Abstract
Petri nets provide a unifying and versatile framework for the synthesis and engineering of computational models of biochemical reaction networks and of gene regulatory networks. Starting with the basic definitions, we provide an introduction into the different classes of Petri nets that reinterpret a Petri net graph as a qualitative, stochastic, continuous, or hybrid model. Static and dynamic analysis in addition to simulative model checking provide a rich choice of methods for the analysis of the structure and dynamic behavior of Petri net models. Coloring of Petri nets of all classes is powerful for multiscale modeling and for the representation of location and space in reaction networks since it combines the concept of Petri nets with the computational mightiness of a programming language. In the context of the Petri net framework, we provide two most recently developed approaches to biomodel engineering, the database-assisted automatic composition and modification of Petri nets with the help of reusable, metadata-containing modules, and the automatic reconstruction of networks based on time series data sets. With all these features the framework provides multiple options for biomodel engineering in the context of systems and synthetic biology.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsReferences
Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. Comput. Log. 1(1), 162–170 (2000)
Baier, C., Haverkort, B., Hermanns, H., Katoen, J.P.: Model-checking algorithms for continuous-time Markov chains. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)
Ballarini, P., Mardare, R., Mura, I.: Analysing biochemical oscillation through probabilistic model checking. Electron. Notes Theor. Comput. Sci. 229(1), 3–19 (2009)
Baumgarten, B.: Petri-Netze—Grundlagen und Anwendungen. Spektrum, München (1996)
Blätke, M.A., Meyer, S., Stein, C., Marwan, W.: Petri net modeling via a modular and hierarchical approach applied to nociception. In: Int. Workshop on Biological Processes & Petri Nets (BioPPN), Satellite Event of Petri Nets 2010, pp. 131–145 (2010)
Blätke, M.A., Heiner, M., Marwan, W.: Tutorial—Petri Nets in Systems Biology. Otto von Guericke University and Magdeburg, Centre for Systems Biology (2011)
Blätke, M.A., Dittrich, A., Heiner, M., Schaper, F., Marwan, W.: JAK-STAT signaling as example for a database-supported modular modeling concept. In: Gilbert, D., Heiner, M. (eds.) Proceedings of the 10th Conference on Compuational Methods in Systems Biology. LNCS/LNBI, vol. 7605, pp. 362–365. Springer, Berlin (2012)
Blätke, M.A., Heiner, M., Marwan, W.: Predicting phenotype from genotype through automatically composed Petri nets. In: Gilbert, D., Heiner, M. (eds.) Proceedings of the 10th Conference on Compuational Methods in Systems Biology. LNCS/LNBI, vol. 7605, pp. 87–106. Springer, Berlin (2012)
Blätke, M.A., Dittrich, A., Rohr, C., Heiner, M., Schaper, F., Marwan, W.: JAK/STAT signaling—an executable model assembled from molecule-centered modules demonstrating a module-oriented database concept for systems and synthetic biology. Mol. BioSyst. 9(6), 1290–1307 (2013)
Blätke, M.A., Heiner, M., Marwan, W.: Linking protein structure with network behavior to generate biologically meaningful mutations in computational models of regulatory networks. Unpublished work
Breitling, R., Gilbert, D., Heiner, M., Orton, R.: A structured approach for the engineering of biochemical network models, illustrated for signaling pathways. Brief. Bioinform. 9(5), 404–421 (2008)
Breitling, R., Donaldson, R., Gilbert, D., Heiner, M.: Biomodel engineering—from structure to behavior (position paper). In: Transactions on Computational Systems Biology XII, Special Issue on Modeling Methodologies, vol. 5945, pp. 1–12 (2010)
Calzone, L., Chabrier-Rivier, N., Fages, F., Soliman, S.: Machine learning biochemical networks from temporal logic properties. In: Transactions on Computational Systems Biology VI, pp. 68–94 (2006)
Chaouiya, C., Remy, E., Ruet, P., Thieffry, D.: Qualitative modeling of genetic networks: from logical regulatory graphs to standard Petri nets. In: Applications and Theory of Petri Nets 2004, pp. 137–156. Springer, Berlin (2004)
Chaouiya, C., Remy, E., Thieffry, D.: Petri net modeling of biological regulatory networks. J. Discrete Algorithms 6(2), 165–177 (2008)
Chen, L., Qi-Wei, G., Nakata, M., Matsuno, H., Miyano, S.: Modeling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets. J. Biosci. 32(1), 113–127 (2007)
Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)
Curry, E.: Stochastic simulation of entrained circadian rhythm. Master thesis (2006)
Desel, J., Esparza, J.: Free Choice Petri Nets, vol. 40. Cambridge University Press, Cambridge (1995)
Donaldson, R., Gilbert, D.: A model checking approach to the parameter estimation of biochemical pathways. In: Computational Methods in Systems Biology. LNCS (LNBI), vol. 5307, pp. 269–287. Springer, Berlin (2008)
Durzinsky, M., Weismantel, R., Marwan, W.: Automatic reconstruction of molecular and genetic networks from discrete time series data. Biosystems 93(3), 181–190 (2008)
Durzinsky, M., Marwan, W., Ostrowski, M., Schaub, T., Wagler, A.: Automatic network reconstruction using ASP. Theory Pract. Log. Program. 11, 749–766 (2011)
Durzinsky, M., Wagler, A., Marwan, W.: Reconstruction of extended Petri nets from time series data and its application to signal transduction and to gene regulatory networks. BMC Syst. Biol. 5(1), 113 (2011)
Durzinsky, M., Marwan, W., Wagler, A.: Reconstruction of extended Petri nets from time-series data by using logical control functions. J. Math. Biol. 66, 203–223 (2013). doi:10.1007/s00285-012-0511-3
Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403(6767), 335–338 (2000)
Emerson, E.A., Halpern, J.Y.: Sometimes and not never revisited: on branching versus linear time temporal logic. J. ACM 33, 151–178 (1986)
Fisher, J., Henzinger, T.A.: Executable cell biology. Nat. Biotechnol. 25(11), 1239–1249 (2007)
Franzke, A.: Charlie 2.0—a multithreaded Petri net analyzer. Diploma thesis (2009)
Gao, Q., Gilbert, D., Heiner, M., Liu, F., Maccagnola, D., Tree, D.: Multiscale modeling and analysis of planar cell polarity in the Drosophila wing. IEEE/ACM Trans. Comput. Biol. Bioinform. 99, 1 (2012)
Gilbert, D., Heiner, M.: Multiscale modeling for multiscale systems biology (2011). http://multiscalepn.brunel.ac.uk
Gilbert, D., Heiner, M., Rosser, S., Fulton, R., Gu, X., Trybiło, M.: A case study in model-driven synthetic biology. In: IFIP WCC 2008, 2nd IFIP Conference on Biologically Inspired Collaborative Computing (BICC 2008). IFIP, vol. 268, pp. 163–175. Springer, Boston (2008)
Gilbert, D., Heiner, M., Liu, F., Saunders, N.: Coloring space—a colored framework for spatial modeling in systems biology. In: Colom, J., Desel, J. (eds.) Proc. PETRI NETS 2013. LNCS, vol. 7927, pp. 230–249. Springer, Berlin (2013)
Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)
Goss, P.J., Peccoud, J.: Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc. Natl. Acad. Sci. 95(12), 6750–6755 (1998)
Green, M., Sambrook, J.: Molecular Cloning. A Laboratory Manual, 4th edn. Cold Spring Harbor Laboratory Press, Cold Spring Harbor (2012)
Hack, M.: Analysis of production schemata by Petri nets (1972)
Hardy, S., Robillard, P.N.: Petri net-based method for the analysis of the dynamics of signal propagation in signaling pathways. Bioinformatics 24(2), 209–217 (2008)
Hecker, M., Lambeck, S., Toepfer, S., Van Someren, E., Guthke, R.: Gene regulatory network inference: data integration in dynamic models—a review. Biosystems 96(1), 86–103 (2009)
Heiner, M., Gilbert, D.: How might Petri nets enhance your systems biology toolkit. In: LNCS, vol. 6709, pp. 17–37. Springer, Berlin (2011)
Heiner, M., Gilbert, D.: Biomodel engineering for multiscale systems biology. Prog. Biophys. Mol. Biol. 111(2–3), 119–128 (2013)
Heiner, M., Gilbert, D., Donaldson, R.: Petri nets for systems and synthetic biology. In: LNCS, vol. 5016, pp. 215–264. Springer, Berlin (2008)
Heiner, M., Lehrack, S., Gilbert, D., Marwan, W.: Extended stochastic Petri nets for model-based design of wetlab experiments. In: Transactions on Computational Systems Biology XI. LNCS/LNBI, vol. 5750, pp. 138–163. Springer, Berlin (2009)
Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology, pp. 61–97. Jones & Bartlett Learning (2010)
Heiner, M., Herajy, M., Liu, F., Rohr, C., Schwarick, M.: Snoopy—a unifying Petri net tool. In: Proc. PETRI NETS 2012. LNCS, vol. 7347, pp. 398–407. Springer, Berlin (2012)
Heiner, M., Rohr, C., Schwarick, M.: MARCIE—Model checking And Reachability analysis done effiCIEntly. In: Colom, J., Desel, J. (eds.) Proc. PETRI NETS 2013. LNCS, vol. 7927, pp. 389–399. Springer, Berlin (2013)
Herajy, M.: Computational steering of multi-scale biochemical networks. PhD thesis, BTU Cottbus, Department of Computer Science (2013)
Herajy, M., Heiner, M.: Hybrid representation and simulation of stiff biochemical networks. Nonlinear Anal. Hybrid Syst. 6(4), 942–959 (2012)
Hill, A.V.: The combinations of haemoglobin with oxygen and with carbon monoxide. I. Biochem. J. 7(5), 471 (1913)
Hucka, M., Finney, A., Sauro, H.M., Bolouri, H., Doyle, J.C., Kitano, H., Arkin, A.P., Bornstein, B.J., Bray, D., Cornish-Bowden, A., et al.: The systems biology markup language (sbml): a medium for representation and exchange of biochemical network models. Bioinformatics 19(4), 524–531 (2003)
Kiehl, T.R., Mattheyses, R.M., Simmons, M.K.: Hybrid simulation of cellular behavior. Bioinformatics 20(3), 316–322 (2004)
Klipp, E., Liebermeister, W., Wierling, C., Kowald, A., Lehrach, H., Herwig, R.: Systems Biology. A Textbook. Wiley-VCH, Weinheim (2009)
Koch, I., Junker, B.H., Heiner, M.: Application of Petri net theory for modeling and validation of the sucrose breakdown pathway in the potato tuber. Bioinformatics 21(7), 1219–1226 (2005)
Küffner, R., Zimmer, R., Lengauer, T.: Pathway analysis in metabolic databases via differential metabolic display (dmd). Bioinformatics 16(9), 825–836 (2000)
Liu, F.: Colored Petri nets for systems biology. PhD thesis, Brandenburg Technical University (2012)
Liu, F., Heiner, M.: Modeling membrane systems using colored stochastic Petri nets. Nat. Comput. (online), 1–13 (2013). doi:10.1007/s11047-013-9367-8
Liu, F., Heiner, M.: Multiscale modeling of coupled Ca2+ channels using colored stochastic Petri nets. IET Syst. Biol. 7(4), 106–113 (2013)
Liu, F., Heiner, M.: Petri Nets for Modeling and Analyzing Biochemical Reaction Networks. Springer, Berlin (2014). Chap. 9
Liu, F., Heiner, M., Rohr, C.: The manual for colored Petri nets in Snoopy—QPN C/SPN C/CPN C/GHPN C. Tech. Rep. 02-12, Brandenburg University of Technology Cottbus, Department of Computer Science, Cottbus (2012)
Loinger, A., Biham, O.: Stochastic simulations of the repressilator circuit. Phys. Rev. E 76(5), 051,917 (2007)
Marbach, D., Prill, R.J., Schaffter, T., Mattiussi, C., Floreano, D., Stolovitzky, G.: Revealing strengths and weaknesses of methods for gene network inference. Proc. Natl. Acad. Sci. USA 107(14), 6286–6291 (2010)
Marwan, W., Sujatha, A., Starostzik, C.: Reconstructing the regulatory network controlling commitment and sporulation in Physarum polycephalum based on hierarchical Petri net modeling and simulation. J. Theor. Biol. 236, 349–365 (2005)
Marwan, W., Wagler, A., Weismantel, R.: A mathematical approach to solve the network reconstruction problem. Math. Methods Oper. Res. 67(1), 117–132 (2008)
Marwan, W., Rohr, C., Heiner, M.: Petri nets in Snoopy: a unifying framework for the graphical display, computational modeling, and simulation of bacterial regulatory networks. In: Methods in Molecular Biology, vol. 804, pp. 409–437. Humana Press, Clifton (2012). Chap. 21
Michaelis, L., Menten, M.L.: Die Kinetik der Invertinwirkung. Biochem. Z. 49(333–369), 352 (1913)
Miller, O. Jr, Hamkalo, B.A., Thomas, C. Jr: Visualization of bacterial genes in action. Science 169(943), 392 (1970)
Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)
Papin, J.A., Hunter, T., Palsson, B.O., Subramaniam, S.: Reconstruction of cellular signaling networks and analysis of their properties. Nat. Rev. Mol. Cell Biol. 6(2), 99–111 (2005)
Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Technische Hochschule Darmstadt (1962)
Pinney, J.W., Westhead, D.R., McConkey, G.A., et al.: Petri net representations in systems biology. Biochem. Soc. Trans. 31(6), 1513–1515 (2003)
Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, 1977, pp. 46–57. IEEE, New York (1977)
Reddy, V.N., Mavrovouniotis, M.L., Liebman, M.N., et al.: Petri net representations in metabolic pathways. In: Proc. Int. Conf. Intell. Syst. Mol. Biol., vol. 1, p. 96038982 (1993)
Rohr, C.: Simulative model checking of steady-state and time-unbounded temporal operators. In: ToPNoC VIII. LNCS, vol. 8100, pp. 142–158 (2013)
Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7(1), 482 (2006)
Schulz-Trieglaff, O.: Modeling the randomness in biological systems. Master thesis (2005)
Shaw, O., Steggles, J., Wipat, A.: Automatic parameterisation of stochastic Petri net models of biological networks. Electron. Notes Theor. Comput. Sci. 151(3), 111–129 (2006)
Simao, E., Remy, E., Thieffry, D., Chaouiya, C.: Qualitative modeling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. coli. Bioinformatics 21(suppl 2), ii190–ii196 (2005)
Soliman, S., Heiner, M.: A unique transformation from ordinary differential equations to reaction networks. PLoS ONE 5(12), e14284 (2010)
Sontag, E., Kiyatkin, A., Kholodenko, B.N.: Inferring dynamic architecture of cellular networks using time series of gene expression, protein and metabolite data. Bioinformatics 20(12), 1877–1886 (2004)
Srinivasan, A., Bain, M.: Knowledge-guided identification of Petri net models of large biological systems. In: Inductive Logic Programming, pp. 317–331 (2012)
Srivastava, R., Peterson, M.S., Bentley, W.E.: Stochastic kinetic analysis of the Escherichia coli stress circuit using sigma32-targeted antisense. Biotechnol. Bioeng. 75, 120–129 (2001)
Stark, J., Brewer, D., Barenco, M., Tomescu, D., Callard, R., Hubank, M.: Reconstructing gene networks: what are the limits? Biochem. Soc. Trans. 31(Pt 6), 1519–1525 (2003)
Stark, J., Callard, R., Hubank, M.: From the top down: towards a predictive biology of signaling networks. Trends Biotechnol. 21(7), 290–293 (2003)
Zevedei-Oancea, I., Schuster, S.: Topological analysis of metabolic networks based on Petri net theory. In Silico Biol. 3(3), 323–345 (2003)
Acknowledgement
We thank Mostafa Herajy, Fei Liu, and Martin Schwarick for their continuous support in developing Snoopy, Charlie, and MARCIE. Mary-Ann Blätke and Christian Rohr were financially supported by the IMPRS Magdeburg through the Excellence Initiative of Saxony-Anhalt.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Blätke, M.A., Rohr, C., Heiner, M., Marwan, W. (2014). A Petri-Net-Based Framework for Biomodel Engineering. In: Benner, P., Findeisen, R., Flockerzi, D., Reichl, U., Sundmacher, K. (eds) Large-Scale Networks in Engineering and Life Sciences. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-08437-4_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-08437-4_6
Publisher Name: Birkhäuser, Cham
Print ISBN: 978-3-319-08436-7
Online ISBN: 978-3-319-08437-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)