Skip to main content

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 to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. Comput. Log. 1(1), 162–170 (2000)

    Article  MathSciNet  Google Scholar 

  2. 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)

    Article  Google Scholar 

  3. Ballarini, P., Mardare, R., Mura, I.: Analysing biochemical oscillation through probabilistic model checking. Electron. Notes Theor. Comput. Sci. 229(1), 3–19 (2009)

    Article  MathSciNet  Google Scholar 

  4. Baumgarten, B.: Petri-Netze—Grundlagen und Anwendungen. Spektrum, München (1996)

    Google Scholar 

  5. 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)

    Google Scholar 

  6. Blätke, M.A., Heiner, M., Marwan, W.: Tutorial—Petri Nets in Systems Biology. Otto von Guericke University and Magdeburg, Centre for Systems Biology (2011)

    Google Scholar 

  7. 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)

    Chapter  Google Scholar 

  8. 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)

    Chapter  Google Scholar 

  9. 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)

    Article  Google Scholar 

  10. 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

    Google Scholar 

  11. 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)

    Article  Google Scholar 

  12. 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)

    Chapter  Google Scholar 

  13. 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)

    Chapter  Google Scholar 

  14. 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)

    Chapter  Google Scholar 

  15. Chaouiya, C., Remy, E., Thieffry, D.: Petri net modeling of biological regulatory networks. J. Discrete Algorithms 6(2), 165–177 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  16. 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)

    Article  Google Scholar 

  17. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (2000)

    Google Scholar 

  18. Curry, E.: Stochastic simulation of entrained circadian rhythm. Master thesis (2006)

    Google Scholar 

  19. Desel, J., Esparza, J.: Free Choice Petri Nets, vol. 40. Cambridge University Press, Cambridge (1995)

    Book  MATH  Google Scholar 

  20. 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)

    Chapter  Google Scholar 

  21. Durzinsky, M., Weismantel, R., Marwan, W.: Automatic reconstruction of molecular and genetic networks from discrete time series data. Biosystems 93(3), 181–190 (2008)

    Article  Google Scholar 

  22. Durzinsky, M., Marwan, W., Ostrowski, M., Schaub, T., Wagler, A.: Automatic network reconstruction using ASP. Theory Pract. Log. Program. 11, 749–766 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  23. 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)

    Article  Google Scholar 

  24. 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

    Article  MathSciNet  MATH  Google Scholar 

  25. Elowitz, M.B., Leibler, S.: A synthetic oscillatory network of transcriptional regulators. Nature 403(6767), 335–338 (2000)

    Article  Google Scholar 

  26. Emerson, E.A., Halpern, J.Y.: Sometimes and not never revisited: on branching versus linear time temporal logic. J. ACM 33, 151–178 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  27. Fisher, J., Henzinger, T.A.: Executable cell biology. Nat. Biotechnol. 25(11), 1239–1249 (2007)

    Article  Google Scholar 

  28. Franzke, A.: Charlie 2.0—a multithreaded Petri net analyzer. Diploma thesis (2009)

    Google Scholar 

  29. 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)

    Google Scholar 

  30. Gilbert, D., Heiner, M.: Multiscale modeling for multiscale systems biology (2011). http://multiscalepn.brunel.ac.uk

  31. 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)

    Google Scholar 

  32. 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)

    Google Scholar 

  33. Gillespie, D.T.: Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. 81(25), 2340–2361 (1977)

    Article  Google Scholar 

  34. 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)

    Article  Google Scholar 

  35. Green, M., Sambrook, J.: Molecular Cloning. A Laboratory Manual, 4th edn. Cold Spring Harbor Laboratory Press, Cold Spring Harbor (2012)

    Google Scholar 

  36. Hack, M.: Analysis of production schemata by Petri nets (1972)

    Google Scholar 

  37. 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)

    Article  Google Scholar 

  38. 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)

    Article  Google Scholar 

  39. Heiner, M., Gilbert, D.: How might Petri nets enhance your systems biology toolkit. In: LNCS, vol. 6709, pp. 17–37. Springer, Berlin (2011)

    Google Scholar 

  40. Heiner, M., Gilbert, D.: Biomodel engineering for multiscale systems biology. Prog. Biophys. Mol. Biol. 111(2–3), 119–128 (2013)

    Article  Google Scholar 

  41. Heiner, M., Gilbert, D., Donaldson, R.: Petri nets for systems and synthetic biology. In: LNCS, vol. 5016, pp. 215–264. Springer, Berlin (2008)

    Google Scholar 

  42. 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)

    Chapter  Google Scholar 

  43. Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology, pp. 61–97. Jones & Bartlett Learning (2010)

    Google Scholar 

  44. 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)

    Google Scholar 

  45. 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)

    Google Scholar 

  46. Herajy, M.: Computational steering of multi-scale biochemical networks. PhD thesis, BTU Cottbus, Department of Computer Science (2013)

    Google Scholar 

  47. Herajy, M., Heiner, M.: Hybrid representation and simulation of stiff biochemical networks. Nonlinear Anal. Hybrid Syst. 6(4), 942–959 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  48. Hill, A.V.: The combinations of haemoglobin with oxygen and with carbon monoxide. I. Biochem. J. 7(5), 471 (1913)

    Google Scholar 

  49. 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)

    Article  Google Scholar 

  50. Kiehl, T.R., Mattheyses, R.M., Simmons, M.K.: Hybrid simulation of cellular behavior. Bioinformatics 20(3), 316–322 (2004)

    Article  Google Scholar 

  51. Klipp, E., Liebermeister, W., Wierling, C., Kowald, A., Lehrach, H., Herwig, R.: Systems Biology. A Textbook. Wiley-VCH, Weinheim (2009)

    Google Scholar 

  52. 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)

    Article  Google Scholar 

  53. Küffner, R., Zimmer, R., Lengauer, T.: Pathway analysis in metabolic databases via differential metabolic display (dmd). Bioinformatics 16(9), 825–836 (2000)

    Article  Google Scholar 

  54. Liu, F.: Colored Petri nets for systems biology. PhD thesis, Brandenburg Technical University (2012)

    Google Scholar 

  55. 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

  56. Liu, F., Heiner, M.: Multiscale modeling of coupled Ca2+ channels using colored stochastic Petri nets. IET Syst. Biol. 7(4), 106–113 (2013)

    Article  MathSciNet  Google Scholar 

  57. Liu, F., Heiner, M.: Petri Nets for Modeling and Analyzing Biochemical Reaction Networks. Springer, Berlin (2014). Chap. 9

    Google Scholar 

  58. 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)

    Google Scholar 

  59. Loinger, A., Biham, O.: Stochastic simulations of the repressilator circuit. Phys. Rev. E 76(5), 051,917 (2007)

    Article  Google Scholar 

  60. 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)

    Article  Google Scholar 

  61. 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)

    Article  Google Scholar 

  62. Marwan, W., Wagler, A., Weismantel, R.: A mathematical approach to solve the network reconstruction problem. Math. Methods Oper. Res. 67(1), 117–132 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  63. 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

    Google Scholar 

  64. Michaelis, L., Menten, M.L.: Die Kinetik der Invertinwirkung. Biochem. Z. 49(333–369), 352 (1913)

    Google Scholar 

  65. Miller, O. Jr, Hamkalo, B.A., Thomas, C. Jr: Visualization of bacterial genes in action. Science 169(943), 392 (1970)

    Article  Google Scholar 

  66. Murata, T.: Petri nets: properties, analysis and applications. Proc. IEEE 77(4), 541–580 (1989)

    Article  Google Scholar 

  67. 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)

    Article  Google Scholar 

  68. Petri, C.A.: Kommunikation mit Automaten. PhD thesis, Technische Hochschule Darmstadt (1962)

    Google Scholar 

  69. 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)

    Article  Google Scholar 

  70. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, 1977, pp. 46–57. IEEE, New York (1977)

    Google Scholar 

  71. 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)

    Google Scholar 

  72. Rohr, C.: Simulative model checking of steady-state and time-unbounded temporal operators. In: ToPNoC VIII. LNCS, vol. 8100, pp. 142–158 (2013)

    Google Scholar 

  73. Sackmann, A., Heiner, M., Koch, I.: Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinform. 7(1), 482 (2006)

    Article  Google Scholar 

  74. Schulz-Trieglaff, O.: Modeling the randomness in biological systems. Master thesis (2005)

    Google Scholar 

  75. 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)

    Article  Google Scholar 

  76. 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)

    Article  Google Scholar 

  77. Soliman, S., Heiner, M.: A unique transformation from ordinary differential equations to reaction networks. PLoS ONE 5(12), e14284 (2010)

    Article  Google Scholar 

  78. 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)

    Article  Google Scholar 

  79. Srinivasan, A., Bain, M.: Knowledge-guided identification of Petri net models of large biological systems. In: Inductive Logic Programming, pp. 317–331 (2012)

    Chapter  Google Scholar 

  80. 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)

    Article  Google Scholar 

  81. 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)

    Article  Google Scholar 

  82. Stark, J., Callard, R., Hubank, M.: From the top down: towards a predictive biology of signaling networks. Trends Biotechnol. 21(7), 290–293 (2003)

    Article  Google Scholar 

  83. Zevedei-Oancea, I., Schuster, S.: Topological analysis of metabolic networks based on Petri net theory. In Silico Biol. 3(3), 323–345 (2003)

    Google Scholar 

Download references

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

Authors

Corresponding author

Correspondence to Wolfgang Marwan .

Editor information

Editors and Affiliations

Rights and permissions

Reprints 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

Publish with us

Policies and ethics