Skip to main content

Network Stoichiometry

This chapter describes approaches to modeling metabolic pathways that are based on biochemical reaction stoichiometry. These methods have some advantages over kinetic models because they do not require the determination of complicated kinetic expressions and associated kinetic parameters. Although based only upon reaction stoichiometry and mass balances, the techniques can be quite powerful in exploring the capabilities of a metabolic network. Stoichiometry-based models enable efficient calculation of theoretical yields on any nutrient [78]. The models may be used to rationally select genes for addition and/or deletion in the genome which have the most promise to significantly improve desired product yield. New targets for herbicides can be selected through a mathematical analysis of the sensitivity of inhibiting specific enzymes on growth fluxes [87]. Perhaps their greatest promise in conjunction with optimization strategies is the ability to predict metabolic fluxes to specific products or growth as a function of the environment.

Keywords

  • Metabolic Network
  • Flux Distribution
  • Flux Balance Analysis
  • Stoichiometric Matrix
  • Thermodynamic Constraint

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • DOI: 10.1007/978-0-387-78745-9_8
  • Chapter length: 33 pages
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
eBook
USD   169.00
Price excludes VAT (USA)
  • ISBN: 978-0-387-78745-9
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD   219.99
Price excludes VAT (USA)
Hardcover Book
USD   249.99
Price excludes VAT (USA)
Fig. 8.1
Fig. 8.2
Fig. 8.3
Fig. 8.4
Fig. 8.5
Fig. 8.6
Fig. 8.7
Fig. 8.8

References

  1. Albertsson PA (2001) A quantitative model of the domain structure of the photosynthetic membrane. Trends Plant Sci 6:349–358.

    PubMed  CrossRef  CAS  Google Scholar 

  2. Allen JF (2002) Photosynthesis of ATP – electrons, proton pumps, roters and poise. Cell 110:273–276.

    PubMed  CrossRef  CAS  Google Scholar 

  3. Arnon DI (1948) Copper enzymes in isolated chloroplasts polyphenoloxidase in Beta vulgaris. Plant Physiol 24:1–15.

    CrossRef  Google Scholar 

  4. Beard DA, Babson E, Curtis E, Qian H (2004) Thermodynamic constraints for biochemical networks. J Theor Biol 228:327–333.

    PubMed  CrossRef  CAS  Google Scholar 

  5. Beard DA, Liang SD, Qian H (2002) Energy balance for analysis of complex metabolic networks. Biophys J 83:79–86.

    PubMed  CrossRef  CAS  Google Scholar 

  6. Becker S, Palsson B (2005) Genome-scale reconstruction of the metabolic network in Staphylococcus aureus N315: an initial draft to the two-dimensional annotation. BMC Microbiology 5:8.

    PubMed  CrossRef  Google Scholar 

  7. Bell SL, Palsson BO (2005) expa: a program for calculating extreme pathways in biochemical reaction networks. Bioinformatics 21:1739–1740.

    PubMed  CrossRef  CAS  Google Scholar 

  8. Borodina I, Krabben P, Nielsen J (2005) Genome-scale analysis of Streptomyces coelicolor A3(2) metabolism. Genome Res 15:820–829.

    PubMed  CrossRef  CAS  Google Scholar 

  9. Burgard A, Maranas C (2001) Probing the performance limits of the Escherichia coli metabolic network subject to gene additions or deletions. Biotechnnol Bioeng 74: 364–375.

    CrossRef  CAS  Google Scholar 

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

    PubMed  CrossRef  CAS  Google Scholar 

  11. Çakir T, Kirdar B, Ülgen KÖ (2004) Metabolic pathway analysis of yeast strengthens the bridge between transcriptomics and metabolic networks. Biotechnol Bioeng 86:251–260.

    PubMed  CrossRef  Google Scholar 

  12. Carlson R, Srienc F (2004) Fundamental Escherichia coli biochemical pathways for biomass and energy production: Creation of overall flux states. Biotechnol Bioeng 86:149–162.

    PubMed  CrossRef  CAS  Google Scholar 

  13. Caspi R, Foerster H, Fulcher C, Kaipa P, Krummenacker M, Latendresse M, Paley S, Rhee S, Shearer A, Tissier C, Walk T, Zhang P, Karp P (2006) MetaCyc: A multiorganism database of metabolic pathways and enzymes. Nucleic Acids Res 34:D511–D516.

    PubMed  CrossRef  CAS  Google Scholar 

  14. Chvatal V (1983) Linear Programming. W. H. Freeman and Company, New York.

    Google Scholar 

  15. Clarke B (1988) Stoichiometric network analysis. Cell Biophy 12:237–253.

    CAS  Google Scholar 

  16. Cogne G, Gros JB, Dussap CG (2003) Identification of a metabolic network structure representative of Arthrospira (Spirulina) platensis metabolism. Biotechnol Bioeng 84:667–676.

    PubMed  CrossRef  CAS  Google Scholar 

  17. Covert MW, Schilling CH, Palsson B (2001) Regulation of gene expression in flux balance models of metabolism. J Theor Biol 213:73–88.

    PubMed  CrossRef  CAS  Google Scholar 

  18. DeJongh M, Formsma K, Boillot P, Gould J, Rycenga M, Best A (2007) Toward the automated generation of genome-scale metabolic networks in the SEED. BMC Bioinformatics 8:139.

    PubMed  CrossRef  Google Scholar 

  19. Duarte N, Herrgard MJ, Palsson BO (2007) Reconstruction and validation of Saccharomyces cerevisiae iND750, a fully compartmentalized genome-scale metabolic model. Genome Res 14:1298–1309.

    CrossRef  Google Scholar 

  20. Edwards J, Palsson B (2000) The Escherichia coli MG1655 in silico metabolic genotyope: its definition, characteristics, and capabilities. Proc Natl Acad Sci USA 97:5528–5533.

    PubMed  CrossRef  CAS  Google Scholar 

  21. Edwards J, Ramakrishna R, Palsson B (2002) Characterizing the metabolic phenotype: a phenotype phase plane analysis. Biotechnnol Bioeng 77:27–36.

    CrossRef  CAS  Google Scholar 

  22. Edwards JS, Palsson BO (1999) Systems properties of the Haemophilus influenzae Rd metabolic genotype. J Biol Chem 274:17410–17416.

    PubMed  CrossRef  CAS  Google Scholar 

  23. Emanuelsson O, Nielsen H, Brunak S, Heijne Gv (2000) Predicting subcellular localization of proteins based on their N-terminal amino acid sequence. J Mol Biol 300:1005–1016.

    PubMed  CrossRef  CAS  Google Scholar 

  24. Emmerling M, Dauner M, Ponti A, Fiaux J, Hochuli M, Szyperski T, Wuthrich K, Bailey JE, Sauer U (2002) Metabolic flux responses to pyruvate kinase knockout in Escherichia coli. J Bacteriol 184: 152–164.

    PubMed  CrossRef  CAS  Google Scholar 

  25. Famili I, Forster J, Nielson J, Palsson BO (2003) Saccharomyces cerevisiae phenotypes can be predicted by using constraint-based analysis of a genome-scale reconstructed metabolic network. Proc Natl Acad Sci USA 100:13134–13139.

    PubMed  CrossRef  CAS  Google Scholar 

  26. Feist AM, Henry CS, Reed JL, Krummenacker M, Joyce AR, Karp PD, Broadbelt LJ, Hatzimanikatis V, Palsson BO (2007) A genome-scale metabolic reconstruction for Escherichia coli K-12 MG1655 that accounts for 1260 ORFs and thermodynamic information. Mol Syst Biol 3: 121.

    PubMed  CrossRef  Google Scholar 

  27. Fell DA, Small JR (1986) Fat synthesis in adipose tissue – an examination of stoichiometric constraints. Biochem J 238:781–786.

    PubMed  CAS  Google Scholar 

  28. Fischer E, Sauer U (2005) Large-scale in vivo flux analysis shows rigidity and suboptimal performance of Bacillus subtilis metabolism. Nature Genet 37:636–640.

    PubMed  CrossRef  CAS  Google Scholar 

  29. Forster J, Famili I, Fu P, Palsson BO, Nielsen J (2003) Genome-scale reconstruction of the Saccharomyces cerevisiae metabolic network. Genome Res 13:244–253.

    PubMed  CrossRef  CAS  Google Scholar 

  30. Gibaldi M, Perrier D (1983) Pharmacokinetics. Marcel Dekker, New York.

    Google Scholar 

  31. Harary F (1994) Graph Theory. Perseus Books, Reading Westview Press, Boulder, CO.

    Google Scholar 

  32. Heinemann M, Kümmel A, Ruinatscha R, Panke S (2005) In silico genome-scale reconstruction and validation of the Staphylococcus aureus metabolic network. Biotechnol Bioeng 92:850–864.

    PubMed  CrossRef  CAS  Google Scholar 

  33. Henriksen CM, Christensen LH, Nielsen J, Villadsen J (1996) Growth energetics and metabolic fluxes in continuous cultures of Penicillium chrysogenum. J Biotechnol 45: 149–164.

    PubMed  CrossRef  CAS  Google Scholar 

  34. Henry CS, Broadbelt LJ, Hatzimanikatis V (2007) Thermodynamics-based metabolic flux analysis. Biophys J 92:1792–1805.

    PubMed  CrossRef  CAS  Google Scholar 

  35. Henry CS, Jankowski MD, Broadbelt LJ, Hatzimanikatis V (2006) Genome-scale thermodynamic analysis of Escherichia coli metabolism. Biophys J 90:1453–1461.

    PubMed  CrossRef  CAS  Google Scholar 

  36. Hjersted JL, Henson MA (2006) Optimization of fed-batch Saccharomyces cerevisiae fermentation using dynamic flux balance models. Biotechnol Prog 22:1239–1248.

    PubMed  CrossRef  CAS  Google Scholar 

  37. Hjersted JL, Henson MA, Mahadevan R (2007) Genome-scale analysis of Saccharomyces cerevisiae metabolism and ethanol production in fed-batch culture. Biotechnol Bioeng 97:1190–1204.

    PubMed  CrossRef  CAS  Google Scholar 

  38. Ibarra RU, Edwards JS, Palsson BO (2002) Escherichia coli K-12 undergoes adaptive evolution to achieve in silico predicted optimal growth. Nature 420:186–189.

    PubMed  CrossRef  CAS  Google Scholar 

  39. Jorgensen H, Nielsen J, Villadsen J, Mollgaard H (1995) Metabolic flux distributions in Penicillium chrysogenum during fed-batch cultivations. Biotechnol Bioeng 46:117–131.

    PubMed  CrossRef  CAS  Google Scholar 

  40. Kanehisa M, Goto S, Hattori M, Aoki-Kinoshita KF, Itoh M, Kawashima S, Katayama T, Araki M, Hirakawa M (2006) From genomics to chemical genomics: new developments in KEGG. Nucleic Acids Res 34:D354–357.

    PubMed  CrossRef  CAS  Google Scholar 

  41. Karp PD, Paley S, Romero P (2002) The pathway tools software. Bioinformatics 18: S225–232.

    PubMed  Google Scholar 

  42. Kelly GJ, Latzko E (1977) Chloroplast phosphofructokinase .1. Proof of phosphofructokinase activity in chloroplasts. Plant Physiol 60:290–294.

    PubMed  CrossRef  CAS  Google Scholar 

  43. Kim HU, Kim TY, Lee SY (2008) Metabolic flux analysis and metabolic engineering of microorganisms. Mol BioSyst 4:113–120.

    PubMed  CrossRef  Google Scholar 

  44. Klamt S, Stelling J. 2003. Stoichiometric analysis of metabolic networks. in: Proceedings of the Tutorial at the 4th International Conference on Systems Biology, Heidelberg, Germany.

    Google Scholar 

  45. Klamt S, Stelling J (2003) Two approaches for metabolic pathway analysis? Trends Biotechnol 21:64–69.

    PubMed  CrossRef  CAS  Google Scholar 

  46. Klamt S, Stelling J, Ginkel M, Gilles ED (2003) FluxAnalyzer: exploring structure, pathways, flux distributions in metabolic networks on interactive flux maps. Bioinformatics 19: 261–269.

    PubMed  CrossRef  CAS  Google Scholar 

  47. Kummel A, Panke S, Heinemann M (2006) Systematic assignment of thermodynamic constraints in metabolic network models. BMC Bioinformatics 7.

    Google Scholar 

  48. Lee S, Palakornkule C, Domach MM, Grossmann IE (2000) Recursive MILP model for finding all the alternate optima in LP models for metabolic networks. Comput Chem Eng 24: 711–716.

    CrossRef  CAS  Google Scholar 

  49. Li K, Frost JW (1998) Synthesis of vanillin from glucose. J Am Chem Soc 120:10545–10546.

    CrossRef  CAS  Google Scholar 

  50. Mahadevan R, Edwards JS, Doyle FJ, III (2002) Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J 83:1331–1340.

    PubMed  CrossRef  CAS  Google Scholar 

  51. Mahadevan R, Schilling CH (2003) The effects of alternate optimal solutions in constraint-based genome-scale metabolic models. Metabol Eng 5:264–276.

    CrossRef  CAS  Google Scholar 

  52. Majewski RA, Domach MM (1990) Simple constrained optimization view of acetate overflow in Escherichia coli. Biotechnol Bioeng 35:732–738.

    PubMed  CrossRef  CAS  Google Scholar 

  53. Mavrovouniotis ML (1990) Group contributions for estimating standard Gibbs energies of formation of biochemical compounds in aqueous solution. Biotechnol Bioeng 36: 1070–1082.

    PubMed  CrossRef  CAS  Google Scholar 

  54. Nelson DL, Cox MM (2005) Lehninger Principles of Biochemistry. W.H. Freeman and Company, New York.

    Google Scholar 

  55. Oliveira A, Nielsen J, Forster J (2005) Modeling Lactococcus lactis using a genome-scale flux model. BMC Microbiology 5:39.

    PubMed  CrossRef  Google Scholar 

  56. Papin JA, Stelling J, Price ND, Klamt S, Schuster S, Palsson BO (2004) Comparison of network-based pathway analysis methods. Trends Biotechnol 22:400–405.

    PubMed  CrossRef  CAS  Google Scholar 

  57. Park SM, Sinskey AJ, Stephanopoulos G (1997) Metabolic and physiological studies of Corynebacterium glutamicum mutants. Biotechnol Bioeng 55:864–879.

    PubMed  CrossRef  CAS  Google Scholar 

  58. Pharkya P, Burgard AP, Maranas CD (2003) Exploring the overproduction of amino acids using the bilevel optimization framework OptKnock. Biotechnol Bioeng 84:887–899.

    PubMed  CrossRef  CAS  Google Scholar 

  59. Plaxton WC (1996) The organization and regulation of plant glycolysis. Annu Rev Plant Physiol Plant Mol Biol 47:185–214.

    PubMed  CrossRef  CAS  Google Scholar 

  60. Poolman MG, Fell DA, Raines CA (2003) Elementary modes analysis of photosynthate metabolism in the chloroplast stroma. Eur J Biochem 270:430–439.

    PubMed  CrossRef  CAS  Google Scholar 

  61. Pramanik J, Keasling JD (1997) Stoichiometric model of Escherichia coli metabolism: Incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. Biotechnol Bioeng 56:398–421.

    PubMed  CrossRef  CAS  Google Scholar 

  62. Price ND, Famili I, Beard DA, Palsson BO (2002) Extreme Pathways and Kirchhoff’s Second Law. Biophys J 83:2879–2882.

    PubMed  CrossRef  CAS  Google Scholar 

  63. Price ND, Papin JA, Palsson BO (2002) Determination of redundancy and systems properties of the metabolic network of Helicobacter pylori using genome-scale extreme pathway analysis. Genome Res 12:760–769.

    PubMed  CAS  Google Scholar 

  64. Price ND, Thiele I, Palsson BO (2006) Candidate states of Helicobacter pylori’s genome-scale metabolic network upon application of “loop law” thermodynamic constraints. Biophys J 90:3919–3928.

    PubMed  CrossRef  CAS  Google Scholar 

  65. Ramakrishna R, Edwards J, McCulloch A, Palsson B (2001) Flux balance analysis of mitochondrial energy metabolism: consequences of systemic stoichiometry constraints. Am J Physiolo Regul Integr Comp Physiol 280:R695–R704.

    CAS  Google Scholar 

  66. Reed J, Vo T, Schilling C, Palsson B (2003) An expanded genome-scale model of Escherichia coli K-12 (iJR904 GSM/GPR). Genome Biol 4:R54.

    PubMed  CrossRef  Google Scholar 

  67. Rockafellar RT (1970) Convex Analysis. Princeton University Press, Princeton, NJ.

    Google Scholar 

  68. Sainz J, Pizarro F, Perez-Correa JR, Agosin E (2003) Modeling of yeast metabolism and process dynamics in batch fermentation. Biotechnol Bioeng 81:818–828.

    PubMed  CrossRef  CAS  Google Scholar 

  69. Savinell JM, Palsson BO (1992) Optimal selection of metabolic fluxes for in vivo measurement .1. Development of mathematical methods. J Theor Biol 155:201–214.

    PubMed  CrossRef  CAS  Google Scholar 

  70. Schilling CH, Covert MW, Famili I, Church GM, Edwards JS, Palsson BO (2002) Genome-scale metabolic model of Helicobacter pylori 26695. J Bacteriol 184:4582–4593.

    PubMed  CrossRef  CAS  Google Scholar 

  71. Schilling CH, Letscher D, Palsson BO (2000) 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.

    PubMed  CrossRef  CAS  Google Scholar 

  72. Schuster S, Dandekar T, Fell DA (1999) Detection of elementary flux modes in biochemical networks: a promising tool for pathway analysis and metabolic engineering. Trends Biotechnol 17:53–60.

    PubMed  CrossRef  CAS  Google Scholar 

  73. Schuster S, Fell DA, Dandekar T (2000) A general definition of metabolic pathways useful for systematic organization and analysis of complex metabolic networks. Nat Biotech 18:326–332.

    CrossRef  CAS  Google Scholar 

  74. Schuster S, Hilgetag C (1994) On elementary flux modes in biochemical reaction systems at steady state. J Biol Syst 2:165–182.

    CrossRef  Google Scholar 

  75. Schuster S, Kenanov D (2005) Adenine and adenosine salvage pathways in erythrocytes and the role of S-adenosylhomocysteine hydrolase. A theoretical study using elementary flux modes. FEBS Journal 272:5278–5290.

    PubMed  CrossRef  CAS  Google Scholar 

  76. Schwender J, Goffman F, Ohlrogge JB, Shachar-Hill Y (2004) Rubisco without the Calvin cycle improves the carbon efficiency of developing green seeds. Nature 432:779–782.

    PubMed  CrossRef  CAS  Google Scholar 

  77. Segre D, Vitkup D, Church GM (2002) Analysis of optimality in natural and perturbed metabolic networks. Proc Natl Acad Sci USA 99:15112–15117.

    PubMed  CrossRef  CAS  Google Scholar 

  78. Shastri A, Morgan J (2004) Calculation of theoretical yields in metabolic networks. Biochem Mol Biol Educ 32:314–318.

    CrossRef  CAS  Google Scholar 

  79. Shastri AA, Morgan JA (2005) Flux balance analysis of photoautotrophic metabolism. Biotechnol Prog 21:1617–1626.

    PubMed  CrossRef  CAS  Google Scholar 

  80. Shlomi T, Berkman O, Ruppin E (2005) Regulatory on/off minimization of metabolic flux changes after genetic perturbations. Proc Natl Acad Sci USA 102:7695–7700.

    PubMed  CrossRef  CAS  Google Scholar 

  81. Stelling J, Klamt S, Bettenbrock K, Schuster S, Gilles ED (2002) Metabolic network structure determines key aspects of functionality and regulation. Nature 420:190–193.

    PubMed  CrossRef  CAS  Google Scholar 

  82. Stephanopoulos G, Vallino JJ (1991) Network rigidity and metabolic engineering in metabolite overproduction. Science 252:1675–1681.

    PubMed  CrossRef  CAS  Google Scholar 

  83. Stephanopoulos GN, Aristidou AA, Nielsen J (1998) Metabolic Engineering Principles and Methodologies. Academic Press, San Diego.

    Google Scholar 

  84. Stitt M, Heldt HW (1981) Physiological rates of starch breakdown in isolated intact spinach chloroplasts. Plant Physiol 68:755–761.

    PubMed  CrossRef  CAS  Google Scholar 

  85. Teusink B, Wiersma A, Molenaar D, Francke C, Vos WMd, Siezen RJ, Smid EJ (2006) Analysis of growth of Lactobacillus plantarum WCFS1 on a complex medium using genome-scale metabolic model. J Biol Chem 281:40041–40048.

    PubMed  CrossRef  CAS  Google Scholar 

  86. Thiele I, Vo TD, Price ND, Palsson BO (2005) Expanded metabolic reconstruction of Helicobacter pylori (iIT341 GSM/GPR): an in silico genome-scale characterization of single- and double-deletion mutants J Bacteriol 187:5818–5830.

    PubMed  CrossRef  CAS  Google Scholar 

  87. Trawick JD, Schilling CH (2006) Use of constraint-based modeling for the prediction and validation of antimicrobial targets. Biochem Pharmacol 71:1026–1035.

    PubMed  CrossRef  CAS  Google Scholar 

  88. Trinh CT, Carlson R, Wlaschin A, Srienc F (2006) Design, construction and performance of the most efficient biomass producing E. coli bacterium. Metabol Eng 8:628–638.

    CrossRef  CAS  Google Scholar 

  89. Varma A, Boesch BW, Palsson BO (1993) Biochemical production capabilities of Escherichia coli. Biotechnol Bioeng 42:59–73.

    PubMed  CrossRef  CAS  Google Scholar 

  90. Varma A, Palsson BO (1993) Metabolic capabilities of Escherichia coli. 1. Synthesis of biosynthetic precursors and cofactors. J Theor Biol 165:477–502.

    PubMed  CrossRef  CAS  Google Scholar 

  91. Varma A, Palsson BO (1993) Metabolic capabilities of Escherichia coli. 2. Optimal-growth patterns. J Theor Biol 165:503–522.

    CrossRef  CAS  Google Scholar 

  92. Varma A, Palsson BO (1994) Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl Environ Microbiol 60:3724–3731.

    PubMed  CAS  Google Scholar 

  93. von Kamp A, Schuster S (2006) Metatool 5.0: fast and flexible elementary modes analysis. Bioinformatics 22:1930–1931.

    CrossRef  Google Scholar 

  94. Watson MR (1986) A discrete model of bacterial metabolism. Comput Appl Biosci 2:23–27.

    PubMed  CAS  Google Scholar 

  95. Yang C, Hua Q, Shimizu K (2000) Energetics and carbon metabolism during growth of microalgal cells under photoautotrophic, mixotrophic and cyclic light-autotrophic/dark-heterotrophic conditions. Biochem Eng J 6:87–102.

    PubMed  CrossRef  CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and Permissions

Copyright information

© 2009 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Boyle, N.R., Shastri, A.A., Morgan, J.A. (2009). Network Stoichiometry. In: Schwender, J. (eds) Plant Metabolic Networks. Springer, New York, NY. https://doi.org/10.1007/978-0-387-78745-9_8

Download citation