreier, T., Eicke, S., Lue, W. L., et al. (2014). Plastidial NAD-dependent malate dehydrogenase is critical for embryo development and heterotrophic metabolism in Arabidopsis. Plant Physiol. 164, 1175-1190. doi: 10.1104/pp.113.233866
6. Bell, S. L., and Palsson, B. O. (2005). Expa: a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21, 1739-1740. doi: 10.1093/bioinformatics/bti228
7. Blazier, A. S., and Papin, J. A. (2012). Integration of expression data in genome-scale metabolic network reconstructions. Front. Physiol. 3, 299. doi: 10.3389/fphys.2012.00299
8. Bordel, S., Agren, R., and Nielsen, J. (2010). Sampling the solution space in genome-scale metabolic networks reveals transcriptional regulation in key enzymes. PLoS Comput. Biol. 6:e1000859. doi: 10.1371/journal.pcbi.1000859
9. Borisjuk, L., Neuberger, T., Schwender, J., Heinzel, N., Sunderhaus, S., Fuchs, J., et al. (2013). Seed architecture shapes embryo metabolism in oilseed rape. Plant Cell 25, 1625-1640. doi: 10.1105/tpc.113.111740
10. Bornstein, B. J., Keating, S. M., Jouraku, A., and Hucka, M. (2008). LibSBML: an API library for SBML.Bioinformatics 24, 880-881. doi: 10.1093/bioinformatics/btn051
11. Boyle, N. R., and Morgan, J. A. (2009). Flux balance analysis of primary metabolism in Chlamydomonas reinhardtii. BMC Syst. Biol. 3:4. doi: 10.1186/1752-0509-3-4
12. Buchel, F., Rodriguez, N., Swainston, N., Wrzodek, C., Czauderna, T., Keller, R., et al. (2013). Path2Models: large-scale generation of computational models from biochemical pathway maps. BMC Syst. Biol. 7:116. doi: 10.1186/1752-0509-7-116
13. Burgard, A. P., Pharkya, P., and Maranas, C. D. (2003). Optknock: a bilevel programming framework for identifying gene knockout strategies for microbial strain optimization. Biotechnol. Bioeng. 84, 647-657. doi: 10.1002/bit.10803
14. Chang, R. L., Ghamsari, L., Manichaikul, A., Hom, E. F., Balaji, S., Fu, W., et al. (2011). Metabolic network reconstruction of Chlamydomonas offers insight into light-driven algal metabolism. Mol. Syst. Biol. 7, 518. doi: 10.1038/msb.2011.52
15. Cheng, F., Wu, J., Fang, L., and Wang, X. (2012). Syntenic gene analysis between Brassica rapa and other Brassicaceae species. Front. Plant. Sci. 3:198. doi: 10.3389/fpls.2012.00198
16. Cheung, C. Y., Poolman, M. G., Fell, D. A., Ratcliffe, R. G., and Sweetlove, L. J. (2014). A Diel flux balance model captures interactions between light and dark metabolism during day-night cycles in C3 and crassulacean acid metabolism leaves. Plant Physiol. 165, 917-929. doi: 10.1104/pp.113.234468
17. Cheung, C. Y., Williams, T. C., Poolman, M. G., Fell, D. A., Ratcliffe, R. G., and Sweetlove, L. J. (2013). A method for accounting for maintenance costs in flux balance analysis improves the prediction of plant cell metabolic phenotypes under stress conditions. Plant J. 75, 1050-1061. doi: 10.1111/tpj.12252
18. Choi, H. S., Kim, T. Y., Lee, D. Y., and Lee, S. Y. (2007). Incorporating metabolic flux ratios into constraint-based flux analysis by using artificial metabolites and converging ratio determinants. J. Biotechnol. 129, 696-705. doi: 10.1016/j.jbiotec.2007.02.026
19. Collakova, E., Yen, J. Y., and Senger, R. S. (2012). Are we ready for genome-scale modeling in plants? Plant Sci. 191-192, 53-70. doi: 10.1016/j.plantsci.2012.04.010
20. Dal'molin, C. G., Quek, L. E., Palfreyman, R. W., and Nielsen, L. K. (2011). AlgaGEM-a genome-scale metabolic reconstruction of algae based on the Chlamydomonas reinhardtii genome. BMC Genomics 12(Suppl. 4):S5. doi: 10.1186/1471-2164-12-S4-S5
21. Daran-Lapujade, P., Jansen, M. L., Daran, J. M., Van Gulik, W., De Winde, J. H., and Pronk, J. T. (2004). Role of transcriptional regulation in controlling fluxes in central carbon metabolism of Saccharomyces cerevisiae. A chemostat culture study. J. Biol. Chem. 279, 9125-9138. doi: 10.1074/jbc.M309578200
22. Demartini, D. R., Jain, R., Agrawal, G., and Thelen, J. J. (2011). Proteomic comparison of plastids from developing embryos and leaves of Brassica napus. J. Proteome Res. 10, 2226-2237. doi: 10.1021/pr101047y
23. De Oliveira Dal'molin, C. G., and Nielsen, L. K. (2013). Plant genome-scale metabolic reconstruction and modelling.Curr. Opin. Biotechnol. 24, 271-277. doi: 10.1016/j.copbio.2012.08.007
24. De Oliveira Dal'molin, C. G., Quek, L. E., Palfreyman, R. W., Brumbley, S. M., and Nielsen, L. K. (2010a). AraGEM, a genome-scale reconstruction of the primary metabolic network in Arabidopsis. Plant Physiol. 152, 579-589. doi: 10.1104/pp.109.148817
25. De Oliveira Dal'molin, C. G., Quek, L. E., Palfreyman, R. W., Brumbley, S. M., and Nielsen, L. K. (2010b). C4GEM, a genome-scale metabolic model to study C4 plant metabolism. Plant Physiol. 154, 1871-1885. doi: 10.1104/pp.110.166488
26. Ebrahim, A., Lerman, J. A., Palsson, B. O., and Hyduke, D. R. (2013). COBRApy: COnstraints-Based Reconstruction and Analysis for Python. BMC Syst. Biol. 7:74. doi: 10.1186/1752-0509-7-74
27. Eicks, M., Maurino, V., Knappe, S., Flugge, U. I., and Fischer, K. (2002). The plastidic pentose phosphate translocator represents a link between the cytosolic and the plastidic pentose phosphate pathways in plants. Plant Physiol. 128, 512-522. doi: 10.1104/pp.010576
28. Falginella, L., Castellarin, S. D., Testolin, R., Gambetta, G. A., Morgante, M., and Di Gaspero, G. (2010). Expansion and subfunctionalisation of flavonoid 3′,5′-hydroxylases in the grapevine lineage. BMC Genomics 11:562. doi: 10.1186/1471-2164-11-562
29. Fang, J., Reichelt, M., Hidalgo, W., Agnolet, S., and Schneider, B. (2012). Tissue-specific distribution of secondary metabolites in rapeseed (Brassica napus L.). PLoS ONE 7:e48006. doi: 10.1371/journal.pone.0048006
30. Goffman, F. D., and Mollers, C. (2000). Changes in tocopherol and plastochromanol-8 contents in seeds and oil of oilseed rape (Brassica napus L.) during storage as influenced by temperature and air oxygen. J. Agric. Food Chem. 48, 1605-1609. doi: 10.1021/jf9912755
31. Grafahrend-Belau, E., Junker, A., Eschenroder, A., Muller, J., Schreiber, F., and Junker, B. H. (2013). Multiscale metabolic modeling: dynamic flux balance analysis on a whole-plant scale. Plant Physiol. 163, 637-647. doi: 10.1104/pp.113.224006
32. Grafahrend-Belau, E., Schreiber, F., Koschützki, D., and Junker, B. H. (2009). Flux balance analysis of barley seeds: a computational approach to study systemic properties of central metabolism. Plant Physiol. 149, 585-598. doi: 10.1104/pp.108.129635
33. Gunstone, F. D. (2001). Production and consumption of rapeseed oil on a global scale. Eur. J. Lipid Sci. Technol. 103, 447-449. doi: 10.1002/1438-9312(200107)103:7<447::AID-EJLT447>3.0.CO;2-Q
34. Guo, N., Cheng, F., Wu, J., Liu, B., Zheng, S., Liang, J., et al. (2014). Anthocyanin biosynthetic genes in Brassica rapa. BMC Genomics 15:426. doi: 10.1186/1471-2164-15-426
35. Hamilton, J. J., and Reed, J. L. (2014). Software platforms to facilitate reconstructing genome-scale metabolic networks. Environ. Microbiol. 16, 49-59. doi: 10.1111/1462-2920.12312
36. 13C metabolic flux analysis. Plant J. 67, 513-525. doi: 10.1111/j.1365-313X.2011.04611.x
37. Hay, J. O., and Schwender, J. (2011b). Metabolic network reconstruction and flux variability analysis of storage synthesis in developing oilseed rape (Brassica napus L.) embryos. Plant J. 67, 526-541. doi: 10.1111/j.1365-313X.2011.04613.x
38. Hay, J. O., and Schwender, J. (2014). Flux variability analysis: application to developing oilseed rape embryos using toolboxes for constraint-based modeling. Methods Mol. Biol. 1090, 301-316. doi: 10.1007/978-1-62703-688-7_18
39. Hucka, M., Finney, A., Sauro, H. M., Bolouri, H., Doyle, J. C., Kitano, H., et al. (2003). The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19, 524-531. doi: 10.1093/bioinformatics/btg015
40. Juty, N., Le Novere, N., and Laibe, C. (2012). Identifiers.org and MIRIAM Registry: community resources to provide persistent identification. Nucleic Acids Res. 40, D580-D586. doi: 10.1093/nar/gkr1097
41. Kliphuis, A. M., Klok, A. J., Martens, D. E., Lamers, P. P., Janssen, M., and Wijffels, R. H. (2012). Metabolic modeling of Chlamydomonas reinhardtii: energy requirements for photoautotrophic growth and maintenance. J. Appl. Phycol. 24, 253-266. doi: 10.1007/s10811-011-9674-3
42. Lakshmanan, M., Zhang, Z., Mohanty, B., Kwon, J. Y., Choi, H. Y., Nam, H. J., et al. (2013). Elucidating rice cell metabolism under flooding and drought stresses using flux-based modeling and analysis. Plant Physiol. 162, 2140-2150. doi: 10.1104/pp.113.220178
43. Le Novere, N., Finney, A., Hucka, M., Bhalla, U. S., Campagne, F., Collado-Vides, J., et al. (2005). Minimum information requested in the annotation of biochemical models (MIRIAM). Nat. Biotechnol. 23, 1509-1515. doi: 10.1038/nbt1156
44. Lerman, J. A., Hyduke, D. R., Latif, H., Portnoy, V. A., Lewis, N. E., Orth, J. D., et al. (2012). In silico method for modelling metabolism and gene product expression at genome scale. Nat. Commun. 3, 929. doi: 10.1038/ncomms1928
45. Lewis, N. E., Nagarajan, H., and Palsson, B. O. (2012). Constraining the metabolic genotype-phenotype relationship using a phylogeny of in silico methods. Nat. Rev. Microbiol. 10, 291-305. doi: 10.1038/nrmicro2737
46. Liu, S., Liu, Y., Yang, X., Tong, C., Edwards, D., Parkin, I. A., et al. (2014). The Brassica oleracea genome reveals the asymmetrical evolution of polyploid genomes. Nat. Commun. 5, 3930. doi: 10.1038/ncomms4930
47. Lonien, J., and Schwender, J. (2009). Analysis of metabolic flux phenotypes for two Arabidopsis mutants with severe impairment in seed storage lipid synthesis. Plant Physiol. 151, 1617-1634. doi: 10.1104/pp.109.144121
48. Machado, D., and Herrgard, M. (2014). Systematic evaluation of methods for integration of transcriptomic data into constraint-based models of metabolism. PLoS Comput. Biol. 10:e1003580. doi: 10.1371/journal.pcbi.1003580
49. Mahadevan, R., and Schilling, C. H. (2003). The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab. Eng. 5, 264-276. doi: 10.1016/j.ymben.2003.09.002
50. Manichaikul, A., Ghamsari, L., Hom, E. F., Lin, C., Murray, R. R., Chang, R. L., et al. (2009). Metabolic network analysis integrated with transcript verification for sequenced genomes. Nat. Methods 6, 589-592. doi: 10.1038/nmeth.1348
51. Mcanulty, M. J., Yen, J. Y., Freedman, B. G., and Senger, R. S. (2012). Genome-scale modeling using flux ratio constraints to enable metabolic engineering of clostridial metabolism in silico. BMC Syst. Biol. 6:42. doi: 10.1186/1752-0509-6-42
52. Mintz-Oron, S., Meir, S., Malitsky, S., Ruppin, E., Aharoni, A., and Shlomi, T. (2012). Reconstruction of Arabidopsismetabolic network models accounting for subcellular compartmentalization and tissue-specificity. Proc. Natl. Acad. Sci. U.S.A. 109, 339-344. doi: 10.1073/pnas.1100358109
53. Monk, J., and Palsson, B. O. (2014). Genetics. Predicting microbial growth. Science 344, 1448-1449. doi: 10.1126/science.1253388
54. Mueller, L. A., Zhang, P., and Rhee, S. Y. (2003). AraCyc: a biochemical pathway database for Arabidopsis. Plant Physiol. 132, 453-460. doi: 10.1104/pp.102.017236
55. Muller, A. C., and Bockmayr, A. (2013). Fast thermodynamically constrained flux variability analysis.Bioinformatics 29, 903-909. doi: 10.1093/bioinformatics/btt059
56. Noor, E., Lewis, N. E., and Milo, R. (2012). A proof for loop-law constraints in stoichiometric metabolic networks.BMC Syst. Biol. 6:140. doi: 10.1186/1752-0509-6-140
57. Park, J. M., Kim, T. Y., and Lee, S. Y. (2010). Prediction of metabolic fluxes by incorporating genomic context and flux-converging pattern analyses. Proc. Natl. Acad. Sci. U.S.A. 107, 14931-14936. doi: 10.1073/pnas.1003740107
58. Pilalis, E., Chatziioannou, A., Thomasset, B., and Kolisis, F. (2011). An in silico compartmentalized metabolic model of Brassica napus enables the systemic study of regulatory aspects of plant central metabolism. Biotechnol. Bioeng. 108, 1673-1682. doi: 10.1002/bit.23107
59. Poolman, M. G., Kundu, S., Shaw, R., and Fell, D. A. (2013). Responses to light intensity in a genome-scale model of rice metabolism. Plant Physiol. 162, 1060-1072. doi: 10.1104/pp.113.216762
60. Poolman, M. G., Miguet, L., Sweetlove, L. J., and Fell, D. A. (2009). A genome-scale metabolic model of Arabidopsisand some of its properties. Plant Physiol. 151, 1570-1581. doi: 10.1104/pp.109.141267
61. Reed, J. L. (2012). Shrinking the metabolic solution space using experimental datasets. PLoS Comput. Biol. 8:e1002662. doi: 10.1371/journal.pcbi.1002662
62. Rocha, A. G., Mehlmer, N., Stael, S., Mair, A., Parvin, N., Chigri, F., et al. (2014). Phosphorylation of Arabidopsistransketolase at Ser428 provides a potential paradigm for the metabolic control of chloroplast carbon metabolism.Biochem. J. 458, 313-322. doi: 10.1042/BJ20130631
63. Rolletschek, H., Melkus, G., Grafahrend-Belau, E., Fuchs, J., Heinzel, N., Schreiber, F., et al. (2011). Combined noninvasive imaging and modeling approaches reveal metabolic compartmentation in the barley endosperm. Plant Cell 23, 3041-3054. doi: 10.1105/tpc.111.087015
64. Saha, R., Suthers, P. F., and Maranas, C. D. (2011). Zea mays iRS1563: a comprehensive genome-scale metabolic reconstruction of maize metabolism. PLoS ONE 6:e21784. doi: 10.1371/journal.pone.0021784
65. Scheibe, R. (2004). Malate valves to balance cellular energy supply. Physiol. Plant. 120, 21-26. doi: 10.1111/j.0031-9317.2004.0222.x
66. Schellenberger, J., Lewis, N. E., and Palsson, B. O. (2011a). Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys. J. 100, 544-553. doi: 10.1016/j.bpj.2010.12.3707
67. Schellenberger, J., Park, J. O., Conrad, T. M., and Palsson, B. O. (2010). BiGG: a Biochemical Genetic and Genomic knowledgebase of large scale metabolic reconstructions. BMC Bioinformatics 11:213. doi: 10.1186/1471-2105-11-213
68. Schellenberger, J., Que, R., Fleming, R. M., Thiele, I., Orth, J. D., Feist, A. M., et al. (2011b). Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox v2.0. Nat. Protoc. 6, 1290-1307. doi: 10.1038/nprot.2011.308
69. Schomburg, I., Chang, A., Placzek, S., Sohngen, C., Rother, M., Lang, M., et al. (2013). BRENDA in 2013: integrated reactions, kinetic data, enzyme function data, improved disease classification: new options and contents in BRENDA. Nucleic Acids Res. 41, D764-D772. doi: 10.1093/nar/gks1049
70. Schwender, J. (2008). Metabolic flux analysis as a tool in metabolic engineering of plants. Curr. Opin. Biotechnol. 19, 131-137. doi: 10.1016/j.copbio.2008.02.006
71. Schwender, J. (2011). Experimental flux measurements on a network scale. Front. Plant Sci. 2:63. doi: 10.3389/fpls.2011.00063
72. Schwender, J., and Hay, J. O. (2012). Predictive modeling of biomass component tradeoffs in Brassica napusdeveloping oilseeds based on in silico manipulation of storage metabolism. Plant Physiol. 160, 1218-1236. doi: 10.1104/pp.112.203927
73. Schwender, J., König, C., Klapperstück, M., Heinzel, N., Münz, E., Hebbelmann, I., et al. (2014). Transcript abundance on its own cannot be used to infer fluxes in central metabolism. Front. Plant Sci. 5:668. doi: 10.3389/fpls.2014.00668
74. Schwender, J., and Ohlrogge, J. B. (2002). Probing in vivo metabolism by stable isotope labeling of storage lipids and proteins in developing Brassica napus embryos. Plant Physiol. 130, 347-361. doi: 10.1104/pp.004275
75. Seaver, S. M., Gerdes, S., Frelin, O., Lerma-Ortiz, C., Bradbury, L. M., Zallot, R., et al. (2014). High-throughput comparison, functional annotation, and metabolic modeling of plant genomes using the PlantSEED resource. Proc. Natl. Acad. Sci. U.S.A. 111, 9645-9650. doi: 10.1073/pnas.1401329111
76. Seaver, S. M., Henry, C. S., and Hanson, A. D. (2012). Frontiers in metabolic reconstruction and modeling of plant genomes. J. Exp. Bot. 63, 2247-2258. doi: 10.1093/jxb/err371
77. Selinski, J., Konig, N., Wellmeyer, B., Hanke, G. T., Linke, V., Neuhaus, H. E., et al. (2014). The plastid-localized NAD-dependent malate dehydrogenase is crucial for energy homeostasis in developing Arabidopsis thaliana seeds.Mol. Plant 7, 170-186. doi: 10.1093/mp/sst151
78. Sheahan, J., Cheong, H., and Rechnitz, G. (1998). The colorless flavonoids of Arabidopsis thaliana (Brassicaceae). I. A model system to study the orthodihydroxy structure. Am. J. Bot. 85, 467. doi: 10.2307/2446429
79. Swainston, N., Smallbone, K., Mendes, P., Kell, D., and Paton, N. (2011). The SuBliMinaL Toolbox: automating steps in the reconstruction of metabolic networks. J. Integr. Bioinform. 8, 186. doi: 10.2390/biecoll-jib-2011-186
80. Sweetlove, L. J., Obata, T., and Fernie, A. R. (2014). Systems analysis of metabolic phenotypes: what have we learnt? Trends Plant Sci. 19, 222-230. doi: 10.1016/j.tplants.2013.09.005
81. Sweetlove, L. J., and Ratcliffe, R. G. (2011). Flux-balance modeling of plant metabolism. Front. Plant Sci. 2:38. doi: 10.3389/fpls.2011.00038
82. Tanz, S. K., Castleden, I., Hooper, C. M., Vacher, M., Small, I., and Millar, H. A. (2013). SUBA3: a database for integrating experimentation and prediction to define the SUBcellular location of proteins in Arabidopsis. Nucleic Acids Res. 41, D1185-D1191. doi: 10.1093/nar/gks1151
83. Thiele, I., and Palsson, B. O. (2010). A protocol for generating a high-quality genome-scale metabolic reconstruction. Nat. Protoc. 5, 93-121. doi: 10.1038/nprot.2009.203
84. Thorleifsson, S. G., and Thiele, I. (2011). rBioNet: A COBRA toolbox extension for reconstructing high-quality biochemical networks. Bioinformatics 27, 2009-2010. doi: 10.1093/bioinformatics/btr308
85. Topfer, N., Caldana, C., Grimbs, S., Willmitzer, L., Fernie, A. R., and Nikoloski, Z. (2013). Integration of genome-scale modeling and transcript profiling reveals metabolic pathways underlying light and temperature acclimation in Arabidopsis. Plant Cell 25, 1197-1211. doi: 10.1105/tpc.112.108852
86. Troncoso-Ponce, M. A., Kilaru, A., Cao, X., Durrett, T. P., Fan, J., Jensen, J. K., et al. (2011). Comparative deep transcriptional profiling of four developing oilseeds. Plant J. 68, 1014-1027. doi: 10.1111/j.1365-313X.2011.04751.x
87. Wang, X., Wang, H., Wang, J., Sun, R., Wu, J., Liu, S., et al. (2011). The genome of the mesopolyploid crop speciesBrassica rapa. Nat. Genet. 43, 1035-1039. doi: 10.1038/ng.919
88. Weitzel, M., Noh, K., Dalman, T., Niedenfuhr, S., Stute, B., and Wiechert, W. (2013). 13CFLUX2-high-performance software suite for 13C-metabolic flux analysis. Bioinformatics 29, 143-145. doi: 10.1093/bioinformatics/bts646
89. Wheeler, M. C., Tronconi, M. A., Drincovich, M. F., Andreo, C. S., Flügge, U. I., and Maurino, V. G. (2005). A comprehensive analysis of the NADP-malic enzyme gene family of Arabidopsis. Plant Physiol. 139, 39-51. doi: 10.1104/pp.105.065953
90. Wiback, S. J., Famili, I., Greenberg, H. J., and Palsson, B. O. (2004). Monte Carlo sampling can be used to determine the size and shape of the steady-state flux space. J. Theor. Biol. 228, 437-447. doi: 10.1016/j.jtbi.2004.02.006
91. Williams, T. C., Poolman, M. G., Howden, A. J., Schwarzlander, M., Fell, D. A., Ratcliffe, R. G., et al. (2010). A genome-scale metabolic model accurately predicts fluxes in central carbon metabolism under stress conditions.Plant Physiol. 154, 311-323. doi: 10.1104/pp.110.158535