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A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets

  • David Gilbert
  • Monika Heiner
  • Sebastian Lehrack
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4695)

Abstract

We give a description of a Petri net-based framework for modelling and analysing biochemical pathways, which unifies the qualitative, stochastic and continuous paradigms. Each perspective adds its contribution to the understanding of the system, thus the three approaches do not compete, but complement each other. We illustrate our approach by applying it to an extended model of the three stage cascade, which forms the core of the ERK signal transduction pathway. Consequently our focus is on transient behaviour analysis. We demonstrate how qualitative descriptions are abstractions over stochastic or continuous descriptions, and show that the stochastic and continuous models approximate each other. A key contribution of the paper consists in a precise definition of biochemically interpreted stochastic Petri nets. Although our framework is based on Petri nets, it can be applied more widely to other formalisms which are used to model and analyse biochemical networks.

Keywords

Model Check Hazard Function Extracellular Signal Regulate Kinase Unify Framework Continuous Time Markov Chain 
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.

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References

  1. Angeli, D., De Leenheer, P., Sontag, E.D.: On the structural monotonicity of chemical reaction networks. In: ICATPN 2003, pp. 7–12. IEEE Computer Society Press, Los Alamitos (2006)CrossRefGoogle Scholar
  2. BioNessie. A biochemical pathway simulation and analysis tool. University of Glasgow, http://www.bionessie.org
  3. Bause, F., Kritzinger, P.S.: Stochastic Petri Nets. Vieweg (2002)Google Scholar
  4. Calzone, L., Chabrier-Rivier, N., Fages, F., Soliman, S.: Machine learning biochemical networks from temporal logic properties. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 68–94. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  5. Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2001)Google Scholar
  6. Chickarmane, V., Kholodenko, B.N., Sauro, H.M.: Oscillatory dynamics arising from competitive inhibition and multisite phosphorylation. Journal of Theoretical Biology 244(1), 68–76 (2007)CrossRefMathSciNetGoogle Scholar
  7. Calder, M., Vyshemirsky, V., Gilbert, D., Orton, R.: Analysis of signalling pathways using continuous time Markov chains. In: Priami, C., Plotkin, G. (eds.) Transactions on Computational Systems Biology VI. LNCS (LNBI), vol. 4220, pp. 44–67. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  8. D’Aprile, D., Donatelli, S., Sproston, J.: CSL model checking for the GreatSPN tool. In: Aykanat, C., Dayar, T., Körpeoğlu, İ. (eds.) ISCIS 2004. LNCS, vol. 3280, pp. 543–552. Springer, Heidelberg (2004)Google Scholar
  9. Gilbert, D., Heiner, M.: From Petri nets to differential equations - an integrative approach for biochemical network analysis. In: Donatelli, S., Thiagarajan, P.S. (eds.) ICATPN 2006. LNCS, vol. 4024, pp. 181–200. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  10. Gilbert, D., Heiner, M., Lehrack, S.: A unifying framework for modelling and analysing biochemical pathways using Petri nets. TR I-02, CS Dep., BTU Cottbus (2007)Google Scholar
  11. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)CrossRefGoogle Scholar
  12. Levchenko, A., Bruck, J., Sternberg, P.W.: Scaffold proteins may biphasically affect the levels of mitogen-activated protein kinase signaling and reduce its threshold properties. Proc. Natl. Acad. Sci. USA 97(11), 5818–5823 (2000)CrossRefGoogle Scholar
  13. Max-Gruenebaum-Foundation, http://www.max-gruenebaum-stiftung.de
  14. Murata, T.: Petri nets: Properties, analysis and applications. Proc.of the IEEE 77 4, 541–580 (1989)CrossRefGoogle Scholar
  15. Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)Google Scholar
  16. Snoopy. A tool to design and animate hierarchical graphs. BTU Cottbus, CS Dep., http://www-dssz.informatik.tu-cottbus.de
  17. Shampine, L.F., Reichelt, M.W.: The MATLAB ODE Suite. SIAM Journal on Scientific Computing 18, 1–22 (1997)zbMATHCrossRefMathSciNetGoogle Scholar
  18. Starke, P.H., Roch, S.: INA - The Intergrated Net Analyzer. Humboldt University, Berlin (1999), www.informatik.hu-berlin.de/~starke/ina.html Google Scholar
  19. Schröter, C., Schwoon, S., Esparza, J.: The Model Checking Kit. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 463–472. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  20. Wilkinson, D.J.: Stochastic Modelling for System Biology, 1st edn. CRC Press, New York (2006)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • David Gilbert
    • 1
  • Monika Heiner
    • 2
  • Sebastian Lehrack
    • 3
  1. 1.Bioinformatics Research Centre, University of Glasgow, Glasgow G12 8QQ, ScotlandUK
  2. 2.INRIA Rocquencourt, Projet Contraintes, BP 105, 78153 Le Chesnay CEDEXFrance
  3. 3.Department of Computer Science, Brandenburg University of Technology, Postbox 10 13 44, 03013 CottbusGermany

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