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. 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.
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References
Singhal, V., Aziz, A., Sanwal, K., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. on Computational Logic 1(1), 162–170 (2000)
Angeli, D., De Leenheer, P., Sontag, E.D.: On the structural monotonicity of chemical reaction networks. In: Proc. 45th IEEE Conference on Decision and Control, pp. 7–12 (2006)
Adalsteinsson, D., McMillen, D., Elston, T.C.: Biochemical network stochastic simulator (bionetS): software for stochastic modeling of biochemical networks. BMC Bioinformatics 5, 24 (2004)
Antoniotti, M., Policriti, A., Ugel, N., Mishra, B.: Model building and model checking for biochemical processes. Cell Biochemistry and Biophysics 38, 271–286 (2003)
BioNessie website. A biochemical pathway simulation and analysis tool. University of Glasgow (2008), http://www.bionessie.org
Bause, F., Kritzinger, P.S.: Stochastic Petri Nets. Vieweg (2002)
Hermanns, H., Baier, C., Haverkort, B., Katoen, J.-P.: Model-checking algorithms for continuous-time markov chains. IEEE Trans. on Software Engineering 29(6), 524–541 (2003)
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)
Chabrier, N., Fages, F.: Symbolic model checking of biochemical networks. In: Priami, C. (ed.) CMSB 2003. LNCS, vol. 2602, pp. 149–162. Springer, Heidelberg (2003)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2001) (third printing)
Chaouiya, C.: Petri net modelling of biological networks. Briefings in Bioinformatics 8(4), 210–219 (2007)
Charlie Website. A Tool for the Analysis of Place/Transition Nets. BTU Cottbus (2008), http://www-dssz.informatik.tu-cottbus.de/software/charlie/charlie.html
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)
Curry, E.: Stochastic Simulation of the Entrained Circadian Rhythm. Master thesis, School of Informatics, Univ. of Edinburgh (2006)
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)
David, R., Alla, H.: Discrete, Continuous, and Hybrid Petri Nets. Springer, Heidelberg (2005)
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, Springer, Heidelberg (2004)
Desel, J., Esparza, J.: Free Choice Petri Nets. Cambridge University Press, New York (1995)
Desel, J., Juhás, G.: What is a Petri Net? In: Ehrig, H., Juhás, G., Padberg, J., Rozenberg, G. (eds.) APN 2001. LNCS, vol. 2128, pp. 1–25. Springer, Heidelberg (2001)
Dormand, J.R., Prince, P.J.: A family of embedded runge-kutta formulae. J. Comp. Appl. Math. 6, 1–22 (1980)
Eker, S., Knapp, M., Laderoute, K., Lincoln, P., Meseguer, J., Sonmez, K.: Pathway logic: Symbolic analysis of biological signaling. In: Proc. Seventh Pacific Symposium on Biocomputing, pp. 400–412 (2002)
Fages, F., Rizk, A.: On the analysis of numerical data time series in temporal logic. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 48–63. Springer, Heidelberg (2007)
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. In: TR I-02, CS Dep., BTU Cottbus (2007)
Gilbert, D., Heiner, M., Lehrack, S.: A unifying framework for modelling and analysing biochemical pathways using Petri nets. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS (LNBI), vol. 4695, pp. 200–216. Springer, Heidelberg (2007)
Gilbert, D., Heiner, M., Rosser, S., Fulton, R., Gu, X., Trybiło, M.: A Case Study in Model-driven Synthetic Biology. In: 2nd IFIP Conference on Biologically Inspired Collaborative Computing (BICC), IFIP WCC 2008, Milano (to appear, 2008)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Goss, P.J.E., Peccoud, J.: Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc. Natl. Acad. Sci., USA, 95, 2340–2361 (1998)
Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology. In: Iyengar, M.S. (ed.) Symbolic Systems Biology: Theory and Methods, Jones and Bartlett Publishers, Inc (to appear, 2008)
Hucka, M., Finney, A., Sauro, H.M., Bolouri, H., Doyle, J.C., Kitano, H. et al.: The systems biology markup language (SBML): A medium for representation and exchange of biochemical network models. J. Bioinformatics 19, 524–531 (2003)
Heiner, M., Koch, I.: Petri Net Based Model Validation in Systems Biology. In: Cortadella, J., Reisig, W. (eds.) ICATPN 2004. LNCS, vol. 3099, pp. 216–237. Springer, Heidelberg (2004)
Heath, J., Kwiatkowska, M., Norman, G., Parker, D., Tymchyshyn, O.: Probabilistic model checking of complex biological pathways. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 32–47. Springer, Heidelberg (2006)
Hofestädt, R.: A Petri net application of metabolic processes. Journal of System Analysis, Modeling and Simulation 16, 113–122 (1994)
Heiner, M., Richter, R., Schwarick, M.: Snoopy - A Tool to Design and Animate/Simulate Graph-Based Formalisms. In: Proc. PNTAP 2008, ACM, New York (to appear, 2008)
Koch, I., Heiner, M.: Petri Nets. In: Junker, B.H., Schreiber, F. (eds.) Biological Network Analysis, 7, pp. 139–179. Wiley Book Series on Bioinformatics (2008)
Kierzek, A.M.: STOCKS: STOChastic kinetic simulations of biochemical systems with gillespie algorithm. Bioinformatics 18(3), 470–481 (2002)
Lautenbach, K.: Exact Liveness Conditions of a Petri Net Class (in German). Technical report, GMD Report 82, Bonn (1973)
Levchenko, A., Bruck, J., Sternberg, P.W.: Scaffold proteins 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)
Li, C., Miyano, S., Matsuno, H.: Petri net based descriptions for systematic understanding of biological pathways. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E89-A(11), 3166–3174 (2006)
Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets, 2nd edn. Wiley Series in Parallel Computing. John Wiley and Sons, Chichester (1995)
MC2 Website. MC2 - PLTL model checker. University of Glasgow (2008), http://www.brc.dcs.gla.ac.uk/software/mc2/
Matsuno, H., Fujita, S., Doi, A., Nagasaki, M., Miyano, S.: Towards Pathway Modelling and Simulation. In: van der Aalst, W.M.P., Best, E. (eds.) ICATPN 2003. LNCS, vol. 2679, pp. 3–22. Springer, Heidelberg (2003)
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)
Palsson, B.O.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge (2006)
Petri, C.A.: Communication with Automata (in German). Schriften des Instituts für Instrumentelle Mathematik, Bonn (1962)
Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)
Pnueli, A.: The temporal semantics of concurrent programs. Theor. Comput. Sci. 13, 45–60 (1981)
Priese, L., Wimmel, H.: Theoretcial Informatics - Petri Nets (in German). Springer, Heidelberg (2003)
Reisig, W.: Petri nets; An introduction. Springer, Heidelberg (1982)
Reddy, V.N., Mavrovouniotis, M.L., Liebman, M.L.: Petri Net Representations in Metabolic Pathways. In: Proc. of the Int. Conf. on Intelligent Systems for Molecular Biology (1993)
Salis, H., Kaznessis, Y.: Accurate hybrid stochastic simulation of a system of coupled chemical or biochemical reactions. J. Chem. Phys. 122 (2005)
Snoopy Website. A Tool to Design and Animate/Simulate Graphs. BTU Cottbus (2008), http://www-dssz.informatik.tu-cottbus.de/software/snoopy.html
Srivastava, R., Peterson, M.S., Bentley, W.E.: Stochastic kinetic analysis of the escherichia coli stress circuit using σ 32-targeted antisense. Biotechnology and Bioengineering 75(1), 120–129 (2001)
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)
Shaw, O.J., Steggles, L.J., Wipat, A.: Automatic parameterisation of stochastic Petri net models of biological networks. CS-TR-909, School of CS, Univ. of Newcastle upon Tyne (2005)
Schulz-Trieglaff, O.: Modelling the randomness in biological systems. Master thesis, School of Informatics, University of Edinburgh (2005)
Starke, P.H.: Some Properties of Timed Nets under the Earliest Firing Rule. In: Rozenberg, G. (ed.) APN 1989. LNCS, vol. 424, pp. 418–432. Springer, Heidelberg (1990)
Starke, P.H.: Analysis of Petri Net Models (in German). B.G. Teubner, Stuttgart, Stuttgart (1990)
Stewart, W.J.: Introduction to the Numerical Solution of Markov Chains. Princeton University Press, Princeton (1994)
Tovchigrechko, A.: Model checking using interval decision diagrams. PhD thesis, BTU Cottbus, Dep. of CS, (submitted 2006)
Turner, T.E., Schnell, S., Burrage, K.: Stochastic approaches for modelling in vivo reactions. Comp. Biology and Chemistry 28(3), 165–178 (2004)
Wilkinson, D.J.: Stochastic Modelling for System Biology, 1st edn. CRC Press, New York (2006)
Sujathab, A., Marwan, W., Starostzik, C.: Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri net modeling and simulation. J. of Theoretical Biology 236(4), 349–365 (2005)
Younes, H., Kwiatkowska, M., Norman, G., Parker, D.: Numerical vs. statistical probabilistic model checking. STTT 8(3), 216–228 (2006)
Younes, H.L.S., Simmons, R.G.: Probabilistic verification of descrete event systems using acceptance sampling. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 223–235. Springer, Heidelberg (2002)
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Heiner, M., Gilbert, D., Donaldson, R. (2008). Petri Nets for Systems and Synthetic Biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds) Formal Methods for Computational Systems Biology. SFM 2008. Lecture Notes in Computer Science, vol 5016. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68894-5_7
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DOI: https://doi.org/10.1007/978-3-540-68894-5_7
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