Article series: Modelling

Constraint-based models predict metabolic and associated cellular functions

Journal name:
Nature Reviews Genetics
Volume:
15,
Pages:
107–120
Year published:
DOI:
doi:10.1038/nrg3643
Published online

Abstract

The prediction of cellular function from a genotype is a fundamental goal in biology. For metabolism, constraint-based modelling methods systematize biochemical, genetic and genomic knowledge into a mathematical framework that enables a mechanistic description of metabolic physiology. The use of constraint-based approaches has evolved over ~30 years, and an increasing number of studies have recently combined models with high-throughput data sets for prospective experimentation. These studies have led to validation of increasingly important and relevant biological predictions. As reviewed here, these recent successes have tangible implications in the fields of microbial evolution, interaction networks, genetic engineering and drug discovery.

At a glance

Figures

  1. The multiple uses of high-throughput data in constraint-based models.
    Figure 1: The multiple uses of high-throughput data in constraint-based models.

    Constraint-based modelling can be used to interpret and augment omic data sets by using an underlying cellular network that has been biochemically validated. Metabolites are represented by circles. a | Similarly to pathway enrichment analysis and interaction networks, high-throughput data can be integrated with the metabolic network topology to determine enriched regions and even significantly perturbed metabolites32. b | Omic data add an additional layer of constraints for reaction fluxes. One study48 integrated expression profiling data to determine context-specific flux distributions (pathway shown in red), which increases the fidelity of the data (represented as bars) as well as the accuracy of flux predictions (upper panel). In addition, two other studies77, 78 used omic data to build cell- and tissue-specific models of human metabolism by removing unexpressed reactions (shown as discoloured reactions) from the global human metabolic network (lower panel). Differences in these networks can be exploited to learn unique features of each network. c | Constraint-based analysis predictions can be compared and validated against high-throughput data sets. One study41 compared flux-balance analysis solutions of different objectives against 13C fluxomic data to find a combination of objectives that best fit the in vivo fluxes.

  2. Predictive case studies in understanding underlying principles of interaction networks.
    Figure 2: Predictive case studies in understanding underlying principles of interaction networks.

    Many network types are used to represent cellular behaviour. Recent studies have compared the properties of interaction networks against constraint-based models (CBMs) to learn global principles. a | One study55 compared an experimental set of genetic interactions for metabolic genes against interactions that were predicted by flux-balance analysis (FBA). The CBM was able to recapitulate many of the in vivo principles. However, there was a high number of incorrect model predictions. Using machine learning techniques, key changes to the metabolic network that would improve model accuracy were identified. Using growth screens, the authors validated that the synthesis of NAD+ from amino acids was only possible from L-tryptophan (L-trp) but not from L-aspartate (L-asp). Δbna refers to any of the genes that are related to the kynurenine pathway, including bna1, bna2, bna4 and bna5. b | Another study57 calculated metabolic pathways — Elementary Flux Patterns — for the network. Elementary Flux Patterns decompose the metabolic network into distinct functional pathways (shown by different colours). The degree of co-regulation of the genes of each pathway was calculated, which reveals that some pathways are highly correlated, whereas others are not. Variation in co-regulation was attributed to the 'cost' that is needed for building the proteins in a particular pathway.

  3. Predictive case studies in metabolic engineering and drug targeting.
    Figure 3: Predictive case studies in metabolic engineering and drug targeting.

    Constraint-based models have been used for answering important questions in translational research. a | One study70 used multiple computational and experimental tools to design an Escherichia coli strain that produces 1,4-butanediol (BDO). An unengineered wild-type (WT) strain trades off metabolite production with cellular growth (shown by the solid line in the solution space). Using the OptKnock algorithm, BDO production was 'coupled' with the growth objective of the cell by forcing the synthetic BDO pathway to be the sole route for E. coli to maintain redox balance (shown by black arrows). Thus, the solution space is modified such that BDO production is linked to cellular growth (shown by the dashed line in the solution space). b | In one study81, researchers took an alternative, metabolite-centric approach to drug targeting, which computationally removes consuming reactions of a particular metabolite. The approach was experimentally confirmed for Vibrio vulnificus by a structural analogue of the endogenous metabolite, which also acts as a small-molecule inhibitor. c | Metabolic reactions in the E. coli model were augmented to capture the generation of reactive oxygen species (ROS), which allowed the use of flux-balance analysis to predict ROS production in one study82. In follow-up experiments, the authors show that it is possible to predict drug target strategies to enhance endogenous ROS production to increase the efficacy of other antibiotics. TCA, tricarboxylic acid cycle.

  4. Expanding predictive scope through integrative modelling.
    Figure 4: Expanding predictive scope through integrative modelling.

    The predictive scope of constraint-based modelling has been extended beyond metabolism either by explicitly accounting for non-metabolic components in the constraint-based modelling approach or by coupling with other modelling frameworks. Metabolites are represented by circles. a | The transcription and translation of the necessary mRNA, proteins and cofactors have been explicitly represented in a constraint-based modelling framework alongside the metabolism of Thermotoga maritima83 (upper panel). This allows simultaneous computation of metabolic fluxes, mRNA transcript expression and proteome levels (lower panel). b | Metabolic models have also been coupled with other modelling frameworks. The probability of metabolic gene activation and repression by transcription factors (TFs) can be computed using a probabilistic transcriptional regulatory network that is based on high-throughput data sets (upper panel). The calculated probabilities are then relayed into the constraints of the metabolic reaction fluxes in the constraint-based model89, which allow prediction of TF-knockout phenotypes (lower panel). c | Structural systems biology can predict biophysical properties of proteins. One study91 calculated the individual activity changes of each metabolic enzyme during temperature shift. The combined effect of all the metabolic enzymes on the cell was computed by integrating the individual enzyme changes into the flux constraints of the Escherichia coli constraint-based model (upper panel), which allowed growth rate to be predicted as a function of temperature (lower panel). Enz, enzyme; NTP, nucleoside 5′-triphosphate; P, probability.

References

  1. Feist, A. M., Herrgard, M. J., Thiele, I., Reed, J. L. & Palsson, B. O. Reconstruction of biochemical networks in microorganisms. Nature Rev. Microbiol. 7, 129143 (2009).
    This is a review on constructing and validating a genome-scale metabolic network.
  2. Thiele, I. & Palsson, B. O. A protocol for generating a high-quality genome-scale metabolic reconstruction. Nature Protoc. 5, 93121 (2010).
  3. Lewis, N. E., Nagarajan, H. & Palsson, B. O. Constraining the metabolic genotype–phenotype relationship using a phylogeny of in silico methods. Nature Rev. Microbiol. 10, 291305 (2012).
    This is a thorough review of the various constraint-based modelling methodologies.
  4. Zhuang, K. et al. Genome-scale dynamic modeling of the competition between Rhodoferax and Geobacter in anoxic subsurface environments. ISME J. 5, 305316 (2011).
  5. Klitgord, N. & Segre, D. Environments that induce synthetic microbial ecosystems. PLoS Comput. Biol. 6, e1001002 (2010).
  6. 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).
  7. Bordbar, A., Lewis, N. E., Schellenberger, J., Palsson, B. O. & Jamshidi, N. Insight into human alveolar macrophage and M. tuberculosis interactions via metabolic reconstructions. Mol. Syst. Biol. 6, 422 (2010).
  8. Lewis, N. E. et al. Large-scale in silico modeling of metabolic interactions between cell types in the human brain. Nature Biotech. 28, 12791285 (2010).
  9. Papin, J. A. & Palsson, B. O. The JAK–STAT signaling network in the human B-cell: an extreme signaling pathway analysis. Biophys. J. 87, 3746 (2004).
  10. Li, F., Thiele, I., Jamshidi, N. & Palsson, B. O. Identification of potential pathway mediation targets in Toll-like receptor signaling. PLoS Comput. Biol. 5, e1000292 (2009).
  11. Gianchandani, E. P., Joyce, A. R., Palsson, B. O. & Papin, J. A. Functional states of the genome-scale Escherichia coli transcriptional regulatory system. PLoS Comput. Biol. 5, e1000403 (2009).
  12. Thiele, I., Jamshidi, N., Fleming, R. M. & Palsson, B. O. 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).
  13. Fell, D. A. & Small, J. R. Fat synthesis in adipose tissue. An examination of stoichiometric constraints. Biochem. J. 238, 781786 (1986).
  14. Majewski, R. A. & Domach, M. M. Simple constrained optimization view of acetate overflow in E. coli. Biotechnol. Bioeng. 35, 732738 (1990).
  15. Savinell, J. M. & Palsson, B. O. Optimal selection of metabolic fluxes for in vivo measurement. II. Application to Escherichia coli and hybridoma cell metabolism. J. Theor. Biol. 155, 215242 (1992).
  16. Varma, A. & Palsson, B. O. Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl. Environ. Microbiol. 60, 37243731 (1994).
  17. Schuster, S. & Hilgetag, C. On elementary flux modes in biochemical reaction systems at steady state. J. Biol. Systems 2, 165182 (1994).
  18. Schilling, C. H., Letscher, D. & Palsson, B. O. Theory for the systemic definition of metabolic pathways and their use in interpreting metabolic function from a pathway-oriented perspective. J. Theor. Biol. 203, 229248 (2000).
  19. Clarke, B. L. in Advances in Chemical Physics Vol. 43 (eds. Prigogine, I. & Rice, S. A.) 1215 (Wiley, 1980).
  20. Dandekar, T., Schuster, S., Snel, B., Huynen, M. & Bork, P. Pathway alignment: application to the comparative analysis of glycolytic enzymes. Biochem. J. 343, 115124 (1999).
  21. Liao, J. C., Hou, S. Y. & Chao, Y. P. Pathway analysis, engineering and physiological considerations for redirecting central metabolism. Biotechnol. Bioeng. 52, 129140 (1996).
  22. Fleischmann, R. D. et al. Whole-genome random sequencing and assembly of Haemophilus influenzae Rd. Science 269, 496512 (1995).
  23. Edwards, J. S. & Palsson, B. O. Systems properties of the Haemophilus influenzae Rd metabolic genotype. J. Biol. Chem. 274, 1741017416 (1999).
  24. Edwards, J. S., Ibarra, R. U. & Palsson, B. O. In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nature Biotech. 19, 125130 (2001).
  25. Segre, D., Vitkup, D. & Church, G. M. Analysis of optimality in natural and perturbed metabolic networks. Proc. Natl Acad. Sci. USA 99, 1511215117 (2002).
  26. Stelling, J., Klamt, S., Bettenbrock, K., Schuster, S. & Gilles, E. D. Metabolic network structure determines key aspects of functionality and regulation. Nature 420, 190193 (2002).
  27. Ibarra, R. U., Edwards, J. S. & Palsson, B. O. Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420, 186189 (2002).
  28. Almaas, E., Kovacs, B., Vicsek, T., Oltvai, Z. N. & Barabasi, A. L. Global organization of metabolic fluxes in the bacterium Escherichia coli. Nature 427, 839843 (2004).
  29. Papp, B., Pal, C. & Hurst, L. D. Metabolic network analysis of the causes and evolution of enzyme dispensability in yeast. Nature 429, 661664 (2004).
  30. Pal, C., Papp, B. & Lercher, M. J. Adaptive evolution of bacterial metabolic networks by horizontal gene transfer. Nature Genet. 37, 13721375 (2005).
  31. Hyduke, D. R., Lewis, N. E. & Palsson, B. O. Analysis of omics data with genome-scale models of metabolism. Mol. Biosyst 9, 167174 (2013).
    This is a review of techniques to integrate omic data with CBMs.
  32. Patil, K. R. & Nielsen, J. Uncovering transcriptional regulation of metabolism by using metabolic network topology. Proc. Natl Acad. Sci. USA 102, 26852689 (2005).
  33. Kharchenko, P., Church, G. M. & Vitkup, D. Expression dynamics of a cellular metabolic network. Mol Syst Biol 1, 2005.0016 (2005).
  34. Shlomi, T., Cabili, M. N., Herrgard, M. J., Palsson, B. O. & Ruppin, E. Network-based prediction of human tissue-specific metabolism. Nature Biotech. 26, 10031010 (2008).
  35. Becker, S. A. & Palsson, B. O. Context-specific metabolic networks are consistent with experiments. PLoS Comput. Biol. 4, e1000082 (2008).
  36. Carlson, R. & Srienc, F. Fundamental Escherichia coli biochemical pathways for biomass and energy production: creation of overall flux states. Biotechnol. Bioeng. 86, 149162 (2004).
  37. Carlson, R. & Srienc, F. Fundamental Escherichia coli biochemical pathways for biomass and energy production: identification of reactions. Biotechnol. Bioeng. 85, 119 (2004).
  38. Harcombe, W. R., Delaney, N. F., Leiby, N., Klitgord, N. & Marx, C. J. The ability of flux balance analysis to predict evolution of central metabolism scales with the initial distance to the optimum. PLoS Comput. Biol. 9, e1003091 (2013).
  39. Schuetz, R., Kuepfer, L. & Sauer, U. Systematic evaluation of objective functions for predicting intracellular fluxes in Escherichia coli. Mol Syst Biol. 3, 119 (2007).
  40. Molenaar, D., van Berlo, R., de Ridder, D. & Teusink, B. Shifts in growth strategies reflect tradeoffs in cellular economics. Mol. Syst. Biol. 5, 323 (2009).
  41. Schuetz, R., Zamboni, N., Zampieri, M., Heinemann, M. & Sauer, U. Multidimensional optimality of microbial metabolism. Science 336, 601604 (2012).
  42. 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).
  43. Khersonsky, O. & Tawfik, D. S. Enzyme promiscuity: a mechanistic and evolutionary perspective. Annu. Rev. Biochem. 79, 471505 (2010).
  44. Nam, H. et al. Network context and selection in the evolution to enzyme specificity. Science 337, 11011104 (2012).
  45. 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).
  46. Baba, T. et al. Construction of Escherichia coli K-12 in-frame, single-gene knockout mutants: the Keio collection. Mol Syst Biol. 2, 2006.0008 (2006).
  47. Scheer, M. et al. BRENDA, the enzyme information system in 2011. Nucleic Acids Res. 39, D670D676 (2011).
  48. Lobel, L., Sigal, N., Borovok, I., Ruppin, E. & Herskovits, A. A. Integrative genomic analysis identifies isoleucine and CodY as regulators of Listeria monocytogenes virulence. PLoS Genet. 8, e1002887 (2012).
  49. Costanzo, M. et al. The genetic landscape of a cell. Science 327, 425431 (2010).
  50. Uetz, P. et al. A comprehensive analysis of protein–protein interactions in Saccharomyces cerevisiae. Nature 403, 623627 (2000).
  51. Gama-Castro, S. et al. RegulonDB version 7.0: transcriptional regulation of Escherichia coli K-12 integrated within genetic sensory response units (Gensor Units). Nucleic Acids Res. 39, D98D105 (2011).
  52. Segre, D., DeLuna, A., Church, G. M. & Kishnoy, R. Modular epistasis in yeast metabolism. Nature Genet. 37, 7783 (2005).
  53. Harrison, R., Papp, B., Pal, C., Oliver, S. G. & Delneri, D. Plasticity of genetic interactions in metabolic networks of yeast. Proc. Natl Acad. Sci. USA 104, 23072312 (2007).
  54. He, X., Qian, W., Wang, Z., Li, Y. & Zhang, J. Prevalent positive epistasis in Escherichia coli and Saccharomyces cerevisiae metabolic networks. Nature Genet. 42, 272276 (2010).
  55. Szappanos, B. et al. An integrated approach to characterize genetic interaction networks in yeast metabolism. Nature Genet. 43, 656662 (2011).
  56. Mo, M. L., Palsson, B. O. & Herrgard, M. J. Connecting extracellular metabolomic measurements to intracellular flux states in yeast. BMC Syst. Biol. 3, 37 (2009).
  57. Wessely, F. et al. Optimal regulatory strategies for metabolic pathways in Escherichia coli depending on protein costs. Mol. Syst. Biol. 7, 515 (2011).
  58. Notebaart, R. A., Teusink, B., Siezen, R. J. & Papp, B. Co-regulation of metabolic genes is better explained by flux coupling than by network distance. PLoS Comput. Biol. 4, e26 (2008).
  59. Kaleta, C., de Figueiredo, L. F. & Schuster, S. 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, 18721883 (2009).
  60. Faith, J. J. et al. Many Microbe Microarrays Database: uniformly normalized Affymetrix compendia with structured experimental metadata. Nucleic Acids Res. 36, D866D870 (2008).
  61. Orth, J. D. & Palsson, B. O. Systematizing the generation of missing metabolic knowledge. Biotechnol. Bioeng. 107, 403412 (2010).
    This is a review on techniques and applications of CBMs for a targeted expansion of biochemical knowledge.
  62. Reed, J. L. et al. Systems approach to refining genome annotation. Proc. Natl Acad. Sci. USA 103, 1748017484 (2006).
  63. Duarte, N. C. et al. Global reconstruction of the human metabolic network based on genomic and bibliomic data. Proc. Natl Acad. Sci. USA 104, 17771782 (2007).
  64. Rolfsson, O., Paglia, G., Magnusdottir, M., Palsson, B. O. & Thiele, I. Inferring the metabolism of human orphan metabolites from their metabolic network context affirms human gluconokinase activity. Biochem. J. 449, 427435 (2013).
  65. 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, D109D114 (2012).
  66. Nakahigashi, K. et al. Systematic phenome analysis of Escherichia coli multiple-knockout mutants reveals hidden reactions in central carbon metabolism. Mol. Syst. Biol. 5, 306 (2009).
  67. Lee, S. Y., Lee, D. Y. & Kim, T. Y. Systems biotechnology for strain improvement. Trends Biotechnol. 23, 349358 (2005).
  68. Park, J. H. & Lee, S. Y. Towards systems metabolic engineering of microorganisms for amino acid production. Curr. Opin. Biotechnol. 19, 454460 (2008).
    This is a review of using systems biology methodologies for metabolic engineering applications.
  69. Caspeta, L. & Nielsen, J. Economic and environmental impacts of microbial biodiesel. Nature Biotech. 31, 789793 (2013).
  70. Yim, H. et al. Metabolic engineering of Escherichia coli for direct production of 1,4-butanediol. Nature Chem. Biol. 7, 445452 (2011).
  71. Hatzimanikatis, V. et al. Exploring the diversity of complex metabolic networks. Bioinformatics 21, 16031609 (2005).
  72. Constantinou, L. & Gani, R. New group-contribution method for estimating properties of pure compounds. AIChE J. 40, 16971710 (1994).
  73. Khatri, P., Sirota, M. & Butte, A. J. Ten years of pathway analysis: current approaches and outstanding challenges. PLoS Comput. Biol. 8, e1002375 (2012).
  74. 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, 647657 (2003).
  75. Oberhardt, M. A., Yizhak, K. & Ruppin, E. Metabolically re-modeling the drug pipeline. Curr. Opin. Pharmacol. 13, 778785 (2013).
    This is a review on using constraint-based modelling for drug discovery.
  76. Hsu, P. P. & Sabatini, D. M. Cancer cell metabolism: Warburg and beyond. Cell 134, 703707 (2008).
  77. Folger, O. et al. Predicting selective drug targets in cancer through metabolic networks. Mol. Syst. Biol. 7, 501 (2011).
  78. Frezza, C. et al. Haem oxygenase is synthetically lethal with the tumour suppressor fumarate hydratase. Nature 477, 225228 (2011).
  79. Jerby, L., Shlomi, T. & Ruppin, E. Computational reconstruction of tissue-specific metabolic models: application to human liver metabolism. Mol. Syst. Biol. 6, 401 (2010).
  80. Kim, P. J. et al. Metabolite essentiality elucidates robustness of Escherichia coli metabolism. Proc. Natl Acad. Sci. USA 104, 1363813642 (2007).
  81. Kim, H. U. et al. Integrative genome-scale metabolic analysis of Vibrio vulnificus for drug targeting and discovery. Mol. Syst. Biol. 7, 460 (2011).
  82. Brynildsen, M. P., Winkler, J. A., Spina, C. S., MacDonald, I. C. & Collins, J. J. Potentiating antibacterial activity by predictably enhancing endogenous microbial ROS production. Nature Biotech. 31, 160165 (2013).
  83. Lerman, J. A. et al. In silico method for modelling metabolism and gene product expression at genome scale. Nature Commun. 3, 929 (2012).
  84. Zhang, Y. et al. Three-dimensional structural view of the central metabolic network of Thermotoga maritima. Science 325, 15441549 (2009).
  85. Thiele, I., Fleming, R. M., Bordbar, A., Schellenberger, J. & Palsson, B. O. Functional characterization of alternate optimal solutions of Escherichia coli's transcriptional and translational machinery. Biophys. J. 98, 20722081 (2010).
  86. Pramanik, J. & Keasling, J. D. Effect of Escherichia coli biomass composition on central metabolic fluxes predicted by a stoichiometric model. Biotechnol. Bioeng. 60, 230238 (1998).
  87. Rodionova, I. A. et al. Diversity and versatility of the Thermotoga maritima sugar kinome. J. Bacteriol. 194, 55525563 (2012).
  88. O'Brien, E. J., Lerman, J. A., Chang, R. L., Hyduke, D. R. & Palsson, B. O. Genome-scale models of metabolism and gene expression extend and refine growth phenotype prediction. Mol. Syst. Biol. 9, 693 (2013).
  89. Chandrasekaran, S. & Price, N. D. Probabilistic integrative modeling of genome-scale metabolic and regulatory networks in Escherichia coli and Mycobacterium tuberculosis. Proc. Natl Acad. Sci. USA 107, 1784517850 (2010).
  90. Covert, M. W., Knight, E. M., Reed, J. L., Herrgard, M. J. & Palsson, B. O. Integrating high-throughput and computational data elucidates bacterial networks. Nature 429, 9296 (2004).
  91. Chang, R. L. et al. Structural systems biology evaluation of metabolic thermotolerance in Escherichia coli. Science 340, 12201223 (2013).
  92. Gu, J. & Bourne, P. E. Structural bioinformatics (Wiley-Blackwell, 2009).
  93. Marr, A. G. & Ingraham, J. L. Effect of temperature on the composition of fatty acids in Escherichia coli. J. Bacteriol. 84, 12601267 (1962).
  94. Tenaillon, O. et al. The molecular diversity of adaptive convergence. Science 335, 457461 (2012).
  95. Mörters, P., Peres, Y., Schramm, O. & Werner, W. Brownian motion (Cambridge Univ. Press, 2010).
  96. Karr, J. R. et al. A whole-cell computational model predicts phenotype from genotype. Cell 150, 389401 (2012).
  97. Thiele, I. et al. A community-driven global reconstruction of human metabolism. Nature Biotech. 31, 419425 (2013).
  98. Borenstein, E. Computational systems biology and in silico modeling of the human microbiome. Brief Bioinform. 13, 769780 (2012).
  99. Levy, R. & Borenstein, E. Metabolic modeling of species interaction in the human microbiome elucidates community-level assembly rules. Proc. Natl Acad. Sci. USA 110, 1280412809 (2013).
  100. Atkinson, D. E. The energy charge of the adenylate pool as a regulatory parameter. Interaction with feedback modifiers. Biochemistry 7, 40304034 (1968).
  101. Weisz, P. B. Diffusion and chemical transformation. Science 179, 433440 (1973).
  102. Reed, J. L. Shrinking the metabolic solution space using experimental datasets. PLoS Comput. Biol. 8, e1002662 (2012).
    This is a review of the potential constraints that have been placed on CBMs.
  103. Colijn, C. et al. Interpreting expression data with metabolic flux models: predicting Mycobacterium tuberculosis mycolic acid production. PLoS Comput. Biol. 5, e1000489 (2009).
  104. Orth, J. D., Thiele, I. & Palsson, B. O. What is flux balance analysis? Nature Biotech. 28, 245248 (2010).
    This paper presents a primer on the theory, applications and software toolboxes for FBA.
  105. Mahadevan, R. & Schilling, C. H. The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metab. Eng. 5, 264276 (2003).
  106. Wilkinson, D. J. Stochastic modelling for quantitative description of heterogeneous biological systems. Nature Rev. Genet. 10, 122133 (2009).
  107. Steuer, R. Computational approaches to the topology, stability and dynamics of metabolic networks. Phytochemistry 68, 21392151 (2007).
  108. de Jong, H. Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9, 67103 (2002).
  109. Friedman, N., Linial, M., Nachman, I. & Pe'er, D. Using Bayesian networks to analyze expression data. J. Computat. Biol. 7, 601620 (2000).
  110. Stephens, M. & Balding, D. J. Bayesian statistical methods for genetic association studies. Nature Rev. Genet. 10, 681690 (2009).
  111. Ideker, T. & Krogan, N. J. Differential network biology. Mol. Syst. Biol. 8, 565 (2012).
  112. Califano, A., Butte, A. J., Friend, S., Ideker, T. & Schadt, E. Leveraging models of cell regulation and GWAS data in integrative network-based association studies. Nature Genet. 44, 841847 (2012).

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Affiliations

  1. Department of Bioengineering, University of California, San Diego, 9500 Gilman Dr, La Jolla, California 92093–0412, USA.

    • Aarash Bordbar,
    • Jonathan M. Monk,
    • Zachary A. King &
    • Bernhard O. Palsson

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The authors declare no competing interests.

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  • Aarash Bordbar

    Aarash Bordbar is a Ph.D. candidate in Bioengineering at the University of California, San Diego, USA, and holds a B.S. degree in Bioengineering: Biotechnology from the University of California, San Diego. His current research involves developing and applying novel computational methods to the systems biology of human metabolism; he has a particular focus on infection, inflammation, haematology and personalized medicine.

  • Jonathan M. Monk

    Jonathan M. Monk is a graduate student in Nanoengineering at the University of California, San Diego, USA, and holds a B.S. degree in Chemical Engineering from Princeton University, New Jersey, USA. He is currently researching virulence factors of numerous pathogenic Escherichia coli strains by developing genome-scale metabolic models and experimentally validating them using high-throughput screens.

  • Zachary A. King

    Zachary A. King is a graduate student in Bioengineering at the University of California, San Diego, USA, and holds a B.S.E. degree in Biomedical Engineering from the University of Michigan, Ann Arbor, USA. He is developing multiscale modelling tools for Escherichia coli and investigating basic biological constraints that can be used to predict phenotypes of organisms with genetic modifications.

  • Bernhard O. Palsson

    Bernhard O. Palsson is the Galletti Professor of Bioengineering at the University of California, San Diego, USA; a member of the US National Academy of Engineering; and a fellow of the American Association for the Advancement of Science. His research includes developing methods for analysing metabolic dynamics and formulating complete models of selected cells. He has authored 40 US patents, 3 books and 340 peer-reviewed articles, and is the co-founder of several biotechnology companies. He holds a Ph.D. in Chemical Engineering from the University of Wisconsin–Madison, USA, and a B.S. degree in Chemical Engineering from the University of Kansas, Lawrence, USA. Bernhard O. Palsson's homepage.

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