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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
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)
BioNessie. A biochemical pathway simulation and analysis tool. University of Glasgow, http://www.bionessie.org
Bause, F., Kritzinger, P.S.: Stochastic Petri Nets. Vieweg (2002)
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)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2001)
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)
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)
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)
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)
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)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
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)
Max-Gruenebaum-Foundation, http://www.max-gruenebaum-stiftung.de
Murata, T.: Petri nets: Properties, analysis and applications. Proc.of the IEEE 77 4, 541–580 (1989)
Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)
Snoopy. A tool to design and animate hierarchical graphs. BTU Cottbus, CS Dep., http://www-dssz.informatik.tu-cottbus.de
Shampine, L.F., Reichelt, M.W.: The MATLAB ODE Suite. SIAM Journal on Scientific Computing 18, 1–22 (1997)
Starke, P.H., Roch, S.: INA - The Intergrated Net Analyzer. Humboldt University, Berlin (1999), www.informatik.hu-berlin.de/~starke/ina.html
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)
Wilkinson, D.J.: Stochastic Modelling for System Biology, 1st edn. CRC Press, New York (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gilbert, D., Heiner, M., Lehrack, S. (2007). A Unifying Framework for Modelling and Analysing Biochemical Pathways Using Petri Nets. In: Calder, M., Gilmore, S. (eds) Computational Methods in Systems Biology. CMSB 2007. Lecture Notes in Computer Science(), vol 4695. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75140-3_14
Download citation
DOI: https://doi.org/10.1007/978-3-540-75140-3_14
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75139-7
Online ISBN: 978-3-540-75140-3
eBook Packages: Computer ScienceComputer Science (R0)