Kinetic Modeling of Metabolic Networks

Chapter

Abstract

In the last decade, genome-scale stoichiometric models have played an increasing role in understanding metabolism under steady state. In order to study metabolic response to perturbation at timescales before a steady state is reached, however, a more explicit kinetic model must be developed. While kinetic models of metabolism have been around for longer than their stoichiometric counterparts, progress towards practical and useful kinetics models of metabolism has been slower, due to the difficulty of specifying necessary parameters. However, the increased ability to measure metabolomics and proteomics profiles in high throughput may soon make accurate kinetic models of metabolism a reality. In this chapter, we review theoretical concepts useful for developing kinetic models of metabolism, practical difficulties with constructing such models, and methods that have been developed in an effort to circumvent these difficulties.

Keywords

Kinetic modeling Large-scale Stoichiometric models Kinetic parameters Metabolite profiling Proteome profiling Dynamics Structural hierarchies Temporal hierarchies Spatial heterogeneity Gradients Nonlinearity Law of mass action Gibbs free energy Equilibrium constants Reaction mechanism Haldane Rate laws Elasticity coefficient Michaelis-Menten Hill Linear analysis Matrix Data fitting Parameter sensitivity 

References

  1. 1.
    Michaelis L, Menten ML (1913) Die kinetik der invertinwirkung. Biochem Z 49(333–369):352. doi: citeulike-article-id:5936552 Google Scholar
  2. 2.
    Lotka AJ (1920) Analytical note on certain rhythmic relations in organic systems. Proc Natl Acad Sci USA 6:410–415PubMedCrossRefGoogle Scholar
  3. 3.
    Volterra V (1927) Variazioni e fluttuazioni del numero d’individui in specie animali conviventi. Mem. R. Acad. Lincei 2:1–142Google Scholar
  4. 4.
    Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol Lond 117(4):500–544PubMedGoogle Scholar
  5. 5.
    Karplus M, Weaver DL (1976) Protein-folding dynamics. Nature 260(5550):404–406PubMedCrossRefGoogle Scholar
  6. 6.
    Goldbeter A (2002) Computational approaches to cellular rhythms. Nature 420(6912):238–245. doi: 10.1038/Nature01259 PubMedCrossRefGoogle Scholar
  7. 7.
    Chance B (1943) The kinetics of the enzyme-substrate compound of peroxidase. J Biol Chem 151(2):553–577Google Scholar
  8. 8.
    Rapoport TA, Heinrich R, Rapoport SM (1976) The regulatory principles of glycolysis in erythrocytes in vivo and in vitro. A minimal comprehensive model describing steady states, quasi-steady states and time-dependent processes. Biochem J 154(2):449–469PubMedGoogle Scholar
  9. 9.
    Joshi A, Palsson BO (1990) Metabolic dynamics in the human red cell. Part IV – Data prediction and some model computations. J Theor Biol 142(1):69–85PubMedCrossRefGoogle Scholar
  10. 10.
    Joshi A, Palsson BO (1990) Metabolic dynamics in the human red cell. Part III – Metabolic reaction rates. J Theor Biol 142(1):41–68PubMedCrossRefGoogle Scholar
  11. 11.
    Joshi A, Palsson BO (1989) Metabolic dynamics in the human red cell. Part II – Interactions with the environment. J Theor Biol 141(4):529–545PubMedCrossRefGoogle Scholar
  12. 12.
    Joshi A, Palsson BO (1989) Metabolic dynamics in the human red cell. Part I – A comprehensive kinetic model. J Theor Biol 141(4):515–528PubMedCrossRefGoogle Scholar
  13. 13.
    Nicholson JK, Holmes E, Lindon JC, Wilson ID (2004) The challenges of modeling mammalian biocomplexity. Nat Biotechnol 22(10):1268–1274. doi: 10.1038/Nbt1015 PubMedCrossRefGoogle Scholar
  14. 14.
    Price ND, Papin JA, Schilling CH, Palsson BO (2003) Genome-scale microbial in silico models: the constraints-based approach. Trends Biotechnol 21(4):162–169. doi:S0167779903000301 [pii]PubMedCrossRefGoogle Scholar
  15. 15.
    Jamshidi N, Palsson BO (2008) Formulating genome-scale kinetic models in the post-genome era. Mol Syst Biol 4:171. doi: 10.1038/msb.2008.8 PubMedCrossRefGoogle Scholar
  16. 16.
    Clauset A, Moore C, Newman ME (2008) Hierarchical structure and the prediction of missing links in networks. Nature 453(7191):98–101. doi: 10.1038/nature06830 PubMedCrossRefGoogle Scholar
  17. 17.
    Horler RS, Butcher A, Papangelopoulos N, Ashton PD, Thomas GH (2009) EchoLOCATION: an in silico analysis of the subcellular locations of Escherichia coli proteins and comparison with experimentally derived locations. Bioinformatics 25(2):163–166. doi: 10.1093/bioinformatics/btn596 PubMedCrossRefGoogle Scholar
  18. 18.
    Kurkdjian A, Guern J (1989) Intracellular Ph – measurement and importance in cell-activity. Annu Rev Plant Phys Plant Mol Biol 40:271–303CrossRefGoogle Scholar
  19. 19.
    Dairaghi DJ, Oldham ER, Bacon KB, Schall TJ (1997) Communication – chemokine receptor CCR3 function is highly dependent on local pH and ionic strength. J Biol Chem 272(45):28206–28209PubMedCrossRefGoogle Scholar
  20. 20.
    Minton AP (2001) The influence of macromolecular crowding and macromolecular confinement on biochemical reactions in physiological media. J Biol Chem 276(14):10577–10580. doi: 10.1074/jbc.R100005200 PubMedCrossRefGoogle Scholar
  21. 21.
    Gaal T, Bartlett MS, Ross W, Turnbough CL Jr, Gourse RL (1997) Transcription regulation by initiating NTP concentration: rRNA synthesis in bacteria. Science 278(5346):2092–2097PubMedCrossRefGoogle Scholar
  22. 22.
    Elf J, Nilsson D, Tenson T, Ehrenberg M (2003) Selective charging of tRNA isoacceptors explains patterns of codon usage. Science 300(5626):1718–1722. doi: 10.1126/science.1083811 PubMedCrossRefGoogle Scholar
  23. 23.
    Pogliano J, Lynch AS, Belin D, Lin EC, Beckwith J (1997) Regulation of Escherichia coli cell envelope proteins involved in protein folding and degradation by the Cpx two-component system. Genes Dev 11(9):1169–1182PubMedCrossRefGoogle Scholar
  24. 24.
    Choudhary C, Kumar C, Gnad F, Nielsen ML, Rehman M, Walther TC, Olsen JV, Mann M (2009) Lysine acetylation targets protein complexes and co-regulates major cellular functions. Science 325(5942):834–840. doi: 10.1126/science.1175371 PubMedCrossRefGoogle Scholar
  25. 25.
    Macek B, Mijakovic I, Olsen JV, Gnad F, Kumar C, Jensen PR, Mann M (2007) The serine/threonine/tyrosine phosphoproteome of the model bacterium Bacillus subtilis. Mol Cell Proteomics 6(4):697–707. doi: 10.1074/mcp.M600464-MCP200 PubMedCrossRefGoogle Scholar
  26. 26.
    Low PS, Rathinavelu P, Harrison ML (1993) Regulation of glycolysis via reversible enzyme binding to the membrane protein, band 3. J Biol Chem 268(20):14627–14631PubMedGoogle Scholar
  27. 27.
    Alberty RA (2002) Thermodynamics of systems of biochemical reactions. J Theor Biol 215(4):491–501. doi: 10.1006/jtbi.2001.2516 PubMedCrossRefGoogle Scholar
  28. 28.
    Cavalier-Smith T (1978) Nuclear volume control by nucleoskeletal DNA, selection for cell volume and cell growth rate, and the solution of the DNA C-value paradox. J Cell Sci 34:247–278PubMedGoogle Scholar
  29. 29.
    Elowitz MB, Levine AJ, Siggia ED, Swain PS (2002) Stochastic gene expression in a single cell. Science 297(5584):1183–1186. doi: 10.1126/science.1070919 PubMedCrossRefGoogle Scholar
  30. 30.
    Klamt S, Haus UU, Theis F (2009) Hypergraphs and cellular networks. PLoS Comput Biol 5(5):e1000385. doi: 10.1371/journal.pcbi.1000385 PubMedCrossRefGoogle Scholar
  31. 31.
    Mahadevan R, Edwards JS, Doyle FJ 3rd (2002) Dynamic flux balance analysis of diauxic growth in Escherichia coli. Biophys J 83(3):1331–1340. doi: 10.1016/S0006-3495(02)73903-9 PubMedCrossRefGoogle Scholar
  32. 32.
    Meric PA, Wise MJ (1999) Quantitative, scalable discrete-event simulation of metabolic pathways. Proc Int Conf Intell Syst Mol Biol 187–194Google Scholar
  33. 33.
    Mahan BH (1975) Microscopic reversibility and detailed balance – analysis. J Chem Educ 52(5):299–302CrossRefGoogle Scholar
  34. 34.
    Haldane JBS (1930) Enzymes, Monographs on biochemistry. Longmans/Green, London/New YorkGoogle Scholar
  35. 35.
    Qian H, Beard DA, Liang SD (2003) Stoichiometric network theory for nonequilibrium biochemical systems. Eur J Biochem 270(3):415–421. doi:3357 [pii]PubMedCrossRefGoogle Scholar
  36. 36.
    Zhou HX, Rivas G, Minton AP (2008) Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu Rev Biophys 37:375–397. doi: 10.1146/annurev.biophys.37.032807.125817 PubMedCrossRefGoogle Scholar
  37. 37.
    Schnell S, Turner TE (2004) Reaction kinetics in intracellular environments with macromolecular crowding: simulations and rate laws. Prog Biophys Mol Biol 85(2–3):235–260. doi: 10.1016/j.pbiomolbio.2004.01.012 PubMedCrossRefGoogle Scholar
  38. 38.
    Tucker W, Kutalik Z, Moulton V (2007) Estimating parameters for generalized mass action models using constraint propagation. Math Biosci 208(2):607–620. doi:DOI 10.1016/j.mbs.2006.11.009PubMedCrossRefGoogle Scholar
  39. 39.
    Dreger A, Kronfeld M, Ziller MJ, Supper J, Planatscher H, Magnus JB, Oldiges M, Kohlbacher O, Zell A (2009) Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies. BMC Syst Biol 3. doi: 10.1186/1752-0509-3-5
  40. 40.
    Smallbone K, Simeonidis E, Swainston N, Mendes P (2010) Towards a genome-scale kinetic model of cellular metabolism. BMC Syst Biol 4:6. doi: 10.1186/1752-0509-4-6 PubMedCrossRefGoogle Scholar
  41. 41.
    Steuer R, Junker BH (2009) Computational models of metabolism: stability and regulation in metabolic networks. Adv Chem Phys 142:105–251CrossRefGoogle Scholar
  42. 42.
    Palsson B (2006) Systems biology: properties of reconstructed networks. Cambridge University Press, Cambridge/New YorkCrossRefGoogle Scholar
  43. 43.
    Lehninger AL, Nelson DL, Cox MM (2008) Lehninger principles of biochemistry, 5th edn. W.H. Freeman, New YorkGoogle Scholar
  44. 44.
    Bennett BD, Kimball EH, Gao M, Osterhout R, Van Dien SJ, Rabinowitz JD (2009) Absolute metabolite concentrations and implied enzyme active site occupancy in Escherichia coli. Nat Chem Biol 5(8):593–599. doi: 10.1038/nchembio.186 PubMedCrossRefGoogle Scholar
  45. 45.
    Cornish-Bowden A (1977) An automatic method for deriving steady-state rate equations. Biochem J 165(1):55–59PubMedGoogle Scholar
  46. 46.
    Hill AV (1910) The possible effects of the aggregation of the molecules of haemoglobin on its oxygen dissociation. J Physiol. doi: citeulike-article-id:440501
  47. 47.
    Monod J, Wyman J, Changeux JP (1965) On the nature of allosteric transitions: a plausible model. J Mol Biol 12:88–118PubMedCrossRefGoogle Scholar
  48. 48.
    Changeux JP (1964) Allosteric interactions interpreted in terms of quaternary structure. Brookhaven Symp Biol 17:232–249PubMedGoogle Scholar
  49. 49.
    Strogatz SH (1994) Nonlinear dynamics and Chaos: with applications to physics, biology, chemistry, and engineering, Studies in nonlinearity. Addison-Wesley Pub, ReadingGoogle Scholar
  50. 50.
    Orth JD, Thiele I, Palsson BO (2010) What is flux balance analysis? Nat Biotechnol 28(3):245–248. doi: 10.1038/nbt.1614 PubMedCrossRefGoogle Scholar
  51. 51.
    Edwards JS, Ibarra RU, Palsson BO (2001) In silico predictions of Escherichia coli metabolic capabilities are consistent with experimental data. Nat Biotechnol 19(2):125–130. doi: 10.1038/84379 PubMedCrossRefGoogle Scholar
  52. 52.
    Jamshidi N, Palsson BO (2008) Top-down analysis of temporal hierarchy in biochemical reaction networks. PLoS Comput Biol 4(9):e1000177. doi: 10.1371/journal.pcbi.1000177 PubMedCrossRefGoogle Scholar
  53. 53.
    Heuett WJ, Beard DA, Qian H (2008) Linear analysis near a steady-state of biochemical networks: control analysis, correlation metrics and circuit theory. BMC Syst Biol 2:44. doi: 10.1186/1752-0509-2-44 PubMedCrossRefGoogle Scholar
  54. 54.
    Jamshidi N, Palsson BO (2009) Flux-concentration duality in dynamic nonequilibrium biological networks. Biophys J 97(5):L11–L13. doi: 10.1016/j.bpj.2009.06.049 PubMedCrossRefGoogle Scholar
  55. 55.
    Yugi K, Nakayama Y, Kinoshita A, Tomita M (2005) Hybrid dynamic/static method for large-scale simulation of metabolism. Theor Biol Med Model 2:42. doi: 10.1186/1742-4682-2-42 PubMedCrossRefGoogle Scholar
  56. 56.
    Chassagnole C, Noisommit-Rizzi N, Schmid JW, Mauch K, Reuss M (2002) Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotechnol Bioeng 79(1):53–73PubMedCrossRefGoogle Scholar
  57. 57.
    Mannervik B (1982) Regression-analysis, experimental error, and statistical criteria in the design and analysis of experiments for discrimination between rival kinetic-models. Methods Enzymol 87:370–390PubMedCrossRefGoogle Scholar
  58. 58.
    Dyson F (2004) A meeting with enrico fermi – how one intuitive physicist rescued a team from fruitless research. Nature 427(6972):297. doi: 10.1038/427297a PubMedCrossRefGoogle Scholar
  59. 59.
    Resendis-Antonio O (2009) Filling kinetic gaps: dynamic modeling of metabolism where detailed kinetic information is lacking. PLoS One 4(3). doi: 10.1371/Journal.Pone.0004967
  60. 60.
    Beard DA, Vinnakota KC, Wu F (2008) Detailed enzyme kinetics in terms of biochemical species: study of citrate synthase. PLoS One 3(3):e1825PubMedCrossRefGoogle Scholar
  61. 61.
    Jamshidi N, Palsson BO (2010) Mass action stoichiometric simulation models: incorporating kinetics and regulation into stoichiometric models. Biophys J 98(2):175–185. doi: 10.1016/j.bpj.2009.09.064 PubMedCrossRefGoogle Scholar
  62. 62.
    Tomita M, Hashimoto K, Takahashi K, Shimizu TS, Matsuzaki Y, Miyoshi F, Saito K, Tanida S, Yugi K, Venter JC, Hutchison CA 3rd (1999) E-CELL: software environment for whole-cell simulation. Bioinformatics 15(1):72–84. doi:btc007 [pii]PubMedCrossRefGoogle Scholar
  63. 63.
    Taniguchi Y, Choi PJ, Li GW, Chen H, Babu M, Hearn J, Emili A, Xie XS (2010) Quantifying E. coli proteome and transcriptome with single-molecule sensitivity in single cells. Science 329(5991):533–538. doi: 10.1126/science.1188308 PubMedCrossRefGoogle Scholar
  64. 64.
    Zamboni N, Fendt SM, Ruhl M, Sauer U (2009) (13)C-based metabolic flux analysis. Nat Protoc 4(6):878–892. doi: 10.1038/nprot.2009.58 PubMedCrossRefGoogle Scholar
  65. 65.
    Jankowski MD, Henry CS, Broadbelt LJ, Hatzimanikatis V (2008) Group contribution method for thermodynamic analysis of complex metabolic networks. Biophys J 95(3):1487–1499. doi: 10.1529/biophysj.107.124784 PubMedCrossRefGoogle Scholar
  66. 66.
    Fleming RM, Thiele I, Nasheuer HP (2009) Quantitative assignment of reaction directionality in constraint-based models of metabolism: application to Escherichia coli. Biophys Chem 145(2–3):47–56. doi: 10.1016/j.bpc.2009.08.007 PubMedCrossRefGoogle Scholar
  67. 67.
    Bennett BD, Yuan J, Kimball EH, Rabinowitz JD (2008) Absolute quantitation of intracellular metabolite concentrations by an isotope ratio-based approach. Nat Protoc 3(8):1299–1311. doi: 10.1038/nprot.2008.107 PubMedCrossRefGoogle Scholar
  68. 68.
    Tran LM, Rizk ML, Liao JC (2008) Ensemble modeling of metabolic networks. Biophys J 95(12):5606–5617. doi: 10.1529/biophysj.108.135442 PubMedCrossRefGoogle Scholar
  69. 69.
    Schellenberger J, Palsson BO (2009) Use of randomized sampling for analysis of metabolic networks. J Biol Chem 284(9):5457–5461. doi: 10.1074/jbc.R800048200 PubMedCrossRefGoogle Scholar
  70. 70.
    Famili I, Mahadevan R, Palsson BO (2005) k-Cone analysis: determining all candidate values for kinetic parameters on a network scale. Biophys J 88(3):1616–1625. doi: 10.1529/biophysj.104.050385 PubMedCrossRefGoogle Scholar
  71. 71.
    Thiele I, Price ND, Vo TD, Palsson BO (2005) Candidate metabolic network states in human mitochondria. Impact of diabetes, ischemia, and diet. J Biol Chem 280(12):11683–11695. doi: 10.1074/jbc.M409072200 PubMedCrossRefGoogle Scholar
  72. 72.
    Barrett CL, Price ND, Palsson BO (2006) Network-level analysis of metabolic regulation in the human red blood cell using random sampling and singular value decomposition. BMC Bioinformatics 7. doi: 10.1186/1471-2105-7-132
  73. 73.
    Barrett CL, Herrgard MJ, Palsson B (2009) Decomposing complex reaction networks using random sampling, principal component analysis and basis rotation. BMC Syst Biol 3:30. doi: 10.1186/1752-0509-3-30 PubMedCrossRefGoogle Scholar
  74. 74.
    Steuer R, Gross T, Selbig J, Blasius B (2006) Structural kinetic modeling of metabolic networks. Proc Natl Acad Sci USA 103(32):11868–11873. doi: 10.1073/pnas.0600013103 PubMedCrossRefGoogle Scholar
  75. 75.
    Clarke BL (1988) Stoichiometric network analysis. Cell Biophys 12:237–253PubMedGoogle Scholar
  76. 76.
    Routh EJ (1877) Adams prize essay: a treatise on the stability of a given state of motion, particularly steady motion. Macmillan and co, LondonGoogle Scholar
  77. 77.
    Holzhutter HG, Jacobasch G, Bisdorff A (1985) Mathematical modelling of metabolic pathways affected by an enzyme deficiency. A mathematical model of glycolysis in normal and pyruvate-kinase-deficient red blood cells. Eur J Biochem 149(1):101–111PubMedCrossRefGoogle Scholar
  78. 78.
    Jamshidi N, Wiback SJ, Palsson BO (2002) In silico model-driven assessment of the effects of single nucleotide Polymorphisms (SNPs) on human red blood cell metabolism. Genome Res 12(11):1687–1692. doi: 10.1101/Gr.329302 PubMedCrossRefGoogle Scholar
  79. 79.
    Visser D, Schmid JW, Mauch K, Reuss M, Heijnen JJ (2004) Optimal re-design of primary metabolism in Escherichia coli using linlog kinetics. Metab Eng 6(4):378–390. doi: 10.1016/j.ymben.2004.07.001 PubMedCrossRefGoogle Scholar
  80. 80.
    Schuster S (1999) Use and limitations of modular metabolic control analysis in medicine and biotechnology. Metab Eng 1(3):232–242. doi: 10.1006/mben.1999.0119 PubMedCrossRefGoogle Scholar
  81. 81.
    Fell DA (1992) Metabolic control analysis – a survey of its theoretical and experimental development. Biochem J 286:313–330PubMedGoogle Scholar
  82. 82.
    Bond-Watts BB, Bellerose RJ, Chang MCY (2011) Enzyme mechanism as a kinetic control element for designing synthetic biofuel pathways. Nat Chem Biol 7(4):222–227. doi: http://www.nature.com/nchembio/journal/v7/n4/abs/nchembio.537.html#supplementary-information Google Scholar
  83. 83.
    Andrianantoandro E, Basu S, Karig DK, Weiss R (2006) Synthetic biology: new engineering rules for an emerging discipline. Mol Syst Biol. doi: 10.1038/Msb4100073

Copyright information

© Springer Science+Business Media Dordrecht 2012

Authors and Affiliations

  1. 1.Department of BioengineeringUniversity of CaliforniaSan DiegoUSA

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