Natural Computing

, Volume 10, Issue 2, pp 727–750 | Cite as

Petri net representation of multi-valued logical regulatory graphs

Article

Abstract

Relying on a convenient logical representation of regulatory networks, we propose a generic method to qualitatively model regulatory interactions in the standard elementary and coloured Petri net frameworks. Logical functions governing the behaviours of the components of logical regulatory graphs are efficiently represented by Multivalued Decision Diagrams, which are also at the basis of the translation of logical models in terms of Petri nets. We further delineate a simple strategy to sort trajectories through the introduction of priority classes (in the logical framework) or priority functions (in the Petri net framework). We also focus on qualitative behaviours such as multistationarity or sustained oscillations, identified as specific structures in state transition graphs (for logical models) or in marking graphs (in Petri nets). Regulatory circuits are known to be at the origin of such properties. In this respect, we present a method that allows to determine the functionality contexts of regulatory circuits, i.e. constraints on external regulator states enabling the corresponding dynamical properties. Finally, this approach is illustrated through an application to the modelling of a regulatory network controlling T lymphocyte activation and differentiation.

Keywords

Gene regulation Biological networks Regulatory circuits Logical modelling Petri nets Signal transduction Cell differentiation 

References

  1. Ahmad J, Richard A, Bernot G, Comet J-P, Roux O (2006) Delays in biological regulatory networks (BRN). Lect Notes Comput Sci 3992:887–894CrossRefGoogle Scholar
  2. Alberts B, Johnson A, Lewis J, Raff M, Roberts K, Walter P (2008) Molecular biology of the cell, 5th edn. Garland Science/Taylor & Francis, New YorkGoogle Scholar
  3. Chaouiya C, Remy E, Mossé B, Thieffry D (2003) Qualitative analysis of regulatory graphs: a computational tool based on a discrete formal framework. Lect Notes Control Inf Sci 294:119–126Google Scholar
  4. Chaouiya C, Remy E, Ruet P, Thieffry D (2004) Qualitative modelling of genetic networks: from logical regulatory graphs to standard Petri nets. Lect Notes Comput Sci 3099:137–156MathSciNetCrossRefGoogle Scholar
  5. Chaouiya C, Remy E, Thieffry D (2006) Qualitative Petri net modelling of genetic networks. Lect Notes Comput Sci 4220:95–112MathSciNetCrossRefGoogle Scholar
  6. Chaouiya C, Remy E, Thieffry D (2008) Petri net modelling of biological regulatory networks. J Discrete Algorithms 6(2):165–177MathSciNetMATHGoogle Scholar
  7. Comet J-P, Klaudel H, Liauzu S (2005) Modeling multi-valued genetic regulatory networks using high-level Petri nets. Lect Notes Comput Sci 3536:208–227Google Scholar
  8. de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 1:67–103CrossRefGoogle Scholar
  9. Doi A, Nagasaki M, Matsuno H, Miyano S (2006) Simulation-based validation of the p53 transcriptional activity with hybrid functional Petri net. In Silico Biol 6:1–13Google Scholar
  10. Fauré A, Naldi A, Chaouiya C, Thieffry D (2006) Dynamical analysis of a generic Boolean model for the control of the mammalian cell cycle. Bioinformatics 22:124–131CrossRefGoogle Scholar
  11. Fauré A, Naldi A, Lopez F, Chaouiya C, Ciliberto A, Thieffry D (2009) Modular logical modelling of the budding yeast cell cycle. Mol Biosyst 5:1787–1796CrossRefGoogle Scholar
  12. Garg A, Xenarios I, Mendoza L, De Micheli G (2007) An efficient method for dynamic analysis of gene regulatory networks and in-silico gene perturbation experiments. Lect Notes Comput Sci 4453:62–76CrossRefGoogle Scholar
  13. González A, Chaouiya C, Thieffry D (2008) Logical modelling of the role of the Hh pathway in the patterning of the Drosophila wing disc. Bioinformatics 24:i234–i240CrossRefGoogle Scholar
  14. Goss PJ, Peccoud J (1998) Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc Natl Acad Sci USA 95:6750–6755CrossRefGoogle Scholar
  15. Grafahrend-Belau E, Schreiber F, Heiner M, Sackmann A, Junker BH, Grunwald S, Speer A, Winder K, Koch I (2008) Modularization of biochemical networks based on classification of Petri net t-invariants. BMC Bioinformatics 9:90CrossRefGoogle Scholar
  16. Heiner M, Gilbert D, Donaldson R (2008) Petri nets for systems and synthetic biology. Lect Notes Comput Sci 5016:215–264CrossRefGoogle Scholar
  17. INA, Integrated Net Analyzer, tool for the analysis of (Coloured) PNs: http://www.informatik.hu-berlin.de/~starke/ina.html
  18. Kam T, Villa T, Brayton RK, Sangiovanni-Vincentelli AL (1998) Multi-valued decision diagrams: theory and applications. Int J Multiple-Valued Logic 4:9–62MathSciNetMATHGoogle Scholar
  19. Kauffman S (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, New YorkGoogle Scholar
  20. Klamt S, Saez-Rodriguez J, Lindquist JA, Simeoni L, Gilles ED (2006) A methodology for the structural and functional analysis of signaling and regulatory networks. BMC Bioinformatics 7:56CrossRefGoogle Scholar
  21. Li C, Ge QW, Nakata M, Matsuno H, Miyano S (2007) Modelling and simulation of signal transductions in an apoptosis pathway by using timed Petri nets. J Biosci 32:113–127CrossRefGoogle Scholar
  22. Marsan MA, Balbo G, Conte G, Donatelli S, Franceschinis G (1994) Modelling with generalized stochastic Petri nets. Wiley, New YorkGoogle Scholar
  23. Mendoza L (2006) A network model for the control of the differentiation process in Th cells. Biosystems 84:101–114CrossRefGoogle Scholar
  24. Mura I, Csikasz-Nagy A (2008) Stochastic Petri net extension of a yeast cell cycle model. J Theor Biol 254(4):850–860CrossRefGoogle Scholar
  25. Nagasaki M, Doi A, Matsuno H, Miyano S (2004) A versatile Petri net based architecture for modeling and simulation of complex biological processes. Genome Inform 15:180–197Google Scholar
  26. Naldi A, Thieffry D, Chaouiya C (2007) Decision diagrams for the representation of logical models of regulatory networks. Lect Notes Bioinform 4695:233–247Google Scholar
  27. Naldi A, Berenguier D, Fauré A, Lopez F, Thieffry D, Chaouiya C (2009a) Logical modelling of regulatory networks with GINsim 2.3. Biosystems 97(2):134–139CrossRefGoogle Scholar
  28. Naldi A, Remy E, Thieffry D, Chaouiya C (2009b) A reduction method for logical regulatory graphs preserving essential dynamical properties. Lect Notes Bioinform 5688:266–280Google Scholar
  29. Remy E, Ruet P, Thieffry D (2006a) Positive or negative regulatory circuit inference from multilevel dynamics. Lect Notes Control Inf Sci 341:263–270MathSciNetCrossRefGoogle Scholar
  30. Remy E, Ruet P, Mendoza L, Thieffry D, Chaouiya C (2006b) From logical regulatory graphs to standard Petri nets: dynamical roles and functionality of feedback circuits. Lect Notes Comput Sci 4230:55–72MathSciNetGoogle Scholar
  31. Richard A, Comet J-P (2007) Necessary conditions for multistationarity in discrete dynamical systems. Discret Appl Math 155(18):2403–2413MathSciNetMATHCrossRefGoogle Scholar
  32. Sackmann A, Heiner M, Koch I (2006) Application of Petri net based analysis techniques to signal transduction pathways. BMC Bioinformatics 7:482CrossRefGoogle Scholar
  33. Sánchez L, Chaouiya C, Thieffry D (2008) Segmenting the fly embryo: a logical analysis of the segment polarity cross-regulatory module. Int J Dev Biol 52(8):1059–1075CrossRefGoogle Scholar
  34. Schlitt T, Brazma A (2007) Current approaches to gene regulatory network modelling. BMC Bioinformatics 8:S9CrossRefGoogle Scholar
  35. Siebert H, Bockmayr A (2006) Incorporating time delays into the logical analysis of gene regulatory networks. Lect Notes Comput Sci 4210:169–183MathSciNetCrossRefGoogle Scholar
  36. Siebert H, Bockmayr A (2007) Context sensitivity in logical modeling with time delays. Lect Notes Comput Sci 4695:64–79CrossRefGoogle Scholar
  37. Simão E, Remy E, Thieffry D, Chaouiya C (2005) Qualitative modelling of regulated metabolic pathways: application to the tryptophan biosynthesis in E. coli. Bioinformatics 21:ii190–ii196CrossRefGoogle Scholar
  38. Soulé C (2006) Mathematical approaches to gene regulation and differentiation. CR Acad Sci Paris (Biol) 329:13–20Google Scholar
  39. Srivastava R, Peterson MS, Bentley WE (2001) Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32-targeted antisense. Biotechnol Bioeng 75:120–129CrossRefGoogle Scholar
  40. Steggles LJ, Banks R, Shaw O, Wipat A (2007) Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach. Bioinformatics 23:336–343CrossRefGoogle Scholar
  41. Thieffry D (2007) Dynamical roles of biological regulatory circuits. Brief Bioinform 8:220–225CrossRefGoogle Scholar
  42. Thomas R (1991) Regulatory networks seen as asynchronous automata: a logical description. J Theor Biol 153(1):1–23CrossRefGoogle Scholar
  43. Thomas R, D’Ari R (1990) Biological feedback. CRC Press, Boca RatonMATHGoogle Scholar
  44. Thomas R, Thieffry D, Kaufman M (1995) Dynamical behaviour of biological regulatory networks—I. Biological role of feedback loops and practical use of the concept of the loop-characteristic state. Bull Math Biol 57(2):247–276MATHGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2010

Authors and Affiliations

  • C. Chaouiya
    • 1
    • 2
  • A. Naldi
    • 2
    • 3
  • E. Remy
    • 4
  • D. Thieffry
    • 2
    • 3
    • 5
  1. 1.Instituto Gulbenkian de CiênciaOeirasPortugal
  2. 2.INSERM U928—TAGCMarseilleFrance
  3. 3.Université de la MéditerranéeMarseilleFrance
  4. 4.Institut de Mathématiques de LuminyMarseilleFrance
  5. 5.CONTRAINTES ProjectINRIA-Paris-RocquencourtLe ChesnayFrance

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