Automating Mathematical Modeling of Biochemical Reaction Networks

Chapter
Part of the Systems Biology book series (SYSTBIOL)

Abstract

In this chapter we introduce a five-step modeling pipeline that ultimately leads to a mathematical description of a biochemical reaction system. We discuss how to automate each individual step and how to put these steps together. First, we create a topology of interconversion processes and mutual influences between reactive species. The Systems Biology Markup Language (SBML) encodes the model in a computer-readable form and allows us to add semantic information to each component of the model. Second, from such an annotated network, the procedure known as SBMLsqueezer generates kinetic equations in a context-sensitive manner. The resulting model can then be combined with already existing models. Third, we estimate the values of all newly introduced parameters in each created rate law. This procedure requires that a time series of quantitative measurements of the reactive species within this system be available, because we calibrate the parameters with the aim that the model will fit these experimental data. Fourth, an experimental validation of the resulting model is advisable. Fifth, a model report is generated automatically to document the model with all of its components. For a better understanding, we will begin with an introduction to current standardization attempts in systems biology and generalized approaches for common rate equations before discussing computer-aided modeling, parameter estimation, and automatic report generation. We complete this chapter with a discussion of possible further improvements to our modeling pipeline.

Keywords

Computer aided modeling Automatic rate law generation Model documentation Model annotation Model semantics Model merging Modeling tools Software in systems biology 

Notes

Acknowledgments

The authors are grateful to Michael J. Ziller, Marcel Kronfeld, Catherine Lloyd, Falko Krause, and Wolfram Liebermeister for helpful advice, discussion, and contribution. This work was funded by the German Federal Ministry of Education and Research (BMBF) in the two projects, National Genome Research Network (NGFN-II EP under grant number 0313323, later NGFN-Plus under grant number 01GS08134) and HepatoSys under grant number 0313080 L, and the German Federal State of Baden-Württemberg in the two projects Identifikation und Analyse metabolischer Netze aus experimentellen Daten under contract number 7532.22-26-18 and Tübinger Bioinformatik-Grid under contract number 23-7532.24-4-18/1.

References

  1. Albert R (2007) Network Inference, Analysis, and Modeling in Systems Biology. Plant Cell 19(11):3327–3338. doi:10.1105/tpc.107.054700. http://www.plantcell.org/cgi/reprint/19/11/3327.pdf
  2. Alves R, Antunes F, Salvador A (2006) Tools for kinetic modeling of biochemical networks. Nat Biotechnol 24(6):667–672. doi:10.1038/nbt0606-667. http://dx.doi.org/10.1038/nbt0606-667 Google Scholar
  3. Ashburner M, Ball CA, Blake JA, Botstein D, Butler H, Cherry JM, Davis AP, Dolinski K, Dwight SS, Eppig JT, Harris MA, Hill DP, Issel-Tarver L, Kasarskis A, Lewis S, Matese JC, Richardson JE, Ringwald M, Rubin GM, Sherlock G (2000) Gene ontology: tool for the unification of biology. Nat. Genet 25(1):25–29. doi:10.1038/75556. http://dx.doi.org/10.1038/75556 Google Scholar
  4. Balsa-Canto E, Peifer M, Banga JR, Timmer J, Fleck C (2008) Hybrid optimization method with general switching strategy for parameter estimation. BMC Syst Biol 2(1):26. doi:10.1186/1752-0509-2-26. http://dx.doi.org/10.1186/1752-0509-2-26
  5. Banga JR (2008) Optimization in computational systems biology. BMC Systems Biol 2:47. doi:10.1186/1752-0509-2-47. http://www.biomedcentral.com/1752-0509/2/47/
  6. Barthelmes J, Ebeling C, Chang A, Schomburg I, Schomburg D (2007) BRENDA, AMENDA and FRENDA: the enzyme information system in 2007. Nucl Acids Res 35(Suppl_1):D511–514. doi:10.1093/nar/gkl972. http://nar.oxfordjournals.org/cgi/content/abstract/35/suppl_1/D511, http://nar.oxfordjournals.org/cgi/reprint/35/suppl_1/D511.pdf
  7. Bisswanger H (2000) Enzymkinetik – Theorie und Methoden, 3rd edn. Wiley-VCH, WeinheimCrossRefGoogle Scholar
  8. Borger S, Liebermeister W, Uhlendorf J, Klipp E (2007a) Automatically generated model of a metabolic network. Int Conf Genome Inform 18:215–224. doi:10.1142/9781860949920_0021. http://eproceedings.worldscinet.com/9781860949920/9781860949920_0021.html
  9. Borger S, Uhlendorf J, Helbig A, Liebermeister W (2007b) Integration of enzyme kinetic data from various sources. Silico Biol 7(2 Suppl):S73–S79. http://www.bioinfo.de/isb/2007/07/S1/09/ Google Scholar
  10. Bornstein BJ, Keating SM, Jouraku A, Hucka M (2008) LibSBML: an API Library for SBML. Bioinformatics 24(6):880–881, doi:10.1093/bioinformatics/btn051, http://bioinformatics.oxfordjournals.org/cgi/content/abstract/24/6/880, http://bioinformatics.oxfordjournals.org/cgi/reprint/24/6/880.pdf Google Scholar
  11. Bulik S, Grimbs S, Huthmacher C, Selbig J, Holzhütter HG (2009) Kinetic hybrid models composed of mechanistic and simplified enzymatic rate laws-a promising method for speeding up the kinetic modelling of complex metabolic networks. FEBS J 276(2):410–424. doi:10.1111/j.1742-4658.2008.06784.x, http://www3.interscience.wiley.com/journal/121588609/abstract
  12. Burnham KP, Anderson DR (2002) Model selection and multimodel inference: a practical information-theoretic approach, 2nd edn. Springer, New York, NY. http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-95364-9?cm
  13. Calzone L, Gelay A, Zinovyev A, Radvanyi F, Barillot E (2008) A comprehensive modular map of molecular interactions in rb/e2f pathway. Mol Syst Biol 4:173, doi:10.1038/msb.2008.7. http://dx.doi.org/10.1038/msb.2008.7
  14. Caspi R, Foerster H, Fulcher CA, Kaipa P, Krummenacker M, Latendresse M, Paley S, Rhee SY, Shearer AG, Tissier C, Walk TC, Zhang P, Karp PD (2008) The MetaCyc Database of metabolic pathways and enzymes and the BioCyc collection of Pathway/Genome Databases. Nucleic Acids Res 36(Database issue):D623–D631. doi: 10.1093/nar/gkm900. http://nar.oxfordjournals.org/cgi/content/abstract/36/suppl_1/D623
  15. Chang A, Scheer M, Grote A, Schomburg I, Schomburg D (2009) BRENDA, AMENDA and FRENDA the enzyme information system: new content and tools in 2009. Nucleic Acids Res 37(Database issue):D588–D592. doi:10.1093/nar/gkn820. http://nar.oxfordjournals.org/cgi/content/full/gkn820, http://nar.oxfordjournals.org/cgi/reprint/37/suppl_1/D588.pdf
  16. Chassagnole C, Noisommit-Rizzi N, Schmid JW, Mauch K, Reuss M (2002) Dynamic modeling of the central carbon metabolism of Escherichia coli. Biotechnol Bioengineer 79(1):54–73. doi:10.1002/bit.10288. http://www3.interscience.wiley.com/journal/93519745/abstract Google Scholar
  17. Cherry JM, Adler C, Ball C, Chervitz SA, Dwight SS, Hester ET, Jia Y, Juvik G, Roe T, Schroeder M, Weng S, Botstein D (1998) SGD: Saccharomyces Genome Database. Nucleic Acids Res 26(1):73–79. doi:10.1093/nar/26.1.73. http://nar.oxfordjournals.org/cgi/content/abstract/26/1/73
  18. Clerc M (2005) Particle swarm optimization. ISTE Ltd, LondonGoogle Scholar
  19. Clerc M, Kennedy J (2002) The particle swarm–explosion, stability, and convergence in a multidimensional complex space. IEEE Trans on Evol Comput 6(1):58–73CrossRefGoogle Scholar
  20. Cornish-Bowden A (2004) Fundamentals of enzyme kinetics, 3rd edn. Portland Press Ltd., 59 Portland Place, LondonGoogle Scholar
  21. Dampier W, Tozeren A (2007) Signaling perturbations induced by invading H. pylori proteins in the host epithelial cells: a mathematical modeling approach. J Theor Biol 248(1):130–144. doi:10.1016/j.jtbi.2007.03.014. http://dx.doi.org/10.1016/j.jtbi.2007.03.014 Google Scholar
  22. Deckard A, Bergmann FT, Sauro HM (2006) Supporting the SBML layout extension. Bioinformatics 22(23):2966–2967. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/23/2966, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/23/2966.pdf Google Scholar
  23. Degtyarenko K, Matos Pd, Ennis M, Hastings J, Zbinden M, McNaught A, Alcántara R, Darsow M, Guedj M, Ashburner M (2008) ChEBI: a database and ontology for chemical entities of biological interest. Nucleic Acids Res 36(Database issue):D344–D350. doi:10.1093/nar/gkm791. http://nar.oxfordjournals.org/cgi/content/full/gkm791v1
  24. Dräger A, Kronfeld M, Supper J, Planatscher H, Magnus JB, Oldiges M, Zell A (2007a) Benchmarking evolutionary algorithms on convenience kinetics models of the Valine and Leucine Biosynthesis in C. glutamicum. In: Srinivasan D, Wang L (eds) 2007 IEEE congress on evolutionary computation, IEEE computational intelligence society. IEEE Press, Singapore, pp 896–903CrossRefGoogle Scholar
  25. Dräger A, Supper J, Planatscher H, Magnus JB, Oldiges M, Zell A (2007b) Comparing various evolutionary algorithms on the parameter optimization of the valine and leucine biosynthesis in Corynebacterium glutamicum. In: Srinivasan D, Wang L (eds) 2007 IEEE congress on evolutionary computation, IEEE computational intelligence society, IEEE Press, Singapore, pp 620–627CrossRefGoogle Scholar
  26. Dräger A, Hassis N, Supper J, Schröder A, Zell A (2008) SBMLsqueezer: a CellDesigner plug-in to generate kinetic rate equations for biochemical networks. BMC Syst Biol 2(1):39. doi:10.1186/1752-0509-2-39. http://dx.doi.org/10.1186/1752-0509-2-39
  27. Dräger A, Kronfeld M, Ziller MJ, Supper J, Planatscher H, Magnus JB, Oldiges M, Kohlbacher O, Zell A (2009a) Modeling metabolic networks in C. glutamicum: a comparison of rate laws in combination with various parameter optimization strategies. BMC Syst Biol 3:5. doi:10.1186/1752-0509-3-5. http://www.biomedcentral.com/1752-0509/3/5
  28. Dräger A, Planatscher H, Wouamba DM, Schröder A, Hucka M, Endler L, Golebiewski M, Müller W, Zell A (2009b) SBML2LaTeX: Conversion of SBML files into human-readable reports. Bioinformatics doi:10.1093/bioinformatics/btp170. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btp170v1, http://bioinformatics.oxfordjournals.org/cgi/reprint/btp170v1.pdf
  29. Finney A, Hucka M (2003) Systems biology markup language: Level 2 and beyond. Biochem Soc Trans 31(Pt 6):1472–1473. doi:10.1042/. http://www.biochemsoctrans.org/bst/031/1472/bst0311472.htm Google Scholar
  30. Fujibuchi W, Goto S, Migimatsu H, Uchiyama I, Ogiwara A, Akiyama Y, Kanehisa M (1998) DBGET/LinkDB: an integrated database retrieval system. Pac Symp Biocomput pp 683–694Google Scholar
  31. Funahashi A, Tanimura N, Morohashi M, Kitano H (2003) CellDesigner: a process diagram editor for gene-regulatory and biochemical networks. BioSilico 1(5): 159–162. doi:10.1016/S1478-5382(03)02370-9. http://www.sciencedirect.com/science/article/B75GS-4BS08JD-5/2/5531c80ca62a425f55d224b8a0d3f702
  32. Funahashi A, Jouraku A, Matsuoka Y, Kitano H (2007a) Integration of CellDesigner and SABIO-RK. Silico Biology 7(2 Suppl):S81–S90. http://www.bioinfo.de/isb/200707S110/main.html
  33. Funahashi A, Morohashi M, Matsuoka Y, Jouraku A, Kitano H (2007b) Cell Designer: a graphical biological network editor and workbench interfacing simulator. In: Choi S (ed) Introduction to systems biology, Humana Press, chap 21, pp 422–434. doi:10.1007/978-1-59745-531-2_21. http://www.springerlink.com/content/hqk374162wg70146/
  34. Gauges R, Rost U, Sahle S, Wegner K (2006) A model diagram layout extension for SBML. Bioinformatics 22(15):1879–1885. doi:10.1093/bioinformatics/btl195. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/15/1879, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/15/1879.pdf Google Scholar
  35. Gillespie DT (2000) The chemical Langevin equation. J. Chem Phys 113:297–306. doi:10.1063/1.481811. http://link.aip.org/link/?JCPSA6/113/297/1 Google Scholar
  36. Gruber TR (1993) Toward principles for the design of ontologies used for knowledge sharing? Int J Hum Compu Stud 43(5–6):907–928, http://dx.doi.org/10.1006/ijhc.1995.1081
  37. Hatzimanikatis V, Bailey J (1996) MCA has more to say. theor Biolo 182(3):233–342. doi:10.1006/jtbi.1996.0160. http://dx.doi.org/10.1006/jtbi.1996.0160
  38. Hatzimanikatis V, Floudas CA, Bailey JE (1996) Analysis and design of metabolic reaction networks via mixed-integer linear optimization. AIChE 42(5):1277–1292. doi:10.1002/aic.690420509CrossRefGoogle Scholar
  39. Heinrich R, Schuster S (1996) The regulation of cellular systems. Chapman and Hall, New York, NYCrossRefGoogle Scholar
  40. Hinze T, Hayat S, Lenser T, Matsumaru N, Dittrich P (2007) Hill Kinetics meets P systems: a case study on gene regulatory networks as computing agents in silico and in vivo. In: Eleftherakis G, Kefalas P, Paun G (eds) Proceedings of the Eight Workshop on Membrane Computing, SEERC, pp 363–381Google Scholar
  41. Hoffmann R, Valencia A (2004) A gene network for navigating the literature. Nature Genetetics 36(7):664. doi:10.1038/ng0704-664. http://www.nature.com/ng/journal/v36/n7/full/ng0704-664.html Google Scholar
  42. Holland JH (1975) Adaptation in natural and artificial systems. The University of Michigan Press, Cambridge, MAGoogle Scholar
  43. Hoops S, Sahle S, Gauges R, Lee C, Pahle J, Simus N, Singhal M, Xu L, Mendes P, Kummer U (2006) COPASI–a COmplex PAthway SImulator. Bioinformatics 22(24) :3067–3074. doi:10.1093/bioinformatics/btl485. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/24/3067, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/24/3067.pdf Google Scholar
  44. Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H (2002) The erato systems biology workbench: enabling interaction and exchange between software tools for computational biology. Pac Symp Biocomput 450–461Google Scholar
  45. Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H, Arkin AP, Bornstein BJ, Bray D, Cornish-Bowden A, Cuellar AA, Dronov S, Gilles ED, Ginkel M, Gor V, Goryanin II, Hedley WJ, Hodgman TC, Hofmeyr JHS, Hunter PJ, Juty NS, Kasberger JL, Kremling A, Kummer U, Le Novère N, Loew LM, Lucio D, Mendes P, Minch E, Mjolsness ED, Nakayama Y, Nelson MR, Nielsen PF, Sakurada T, Schaff JC, Shapiro BE, Shimizu TS, Spence HD, Stelling J, Takahashi K, Tomita M, Wagner JM, Wang J, the rest of the SBML Forum (2003) The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4):524–531. doi:10.1093/bioinformatics/btg015. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/19/4/524, http://bioinformatics.oxfordjournals.org/cgi/reprint/19/4/524.pdf
  46. Hucka M, Finney A, Bornstein BJ, Keating SM, Shapiro BE, Matthews J, Kovitz BL, Schilstra MJ, Funahashi A, Doyle JC, Kitano H (2004) Evolving a lingua franca and associated software infrastructure for computational systems biology: the systems biology markup language (SBML) project. Syst Biol IEE 1(1):41–53. http://ieeexplore.ieee.org/xpls/abs_all.jsp?arnumber=1334988
  47. Hucka M, Finney A, Hoops S, Keating SM, Le Novère N (2008) Systems biology markup language (SBML) Level 2: structures and facilities for model definitions. Tech. rep., Nat Proce doi:10.1038/npre.2008.2715.1. http://dx.doi.org/10.1038/npre.2008.2715.1
  48. 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. Nucl Acids Res 34(1):D354–357. doi:10.1093/nar/gkj102. http://nar.oxfordjournals.org/cgi/content/full/34/suppl_1/D354
  49. King EL, Altman C (1956) A schematic method of deriving the rate laws for enzyme-catalyzed reactions. J Phys Chem 60(10):1375–1378. doi:10.1021/j150544a010. http://pubs.acs.org/doi/abs/10.1021/j150544a010 Google Scholar
  50. Kirkpatrick S, Gelatt CD, Vecchi MP (1983) Optimization by simulated annealing. Science 220(4598):671–680. http://www.sciencemag.org/cgi/content/abstract/220/4598/671 Google Scholar
  51. Kitano H (2002a) Computational systems biology. Nature 420(6912):206–210. http://dx.doi.org/10.1038/nature01254 Google Scholar
  52. Kitano H (2002b) Systems biology: a brief overview. Science 295(5560):1662–1664. http://www.sciencemag.org/cgi/content/abstract/295/5560/1662 Google Scholar
  53. Kitano H, Funahashi A, Matsuoka Y, Oda K (2005) Using process diagrams for the graphical representation of biological networks. Nat Biotechnol 23(8):961–966. http://dx.doi.org/10.1038/nbt1111 Google Scholar
  54. Klipp E, Liebermeister W, Helbig A, Kowald A, Schaber J (2007) Systems biology standards–the community speaks. Nat Biotechnol 25(4):390–391Google Scholar
  55. Krebs O, Golebiewski M, Kania R, Mir S, Saric J, Weidemann A, Wittig U, Rojas I (2007) SABIO-RK: A data warehouse for biochemical reactions and their kinetics. J Integra Bioinform 4(1). doi:10.2390/biecoll-jib-2007-49. http://journal.imbio.de/index.php?paper_id=49 Google Scholar
  56. Kronfeld M (2008) EvA2 Short documentation. University of Tübingen, Deptartment of Computer Architecture, Tübingen, Germany, http://www.ra.cs.uni-tuebingen.de/software/EvA2
  57. Laible C, Le Novère N (2007) MIRIAM Resources: tools to generate and resolve robust cross-references in Systems Biology. BMC Syst Biol 13(58):58–67. doi:10.1186/1752-0509-1-58. http://www.biomedcentral.com/1752-0509/1/58
  58. Le Novère N (2006) Model storage, exchange and integration. BMC Neurosci 7 (Suppl 1):S11. doi:10.1186/1471-2202-7-S1-S11. http://dx.doi.org/10.1186/1471-2202-7-S1-S11
  59. Le Novère N, Finney A, Hucka M, Bhalla US, Campagne F, Collado-Vides J, Crampin EJ, Halstead M, Klipp E, Mendes P, Nielsen P, Sauro H, Shapiro BE, Snoep JL, Spence HD, Wanner BL (2005) Minimum information requested in the annotation of biochemical models (MIRIAM). Nat. Biotechnol 23(12):1509–1515. doi:10.1038/nbt1156. http://www.nature.com/nbt/journal/v23/n12/abs/nbt1156.html
  60. Le Novère N, Bornstein BJ, Broicher A, Courtot M, Donizelli M, Dharuri H, Li L, Sauro H, Schilstra M, Shapiro B, Snoep JL, Hucka M (2006a) BioModels Database: a free, centralized database of curated, published, quantitative kinetic models of biochemical and cellular systems. Nucleic Acids Res 34:D689–D691. doi:10.1093/nar/gkj092. http://nar.oxfordjournals.org/cgi/content/full/34/suppl_1/D689
  61. Le Novère N, Courtot M, Laibe C (2006b) Adding semantics in kinetics models of biochemical pathways. In: Kettner C, Hicks MG (eds) 2nd International ESCEC workshop on experimental standard conditions on enzyme characterizations. Beilstein Institut, Rüdesheim, Germany, ESEC, Rüdessheim/Rhein, Germany, pp 137–153. http://www.beilstein-institut.de/escec2006/proceedings/LeNovere/LeNovere.pdf
  62. Le Novère N, Moodie S, Sorokin A, Hucka M, Schreiber F, Demir E, Mi H, Matsuoka Y, Wegner K, Kitano H (2008) Systems biology graphical notation: process diagram level 1. Tech. Rep., Nat Proced. doi:hdl:10101/npre.2008.2320.1. http://hdl.handle.net/10101/npre.2008.2320.1
  63. Liebermeister W (2008) Validity and combination of biochemical models. In: Kettner C, Hicks MG (eds) Proceedings of 3rd International ESCEC Workshop on experimental standard conditions on enzyme characterizations, ESEC, Rüdessheim/Rhein, pp 163–179. http://www.molgen.mpg.de/~lieberme/data/Liebermeister_Merging_Validity_2008.pdf
  64. Liebermeister W, Klipp E (2005) Biochemical networks with uncertain parameters. IEE Proce Syst Biol 152(3):97–107, doi:10.1049/ip-syb:20045033. http://link.aip.org/link/?BDJ/152/97/1
  65. Liebermeister W, Klipp E (2006) Bringing metabolic networks to life: convenience rate law and thermodynamic constraints. Theor Biol Med Model 3(42):41. doi:10.1186/1742-4682-3-41. http://dx.doi.org/10.1186/1742-4682-3-41
  66. Liebermeister W, Krause F, Klipp E (2008) Merging of systems biology models with semanticSBML. Tech. Rep., Max Planck Institute for Molecular Genetics, Berlin. http://www.molgen.mpg.de/~lieberme/data/semanticSBML_heidelberg_2008.pdf
  67. Liebermeister W, Krause F, Uhlendorf J, Lubitz T, Klipp E (2009) SemanticSBML: a tool for annotating, checking, and merging of biochemical models in SBML format. In: 3rd International biocuration conference, Nature Publishing Group. doi:10.1038/npre.2009.3093.1. http://dx.doi.org/10.1038/npre.2009.3093.1
  68. Lister AL, Pocock M, Taschuk M, Wipat A (2009) Saint: a lightweight integration environment for model annotation. Bioinformatics p btp523. doi:10.1093/bioinformatics/btp523. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/btp523v2 http://bioinformatics.oxfordjournals.org/cgi/reprint/btp523v2.pdf
  69. Lloyd CM, Halstead MDB, Nielsen PF (2004) CellML: its future, present and past. Prog Biophys Mol Biol 85(2-3):433–450. doi:10.1016/j.pbiomolbio.2004.01.004 http://dx.doi.org/10.1016/j.pbiomolbio.2004.01.004
  70. Machné R, Finney A, Müller S, Lu J, Widder S, Flamm C (2006) The SBML ODE Solver Library: a native API for symbolic and fast numerical analysis of reaction networks. Bioinformatics 22(11):1406–1407. doi:10.1093/bioinformatics/btl086. http://dx.doi.org/10.1093/bioinformatics/btl086 http://bioinformatics.oxfordjournals.org/cgi/reprint/22/11/1406.pdf
  71. Magnus JB, Hollwedel D, Oldiges M, Takors R (2006) Monitoring and modeling of the reaction dynamics in the valine/leucine synthesis pathway in Corynebacterium glutamicum. Biotechnol Prog 22(4):1071–1083. http://dx.doi.org/10.1021/bp060072f Google Scholar
  72. Moles CG, Mendes P, Banga JR (2003) Parameter estimation in biochemical pathways: a comparison of global optimization methods. Genome Res 13(11):2467–2474. doi:10.1101/gr.1262503. http://www.genome.org/cgi/doi/10.1101/gr.1262503 Google Scholar
  73. Nickerson DP, Buist ML (2009) A physiome standards-based model publication paradigm. Phil Trans R Soc A 367:1823–1844. doi:10.1098/rsta.2008.0296PubMedCrossRefGoogle Scholar
  74. Oda K, Matsuoka Y, Funahashi A, Kitano H (2005) A comprehensive pathway map of epidermal growth factor receptor signaling. Mol Syst Biol 1:2005.0010. doi:10.1038/msb4100014. http://dx.doi.org/10.1038/msb4100014
  75. Ogata H, Goto S, Sato K, Fujibuchi W, Bono H, Kanehisa M (2000) KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Res 27(1):29–34CrossRefGoogle Scholar
  76. Olivier BG, Snoep JL (2004) Web-based kinetic modelling using JWS Online. Bioinformatics 20 (13):2143–2144. doi:10.1093/bioinformatics/bth200. http://dx.doi.org/10.1093/bioinformatics/bth200 Google Scholar
  77. Rechenberg I (1973) Evolutionsstrategie: optimierung technischer systeme nach prinzipien der biologischen evolution. Fromman-Holzboog, StuttgartGoogle Scholar
  78. Rodriguez N, Donizelli M, Le Novère N (2007) SBMLeditor: effective creation of models in the systems biology markup language (SBML). BMC Bioinform 8:79. doi:10.1186/1471-2105-8-79. http://dx.doi.org/10.1186/1471-2105-8-79
  79. Rodriguez-Fernandez M, Egea JA, Banga JR (2006a) Novel metaheuristic for parameter estimation in nonlinear dynamic biological systems. BMC Bioinform 7:483. doi:10.1186/1471-2105-7-483. http://dx.doi.org/10.1186/1471-2105-7-483
  80. Rodriguez-Fernandez MR, Mendes P, Banga JR (2006b) A hybrid approach for efficient and robust parameter estimation in biochemical pathways. Biosystems 83:248–265. doi:10.1016/j.biosystems.2005.06.016. http://www.sciencedirect.com/science/article/B6T2K-4HC776X-4/2/2a48c31a0d9aa413bc616023689e55c8 Google Scholar
  81. Savageau MA (1969a) Biochemical systems analysis. I. Some mathematical properties of the rate law for the component enzymatic reactions. J Theor Biol 25(3):365–369PubMedCrossRefGoogle Scholar
  82. Savageau MA (1969b) Biochemical systems analysis. II. The steady-state solutions for an n-pool system using a power-law approximation. J Theor Biol 25(3):370–379PubMedCrossRefGoogle Scholar
  83. Savageau MA (1970) Biochemical systems analysis. 3. Dynamic solutions using a power-law approximation. J Theor Biol 26(2):215–226PubMedCrossRefGoogle Scholar
  84. Schauer M, Heinrich R (1983) Quasi-steady-state approximation in the mathematical modeling of biochemical reaction networks. Math Biosci 65:155–171CrossRefGoogle Scholar
  85. Schilstra MJ, Li L, Matthews J, Finney A, Hucka M, Le Novère N (2006) CellML2SBML: conversion of CellML into SBML. Bioinformatics 22(8):1018–1020. doi:10.1093/bioinformatics/ btl047. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/8/1018, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/8/1018.pdf
  86. Schmidt H (2007) SBaddon: high performance simulation for the systems biology toolbox for MATLAB. Bioinformatics 23(5):646–647. doi:10.1093/bioinformatics/btl668. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/23/5/646, http://bioinformatics.oxfordjournals.org/cgi/reprint/23/5/646.pdf Google Scholar
  87. Schmidt H, Jirstrand M (2006) Systems biology toolbox for MATLAB: a computational platform for research in systems biology. Bioinformatics 22(4):514–515. doi:10.1093/bioinformatics/bti799. http://dx.doi.org/10.1093/bioinformatics/bti799 Google Scholar
  88. Schmidt H, Drews G, Vera J, Wolkenhauer O (2007) SBML export interface for the systems biology toolbox for MATLAB. Bioinformatics 23(10):1297–1298. doi:10.1093/bioinformatics/btm105. http://dx.doi.org/10.1093/bioinformatics/btm105. http://bioinformatics.oxfordjournals.org/cgi/reprint/23/10/1297.pdf Google Scholar
  89. Schomburg I, Chang A, Schomburg D (2002) BRENDA, enzyme data and metabolic information. Nucl Acids Res 30(1):47–49. doi:10.1093/nar/30.1.47. http://nar.oxfordjournals.org/cgi/content/abstract/30/1/47
  90. Segel IH (1993) Enzyme Kinetics–Behavior and Analysis of Rapid Equilibrium and Steady-State Enzyme Systems. Wiley-Intersciennce, New York, NYGoogle Scholar
  91. Shapiro BE, Finney A, Hucka M, Bornstein BJ, Funahashi A, Jouraku A, Keating SM, Le Novère N, Matthews J, Schilstra MJ (2007) Introduction to systems biology. Humana Press, Totowa, NJ chap SBML Models and MathSBML, pp 395–421. doi:10.1007/978-1-59745-531-2. http://www.springerlink.com/content/q28j426582387022/
  92. Snoep JL, Bruggeman F, Olivier BG, Westerhoff HV (2006) Towards building the silicon cell: a modular approach. Biosystems 83(2-3):207–216. doi:10.1016/j.biosystems.2005.07.006. http://dx.doi.org/10.1016/j.biosystems.2005.07.006 Google Scholar
  93. Spieth C, Streichert F, Speer N, Zell A (2004) Optimizing topology and parameters of gene regulatory network models from time-series experiments. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2004), LNCS, vol 3102 (Part I), pp 461–470Google Scholar
  94. Spieth C, Streichert F, Speer N, Zell A (2005a) Inferring regulatory systems with noisy pathway information. In: German conference on bioinformatics (GCB 2005), vol P-71, pp 193–203Google Scholar
  95. Spieth C, Streichert F, Supper J, Speer N, Zell A (2005b) Feedback memetic algorithms for modeling gene regulatory networks. In: Proceedings of the IEEE symposium on computational intelligence in bioinformatics and computational biology (CIBCB 2005), pp 61–67Google Scholar
  96. Spieth C, Supper J, Streichert F, Speer N, Zell A (2006a) JCell–a Java-based framework for inferring regulatory networks from time series data. Bioinformatics 22(16):2051–2052. doi:10.1093/bioinformatics/btl322. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/16/2051, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/16/2051.pdf Google Scholar
  97. Spieth C, Worzischek R, Streichert F, Supper J, Speer N, Zell A (2006b) Comparing evolutionary algorithms on the problem of network inference. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006)Google Scholar
  98. Storn R (1996) On the usage of differential evolution for function optimization. In: 1996 Biennial Conference of the North American Fuzzy Information Processing Society, IEEE, New York, Berkeley, pp 519–523Google Scholar
  99. Streichert F, Ulmer H (2005) JavaEvA–A Java framework for evolutionary algorithms. Technical Report WSI-2005-06, Center for Bioinformatics Tübingen, University of Tübingen, Tübingen, Germany. doi:urn:nbn:de:bsz:21-opus-17022. http://w210.ub.uni-tuebingen.de/dbt/volltexte/2005/1702/
  100. Teusink B, Passarge J, Reijenga CA, Esgalhado E, van der Weijden CC, Schepper M, Walsh MC, Bakker BM, van Dam K, Westerhoff HV, Snoep JL (2000) Can yeast glycolysis be understood in terms of in vitro kinetics of the constituent enzymes? Testing biochemistry. Eur J Biochem 267(17):5313–5329. doi:10.1046/j.1432-1327.2000.01527.x. http://www3.interscience.wiley.com/journal/119181440/abstract Google Scholar
  101. Tovey CA (1985) Hill climbing with multiple local optima. Alg Disc Meth 6(3):384–393. doi:10.1137/0606040. http://link.aip.org/link/?SML/6/384/1
  102. Ulmer H (2005) Modellunterstützte evolutionäre optimierungsverfahren in javaeva. PhD thesis, Eberhard-Karls-Universität TübingenGoogle Scholar
  103. Visser D, Heijnen JJ (2002) The mathematics of metabolic control analysis revisited. Metab Eng 4:114–123. doi:10.1006/mben.2001.0216. http://www.sciencedirect.com/science/article/B6WN3-45V802C-3/2/d624a20d0e70ca2a1058359d7fd00cb0 Google Scholar
  104. Visser D, Heijnen JJ (2003) Dynamic simulation and metabolic re-design of a branched pathway using linlog kinetics. Metab Eng 5(3):164–176PubMedCrossRefGoogle Scholar
  105. Wilkinson DJ (2006) Stochastic modelling for systems biology. CRC Press, Boca Raton, FLGoogle Scholar
  106. Wittig U, Golebiewski M, Kania R, Krebs O, Mir S, Weidemann A, Anstein S, Saric J, Rojas I (2006) SABIO-RK: Integration and curation of reaction kinetics data. In: Leser U, Naumann F, Eckmann B (eds) Data integration in the life sciences, Springer, Berlin pp 94–103. doi:10.1007/11799511. http://www.springerlink.com/content/kw1kv13614272400
  107. Zi Z, Klipp E (2006) SBML-PET: a systems biology markup language-based parameter estimation tool. Bioinformatics 22(21):2704–2705. doi:10.1093/bioinformatics/btl443. http://bioinformatics.oxfordjournals.org/cgi/content/abstract/22/21/2704, http://bioinformatics.oxfordjournals.org/cgi/reprint/22/21/2704.pdf
  108. Zi Z, Zheng Y, Rundell AE, Klipp E (2008) SBML-SAT: a systems biology markup language (SBML) based sensitivity analysis tool. BMC Bioinforma 9(1):342. doi:10.1186/1471-2105-9-342. http://www.biomedcentral.com/1471-2105/9/342
  109. Ziller MJ (2009) Automatisierte mathematische Modellierung biochemischer Reaktionsnetzwerke. Master’s thesis, Eberhard-Karls-Universität Tübingen, Center for Bioinformatics Tübingen, Sand 1, 72076 TübingenGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Andreas Dräger
    • 1
    • 2
  • Adrian Schröder
    • 1
    • 2
  • Andreas Zell
    • 1
    • 2
  1. 1.Center for Bioinformatics Tübingen (ZBIT)TübingenGermany
  2. 2.University of TübingenTübingenGermany

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