Abstract
Petri nets are a widely used formalism to qualitatively model concurrent systems such as a biological cell. We present techniques for modelling biological processes as Petri nets for further analyses and in-silico experiments. Instead of extending the formalism with ,,colours” or rates, as is most often done, we focus on preserving the simplicity of the formalism and developing an execution semantics which resembles biology – we apply a principle of maximal parallelism and introduce the novel concept of bounded execution with overshooting. A number of modelling solutions are demonstrated using the example of the well-studied C. elegans vulval development process. To date our model is still under development, but first results, based on Monte Carlo simulations, are promising.
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
Alon, U.: An Introduction to Systems Biology: Design Principles of Biological Circuits. Chapman & Hall/CRC (2006)
Genrich, H., Küffner, R., Voss, K.: Executable Petri net models for the analysis of metabolic pathways. International Journal on Software Tools for Technology Transfer (STTT) 3(4), 394–404 (2001)
E-Cell, http://www.e-cell.org
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. The Journal of Physical Chemistry 81(25), 2340–2361 (1977)
Srivastava, R., You, L., Summers, J., Yin, J.: Stochastic vs. deterministic modeling of intracellular viral kinetics. Journal of Theoretical Biology 218(3), 309–321 (2002)
Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinformatics 7, 482 (2006)
Chaouiya, C.: Petri net modelling of biological networks. Briefings in Bioinformatics 8(4), 210–219 (2007)
Wormbook, http://www.wormbook.org
Reddy, V., Mavrovouniotis, M., Liebman, M.: Qualitative analysis of biochemical reaction system. Computers in Biology and Medicine 26(1), 9–24 (1996)
Fisher, J., Piterman, N., Hajnal, A., Henzinger, T.A.: Predictive modeling of signaling crosstalk during C. elegans vulval development. PLoS Computational Biology 3(5), 92 (2007)
Petri, C.A.: Kommunikation mit Automaten. Schriften des IIM Nr. 2, Institut für Instrumentelle Mathematik, Bonn (1962)
Murata, T.: Petri nets: Properties, analysis and applications. Proceedings of the IEEE 77(4), 541–580 (1989)
Kleijn, J.H., Koutny, M., Rozenberg, G.: Towards a Petri net semantics for membrane systems. In: Freund, R., Păun, G., Rozenberg, G., Salomaa, A. (eds.) WMC 2005. LNCS, vol. 3850, pp. 292–309. Springer, Heidelberg (2006)
Distributed ASCI Supercomputer DAS-3, http://www.cs.vu.nl/das3
Petri Net Markup Language, http://www.informatik.hu-berlin.de/top/pnml
TINA, http://www.laas.fr/tina
Fisher, J., Henzinger, T.A., Mateescu, M., Piterman, N.: Bounded asynchrony: A biologically inspired notion of concurrency. Technical report, MTC (2007)
Clarke, D., Costa, D., Arbab, F.: Modelling coordination in biological systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2004. LNCS, vol. 4313, pp. 9–25. Springer, Heidelberg (2006)
Koch, I., Junker, B.H., Heiner, M.: Application of Petri net theory for modelling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21(7), 1219–1226 (2005)
Li, C., Ge, Q.W., Nakata, M., Matsuno, H., Miyando, S.: Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets. Journal of Biosciences 32, 113–127 (2007)
Goss, P., Peccoud, J.: Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proceedings of the National Academy of Sciences of the United States of America (PNAS) 95(12), 6750–6755 (1998)
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)
Matsuno, H., Doi, A., Nagasaki, M., Miyano, S.: Hybrid Petri net representation of gene regulatory network. In: Proceedings of Pacific Symposium on Biocomputing, vol. 5, pp. 341–352 (2000)
Hofestädt, R., Thelen, S.: Quantitative modeling of biochemical networks. In Silico Biology 6, 39–53 (1998)
Matsuno, H., Li, C., Miyano, S.: Petri net based descriptions for systematic understanding of biological pathways. IEICE Transactions on Fundamentals of Electronics, Communications and Computer Science E89-A(11), 3166–3174 (2006)
Simao, E., Remy, E., Thieffry, D., Chaouiya, C.: Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. Coli. Bioinformatics 21(2), 190–196 (2005)
Steggles, L., Banks, R., Wipat, A.: Modelling and analysing genetic networks: From Boolean networks to Petri nets. In: Priami, C. (ed.) CMSB 2006. LNCS (LNBI), vol. 4210, pp. 127–141. Springer, Heidelberg (2006)
Peleg, M., Rubin, D., Altman, R.B.: Using Petri net tools to study properties and dynamics of biological systems. Journal of the American Medical Informatics Association (JAMIA) 12(2), 181–199 (2005)
Fisher, J., Henzinger, T.A.: Executable cell biology. Nature Biotechnology 25(11), 1239–1249 (2007)
Yoo, A.S., Bais, C., Greenwald, I.: Crosstalk between the EGFR and LIN-12/Notch pathways in C. elegans vulval development. Science 303(5658), 663–666 (2004)
Shaye, D.D., Greenwald, I.: Endocytosis-mediated downregulation of LIN-12/Notch upon Ras activation in Caenorhabditis elegans. Nature 420(6916), 686–690 (2002)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Krepska, E. et al. (2008). Design Issues for Qualitative Modelling of Biological Cells with Petri Nets. In: Fisher, J. (eds) Formal Methods in Systems Biology. FMSB 2008. Lecture Notes in Computer Science(), vol 5054. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-68413-8_4
Download citation
DOI: https://doi.org/10.1007/978-3-540-68413-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-68410-7
Online ISBN: 978-3-540-68413-8
eBook Packages: Computer ScienceComputer Science (R0)