How Might Petri Nets Enhance Your Systems Biology Toolkit

  • Monika Heiner
  • David Gilbert
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6709)


“How might Petri nets enhance my Systems Biology toolkit?” – this is one of the questions that we get on a regular basis, which motivated us to write an answer in the form of this paper.

We discuss the extent to which the Petri net approach can be used as an umbrella formalism to support the process of BioModel Engineering. This includes the facilitation of an active and productive interaction between biomodellers and bioscientists during the construction and analysis of dynamic models of biological systems. These models play a crucial role in both Systems Biology, where they can be explanatory and predictive, and synthetic biology, where they are effectively design templates. In this paper we give an overview of the tools and techniques which have been shown to be useful so far, and describe some of the current open challenges.


BioModel Engineering Systems Biology synthetic biology biomolecular networks qualitative stochastic and continuous Petri nets model checking 


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  1. 1.
    Aderem, A.: Systems Biology: Its Practice and Challenges. Cell 121(4), 511–513 (2005)CrossRefGoogle Scholar
  2. 2.
    Angeli, D.: Boundedness analysis for open Chemical Reaction Networks with mass-action kinetics. J. Natural Computing (2009), doi:10.1007/s11047-009-9163-7Google Scholar
  3. 3.
    Angeli, D., De Leenheer, P., Sontag, E.D.: A Petri net approach to the study of persistence in chemical reaction networks. Mathematical Biosciences 210(2), 598–618 (2007)MathSciNetCrossRefzbMATHGoogle Scholar
  4. 4.
    Aziz, A., Sanwal, K., Singhal, V., Brayton, R.: Model checking continuous time Markov chains. ACM Trans. on Computational Logic 1(1) (2000)Google Scholar
  5. 5.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model checking algorithms for continuous-time Markov chains. IEEE Trans. on Software Engineering 29(6) (2003)Google Scholar
  6. 6.
    Baldan, P., Cocco, N., Marin, A., Simeoni, M.: Petri Nets for Modelling Metabolic Pathways: a Survey. J. Natural Computing (9), 955–989 (2010)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Bonzanni, N., Krepska, E., Feenstra, K., Fokkink, W., Kielmann, T., Bal, H., Heringa, J.: Executing multicellular differentiation: quantitative predictive modelling of c. elegans vulval development. Bioinformatics 25, 2049–2056 (2009)CrossRefGoogle Scholar
  8. 8.
    Breitling, R., Donaldson, R.A., Gilbert, D., Heiner, M.: Biomodel Engineering - From Structure to Behavior. Lect. Notes Bioinformatics 5945, 1–12 (2010)zbMATHGoogle Scholar
  9. 9.
    Brightman, F.A., Fell, D.A.: Differential feedback regulation of the MAPK cascade underlies the quantitative differences in EGF and NGF signalling in PC12 cells. FEBS letters 482(3), 169–174 (2000)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Chaouiya, C.: Petri Net Modelling of Biological Networks. Briefings in Bioinformatics 8(4), 210 (2007)CrossRefGoogle Scholar
  13. 13.
    Chen, L., Masao, N., Kazuko, U., Satoru, M.: Simulation-based model checking approach to cell fate specification during c. elegans vulval development by hybrid functional Petri net with extension. BMC Systems Biology 42 (2009)Google Scholar
  14. 14.
    Chen, M., Hariharaputran, S., Hofestädt, R., Kormeier, B., Spangardt, S.: Petri net models for the semi-automatic construction of large scale biological networks. J. Natural Computing (2009), doi:10.1007/s11047-009-9151-yGoogle Scholar
  15. 15.
    Clarke, E.M., Grumberg, O., Peled, D.A.: Model checking. MIT Press, Cambridge (2001)CrossRefGoogle Scholar
  16. 16.
    David, R., Alla, H.: Discrete, Continuous, and Hybrid Petri Nets. Springer, Heidelberg (2010)CrossRefzbMATHGoogle Scholar
  17. 17.
    Doi, A., Drath, R., Nagaska, M., Matsuno, H., Miyano, S.: Protein Dynamics Observations of Lambda-Phage by Hybrid Petri net. Genome Informatics, 217–218 (1999)Google Scholar
  18. 18.
    Donaldson, R., Gilbert, D.: A model checking approach to the parameter estimation of biochemical pathways. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 269–287. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Endy, D.: Foundations for engineering biology. Nature 438(7067), 449–453 (2005)CrossRefGoogle Scholar
  20. 20.
    Fehling, R.: A concept of hierarchical Petri nets with building blocks. In: Rozenberg, G. (ed.) APN 1993. LNCS, vol. 674, pp. 148–168. Springer, Heidelberg (1993)CrossRefGoogle Scholar
  21. 21.
    Feinberg, M.: Mathematical aspects of mass action kinetics. In: Lapidus, L., Amundson, N.R. (eds.) Chemical Reactor Theory: A Review,  ch.1, pp. 1–78. Prentice-Hall, Englewood Cliffs (1977)Google Scholar
  22. 22.
    Franzke, A.: Charlie 2.0 - a multi-threaded Petri net analyzer. Diploma Thesis, Brandenburg University of Technology at Cottbus, CS Dep. (2009)Google Scholar
  23. 23.
    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)CrossRefGoogle Scholar
  24. 24.
    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)CrossRefGoogle Scholar
  25. 25.
    Gilbert, D., Heiner, M., Rosser, S., R., Fulton, X.G., Trybiło, M.: A Case Study in Model-driven Synthetic Biology. In: Proc. 2nd IFIP Conference on Biologically Inspired Collaborative Computing (BICC), IFIP WCC 2008, Milano, pp. 163–175 (2008)Google Scholar
  26. 26.
    Heinemann, M., Panke, S.: Synthetic biology - putting engineering into biology. Bioinformatics 22(22), 2790–2799 (2006), CrossRefGoogle Scholar
  27. 27.
    Heiner, M.: Understanding Network Behaviour by Structured Representations of Transition Invariants – A Petri Net Perspective on Systems and Synthetic Biology. Natural Computing Series, pp. 367–389. Springer, Heidelberg (2009), Google Scholar
  28. 28.
    Heiner, M., Donaldson, R., Gilbert, D.: Petri Nets for Systems Biology. In: Iyengar, M.S. (ed.) Symbolic Systems Biology: Theory and Methods,  ch.21, Jones and Bartlett Publishers, Inc. (2010)Google Scholar
  29. 29.
    Heiner, M., Gilbert, D., Donaldson, R.: Petri nets in systems and synthetic biology. In: Bernardo, M., Degano, P., Tennenholtz, M. (eds.) SFM 2008. LNCS, vol. 5016, pp. 215–264. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  30. 30.
    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)CrossRefGoogle Scholar
  31. 31.
    Heiner, M., Koch, I., Will, J.: Model Validation of Biological Pathways Using Petri Nets - Demonstrated for Apoptosis. BioSystems 75, 15–28 (2004)CrossRefzbMATHGoogle Scholar
  32. 32.
    Heiner, M., Lehrack, S., Gilbert, D., Marwan, W.: Extended Stochastic Petri Nets for Model-Based Design of Wetlab Experiments. Transactions on Computational Systems Biology XI, 138–163 (2009)Google Scholar
  33. 33.
    Heiner, M., Mahulea, C., Silva, M.: On the Importance of the Deadlock Trap Property for Monotonic Liveness. In: Int. Workshop on Biological Processes & Petri Nets (BioPPN), satellite event of Petri Nets 2010 (2010)Google Scholar
  34. 34.
    M., Heiner, C.R., M., Schwarick, S.S.: A Comparative Study of Stochastic Analysis Techniques. In: Proc. CMSB, pp. 96–106 (2010) ; ACM Digital Library 978-1-4503-0068-1/10/09 Google Scholar
  35. 35.
    Heiner, M., Schwarick, M., Tovchigrechko, A.: DSSZ-MC - A Tool for Symbolic Analysis of Extended Petri Nets. In: Franceschinis, G., Wolf, K. (eds.) PETRI NETS 2009. LNCS, vol. 5606, pp. 323–332. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  36. 36.
    Heiner, M., Sriram, K.: Structural analysis to determine the core of hypoxia response network. PLoS ONE 5(1), e8600 (2010),, doi:10.1371/journal.pone.0008600CrossRefGoogle Scholar
  37. 37.
    Herajy, M., Heiner, M.: Hybrid Petri Nets for Modelling of Hybrid Biochemical Interactions. In: Proc. AWPN 2010, CEUR Workshop Proceedings, vol. 643, pp. 66–79. (2010)Google Scholar
  38. 38.
    Hofestädt, R., Thelen, S.: Quantitative modeling of biochemical networks. In Silico Biol. 1, 39–53 (1998)Google Scholar
  39. 39.
    Hood, L.: Systems biology: integrating technology, biology, and computation. Mechanisms of Ageing and Development 124(1), 9–16 (2003)CrossRefGoogle Scholar
  40. 40.
    Hoops, S., Sahle, S., Gauges, R., Lee, C., Pahle, J., Simus, N., Singhal, M., Xu, L., Mendes, P., Kummer, U.: Copasi – a complex pathway simulator. BioInformatics 22(24), 3067–3074 (2006)CrossRefGoogle Scholar
  41. 41.
    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)CrossRefGoogle Scholar
  42. 42.
    Lamprecht, R., Smith, G.D., Kemper, P.: Stochastic Petri net models of Ca 2 +  signaling complexes and their analysis. J. Natural Computing (2009), doi:10.1007/s11047-009-9143-yGoogle Scholar
  43. 43.
    Lautenbach, K., Pinl, A.: A Petri net representation of Bayesian message flows: importance of Bayesian networks for biological applications. J. Natural Computing (2009), doi:10.1007/s11047-009-9142-zGoogle Scholar
  44. 44.
    Liu, F., Heiner, M.: Computation of Enabled Transition Instances for Colored Petri Nets. In: Proc. AWPN 2010, CEUR Workshop Proceedings, vol. 643, pp. 51–65. (2010)Google Scholar
  45. 45.
    Marsan, M.A., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets, 2nd edn. John Wiley and Sons, Chichester (1995)zbMATHGoogle Scholar
  46. 46.
    Marwan, W., Rohr, C., Heiner, M.: Petri nets in Snoopy: A unifying framework for the graphical display, computational modelling, and simulation of bacterial regulatory networks. Methods in Molecular Biology, vol. ch.21. Humana Press (2011)Google Scholar
  47. 47.
    Marwan, W., Sujathab, A., 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)CrossRefGoogle Scholar
  48. 48.
    Marwan, W., Wagler, A., Weismantel, R.: Petri nets as a framework for the reconstruction and analysis of signal transduction pathways and regulatory networks. J. Natural Computing (2009), doi:10.1007/s11047-009-9152-xGoogle Scholar
  49. 49.
    Merlin, P.: A Study of the Recoverability of Computing Systems. Irvine: Univ. California, PhD Thesis, available from Ann Arbor: Univ Microfilms, No. 75–11026 (1974)Google Scholar
  50. 50.
    Nagasaki, M., Saito, A., Doi, A., Matsuno, H., Miyano, S.: Foundations of Systems Biology Using Cell Illustrator and Pathway Databases. Computational Biology, vol. 13. Springer, Heidelberg (2009)zbMATHGoogle Scholar
  51. 51.
    Pagnoni, A.: Error-correcting Petri nets. J. Natural Computing (2009), doi:10.1007/s11047-009-9150-zGoogle Scholar
  52. 52.
    Palsson, B.O.: Systems Biology: Properties of Reconstructed Networks. Cambridge University Press, Cambridge (2006)CrossRefGoogle Scholar
  53. 53.
    Parker, D., Norman, G., Kwiatkowska, M.: PRISM 3.0.beta1 Users’ Guide (2006)Google Scholar
  54. 54.
    Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th IEEE Symposium on the Foundations of Computer Science (FOCS-77), pp. 46–57. IEEE Computer Society Press, Providence (1977)Google Scholar
  55. 55.
    Popova, L., Heiner, M.: Quantitative evaluation of time petri nets and applications to technical and biochemical networks. In: Proc. Int. Workshop on Concurrency, Specification and Programming (CS&P 2007), Lagów, vol. 2, pp. 473–484 (2007)Google Scholar
  56. 56.
    Popova-Zeugmann, L.: On time Petri nets. J. Inform. Process. Cybern. EIK 27(4), 227–244 (1991)zbMATHGoogle Scholar
  57. 57.
    Popova-Zeugmann, L.: Quantitative evaluation of time-dependent Petri nets and applications to biochemical networks. J. Natural Computing (2010), doi:10.1007/s11047-010-9211-3Google Scholar
  58. 58.
    Popova-Zeugmann, L., Heiner, M., Koch, I.: Time Petri Nets for Modelling and Analysis of Biochemical Networks. Fundamenta Informaticae 67 (2005)Google Scholar
  59. 59.
    Rohr, C., W., Marwan, M.H.: Snoopy - a unifying Petri net framework to investigate biomolecular networks. Bioinformatics 26(7), 974–975 (2010)Google Scholar
  60. 60.
    Schwarick, M., Heiner, M.: CSL Model Checking of Biochemical Networks with Interval Decision Diagrams. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 296–312. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  61. 61.
    Shinar, G., Feinberg, M.: Structural Sources of Robustness in Biochemical Reaction Networks. Science 327, 1389–1391 (2010)CrossRefGoogle Scholar
  62. 62.
    Silva, M., Recalde, L.: Petri nets and integrality relaxations: A view of continuous Petri net models. IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews 32(4), 314–327 (2002)CrossRefGoogle Scholar
  63. 63.
    Soliman, S., Heiner, M.: A unique transformation from ordinary differential equations to reaction networks. PlosONE 5(12), e14284 (2010)CrossRefGoogle Scholar
  64. 64.
    Valk, R.: Self-modifying nets, a natural extension of Petri nets. In: Automata, Languages and Programming. LNCS, vol. 62, pp. 464–476. Springer, Heidelberg (1978)CrossRefGoogle Scholar
  65. 65.
    Veliz-Cuba, A., Jarrah, A.S., Laubenbacher, R.: Polynomial algebra of discrete models in systems biology. Bioinformatics 26(13), 1637–1643 (2010)CrossRefzbMATHGoogle Scholar
  66. 66.
    Wagler, A., Weismantel, R.: The combinatorics of modeling and analyzing biological systems. J. Natural Computing (2009), doi:10.1007/s11047-009-9165-5Google Scholar
  67. 67.
    Wimmel, H.: Anastasia – computing traps, siphons, and more (2010),

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Monika Heiner
    • 1
  • David Gilbert
    • 1
  1. 1.School of Information Systems, Computing and MathematicsBrunel UniversityUxbridgeUK

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