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Understanding Network Behavior by Structured Representations of Transition Invariants

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Algorithmic Bioprocesses

Part of the book series: Natural Computing Series ((NCS))

Abstract

Petri nets offer a bipartite and concurrent paradigm, and consequently represent a natural choice for modeling and analyzing biochemical networks. We introduce a Petri net structuring technique contributing to a better understanding of the network behavior and requiring static analysis only. We determine a classification of the transitions into abstract dependent transition sets, which induce connected subnets overlapping in interface places only. This classification allows a structured representation of the transition invariants by network coarsening. The whole approach is algorithmically defined, and thus does not involve human interaction. This structuring technique is especially helpful for analyzing biochemically interpreted Petri nets, where it supports model validation of biochemical reaction systems reflecting current comprehension and assumptions of what has been designed by natural evolution.

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References

  1. Bause F, Kritzinger PS (2002) Stochastic Petri nets. Vieweg, Wiesbaden

    MATH  Google Scholar 

  2. Chaouiya C (2007) Petri net modelling of biological networks. Brief Bioinform 8(4):210–219

    Article  Google Scholar 

  3. Charlie Website (2008) A tool for the analysis of place/transition nets. BTU Cottbus. http://www-dssz.informatik.tu-cottbus.de/software/charlie/charlie.html

  4. Christensen S, Petrucci L (2000) Modular analysis of Petri nets. Comput J 43(3):224–242

    Article  MATH  Google Scholar 

  5. Colom JM, Silva M (1991) Convex geometry and semiflows in P/T nets. In: A comparative study of algorithms for computation of minimal P-semiflows. LNCS, vol 483. Springer, Berlin, pp 79–112

    Google Scholar 

  6. David R, Alla H (2005) Discrete, continuous, and hybrid Petri nets. Springer, Berlin

    MATH  Google Scholar 

  7. Desel J, Juhás G (2001) What is a Petri net? In: Unifying Petri nets—advances in Petri nets, Tokyo, 2001. LNCS, vol 2128. Springer, Berlin, pp 1–25

    Chapter  Google Scholar 

  8. Grafahrend-Belau E, Schreiber F, Heiner M, Sackmann A, Junker B, Grunwald S, Speer A, Winder K, Koch I (2008) Modularization of biochemical networks based on classification of Petri net T-invariants. BMC Bioinform 9:90

    Article  Google Scholar 

  9. Gilbert D, Heiner M (2006) From Petri nets to differential equations—an integrative approach for biochemical network analysis. In: Proceedings of the ICATPN 2006. LNCS, vol 4024. Springer, Berlin, pp 181–200

    Google Scholar 

  10. Gilbert D, Heiner M, Lehrack S (2007) A unifying framework for modelling and analysing biochemical pathways using Petri nets. In: Proceedings of the CMSB 2007. LNCS/LNBI, vol 4695. Springer, Berlin, pp 200–216

    Google Scholar 

  11. Gilbert D, Heiner M, Rosser S, Fulton R, Gu X, Trybiło M (2008) A case study in model-driven synthetic biology. In: Proceedings of the 2nd IFIP conference on biologically inspired collaborative computing (BICC), IFIP WCC 2008, Milano, pp 163–175

    Google Scholar 

  12. Heiner M, Donaldson R, Gilbert D (2010) Petri nets for systems biology. In: Iyengar MS (ed) Symbolic systems biology: theory and methods. Jones and Bartlett, Boston (to appear)

    Google Scholar 

  13. Hucka M, Finney A, Sauro HM, Bolouri H, Doyle JC, Kitano H et al. (2003) The systems biology markup language (SBML): a medium for representation and exchange of biochemical network models. J Bioinform 19:524–531

    Article  Google Scholar 

  14. Heiner M, Gilbert D, Donaldson R (2008) Petri nets in systems and synthetic biology. In: Schools on formal methods (SFM). LNCS, vol 5016. Springer, Berlin, pp 215–264

    Google Scholar 

  15. Heiner M, Koch I (2004) Petri net based model validation in systems biology. In: Proceedings of the 25th ICATPN 2004. LNCS, vol 3099. Springer, Berlin, pp 216–237

    Google Scholar 

  16. Heiner M, Koch I, Will J (2004) Model validation of biological pathways using Petri nets—demonstrated for apoptosis. Biosystems 75:15–28

    Article  Google Scholar 

  17. Hofestädt R (1994) A Petri net application of metabolic processes. J Syst Anal Model Simul 16:113–122

    MATH  Google Scholar 

  18. Heiner M, Richter R, Schwarick M (2008) Snoopy—a tool to design and animate/simulate graph-based formalisms. In: Proceedings of the PNTAP 2008, associated to SIMUTools 2008. ACM digital library

    Google Scholar 

  19. Koch I, Heiner M (2008) Petri nets. In: Junker BH, Schreiber F (eds) Biological network analysis. Book series on bioinformatics. Wiley, New York, pp 139–179

    Chapter  Google Scholar 

  20. Koch I, Junker BH, Heiner M (2005) Application of Petri net theory for modeling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21(7):1219–1226

    Article  Google Scholar 

  21. Kohn KW, Riss J, Aprelikova O, Weinstein JN, Pommier Y, Barrett JC (2004) Properties of switch-like bioregulatory networks studied by simulation of the hypoxia response control system. Mol Cell Biol 15:3042–3052

    Article  Google Scholar 

  22. Lautenbach K (1973) Exact liveness conditions of a Petri net class. GMD Report 82, Bonn (in German)

    Google Scholar 

  23. Larhlimi A, Bockmayr A (2005) Minimal metabolic behaviors and the reversible metabolic space. Preprint No 299, FU Berlin, DFG-Research Center Matheon

    Google Scholar 

  24. Larhlimi A, Bockmayr A (2008) On inner and outer descriptions of the steady-state flux cone of a metabolic network. In: Proceedings of the CMSB 2008. LNCS/LNBI, vol 5307. Springer, Berlin, pp 308–327

    Google Scholar 

  25. Mendes P (1993) GEPASI: a software package for modelling the dynamics, steady states and control of biochemical and other systems. Comput Appl Biosci 9:563–571

    Google Scholar 

  26. Matsuno H, Li C, Miyano S (2006) Petri net based descriptions for systematic understanding of biological pathways. IEICE Trans Fundam Electron Commun Comput Sci E89-A(11):3166–3174

    Google Scholar 

  27. Matsuno H, Tanaka Y, Aoshima H, Doi A, Matsui M, Miyano S (2003) Biopathways representation and simulation on hybrid functional Petri net. In: Silico Biol 3(0032)

    Google Scholar 

  28. Murata T (1989) Petri nets: properties, analysis and applications. Proc IEEE 77 4:541–580

    Article  Google Scholar 

  29. Pagnoni A (1990) Project engineering: computer-oriented planning and operational decision making. Springer, Berlin

    MATH  Google Scholar 

  30. Palsson BO (2006) Systems biology: properties of reconstructed networks. Cambridge University Press, Cambridge

    Google Scholar 

  31. Pascoletti KH (1986) Diophantine systems and solution methods to determine all Petri nets invariants. GMD Report 160, Bonn (in German)

    Google Scholar 

  32. Pedersen M (2008) Compositional definitions of minimal flows in Petri nets. In: Proceedings of the CMSB 2008. LNCS/LNBI, vol 5307. Springer, Berlin, pp 288–307

    Google Scholar 

  33. Petri CA (1962) Communication with Automata (in German). Schriften des Instituts für Instrumentelle Mathematik, Bonn

    Google Scholar 

  34. Peterson JL (1981) Petri net theory and the modeling of systems. Prentice–Hall, New York

    Google Scholar 

  35. Papin JA, Reed JL, Palsson PO (2004) Hierarchical thinking in network biology: the unbiased modularization of biochemical networks. Trends Biochem Sci 29(12):641–647

    Article  Google Scholar 

  36. Priese L, Wimmel H (2003) Theoretical informatics—Petri nets. Springer, Berlin (in German)

    Google Scholar 

  37. Popova-Zeugmann L, Heiner M, Koch I (2005) Time Petri nets for modelling and analysis of biochemical networks. Fundam Inform 67:149–162

    MATH  MathSciNet  Google Scholar 

  38. Reddy VN (1994) Modeling biological pathways: a discrete event systems approach. Master thesis, University of Maryland

    Google Scholar 

  39. Reisig W (1982) Petri nets; an introduction. Springer, Berlin

    Google Scholar 

  40. Reddy VN, Mavrovouniotis ML, Liebman ML (1993) Petri net representations in metabolic pathways. In Proceedings of the international conference on intelligent systems for molecular biology

    Google Scholar 

  41. Sackmann A (2005) Modelling and simulation of signal transduction pathways in saccharomyces cerevisiae using Petri net theory. Diploma thesis, Ernst Moritz Arndt Univ Greifswald (in German)

    Google Scholar 

  42. Sackmann A, Heiner M, Koch I (2006) Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform 7:482

    Article  Google Scholar 

  43. Schuster S, Hilgetag C, Schuster R (1993) Determining elementary modes of functioning in biochemical reaction networks at steady state. In Proceedings of the second Gauss symposium, pp 101–114

    Google Scholar 

  44. 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. Theor Biol 203:229–248

    Article  Google Scholar 

  45. Snoopy website (2008) A tool to design and animate/simulate graphs. BTU Cottbus. http://www-dssz.informatik.tu-cottbus.de/software/snoopy.html

  46. Schuster S, Pfeiffer T, Moldenhauer F, Koch I, Dandekar T (2002) Exploring the pathway structure of metabolism: decomposition into subnetworks and application to mycoplasma pneumoniae. BioInformatics 18(2):351–361

    Article  Google Scholar 

  47. Starke PH (1980) Petri nets: foundations, applications, theory. VEB Deutscher Verlag der Wissenschaften, Berlin (in German)

    Google Scholar 

  48. Starke PH (1990) Analysis of Petri net models. Teubner, Stuttgart (in German)

    MATH  Google Scholar 

  49. Toudic JM (1982) Linear algebra algorithms for the structural analysis of Petri nets. Rev Tech Thomson CSF (France) 14(1):137–156 (in French)

    Google Scholar 

  50. Winder K (2006) Invariant-based structural characterization of Petri nets. Diploma thesis. BTU Cottbus, Dep of CS (in German)

    Google Scholar 

  51. Yu Y, Wang G, Simha R, Peng W, Turano F, Zeng C (2007) Pathway switching explains the sharp response characteristic of hypoxia response network system. PLos Comput Biol 8(3):1657–1668

    MathSciNet  Google Scholar 

  52. Zaitsev DA (2005) Functional Petri nets. TR 224, CNRS

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, Brandenburg University of Technology, Postbox 101344, 03013, Cottbus, Germany

    Monika Heiner

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  1. Monika Heiner
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Correspondence to Monika Heiner .

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Editors and Affiliations

  1. Dept. Computer Science, University of British Columbia, Main Mall 201-2366, Vancouver, V6T 1Z4, Canada

    Anne Condon

  2. Dept. Applied Mathematics, Weizmann Institute of Science, Rehovot, 76100, Israel

    David Harel

  3. Leiden Inst. Advanced Computer Science, Leiden University, Niels Bohrweg 1, Leiden, 2333 CA, Netherlands

    Joost N. Kok

  4. Turku Centre for Computer Science, Lemminkaisenkatu 14 A, Turku, 20520, Finland

    Arto Salomaa

  5. Computer Science, Computation,, California Inst. of Technology, Pasadena, 91125, U.S.A.

    Erik Winfree

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Heiner, M. (2009). Understanding Network Behavior by Structured Representations of Transition Invariants. In: Condon, A., Harel, D., Kok, J., Salomaa, A., Winfree, E. (eds) Algorithmic Bioprocesses. Natural Computing Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88869-7_19

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  • DOI: https://doi.org/10.1007/978-3-540-88869-7_19

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-88868-0

  • Online ISBN: 978-3-540-88869-7

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