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Petri net representation of multi-valued logical regulatory graphs

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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.

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Notes

  1. Multigraphs are also called pseudographs.

  2. \({{\mathbb{N}}}^*\) is the set of non-zero natural numbers.

  3. For \(x\in{\mathbb{Z}}, sign(x)=+1\) if x > 0, − 1 if x < 0, 0 otherwise.

References

  • Ahmad J, Richard A, Bernot G, Comet J-P, Roux O (2006) Delays in biological regulatory networks (BRN). Lect Notes Comput Sci 3992:887–894

    Article  Google Scholar 

  • 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 York

    Google Scholar 

  • 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 294:119–126

    Google Scholar 

  • 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 3099:137–156

    Article  MathSciNet  Google Scholar 

  • Chaouiya C, Remy E, Thieffry D (2006) Qualitative Petri net modelling of genetic networks. Lect Notes Comput Sci 4220:95–112

    Article  MathSciNet  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Comet J-P, Klaudel H, Liauzu S (2005) Modeling multi-valued genetic regulatory networks using high-level Petri nets. Lect Notes Comput Sci 3536:208–227

    Google Scholar 

  • de Jong H (2002) Modeling and simulation of genetic regulatory systems: a literature review. J Comput Biol 1:67–103

    Article  Google Scholar 

  • 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 6:1–13

    Google Scholar 

  • 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 22:124–131

    Article  Google Scholar 

  • Fauré A, Naldi A, Lopez F, Chaouiya C, Ciliberto A, Thieffry D (2009) Modular logical modelling of the budding yeast cell cycle. Mol Biosyst 5:1787–1796

    Article  Google Scholar 

  • 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 4453:62–76

    Article  Google Scholar 

  • GINsim web page: http://gin.univ-mrs.fr/GINsim/

  • 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–i240

    Article  Google Scholar 

  • Goss PJ, Peccoud J (1998) Quantitative modeling of stochastic systems in molecular biology by using stochastic Petri nets. Proc Natl Acad Sci USA 95:6750–6755

    Article  Google Scholar 

  • 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 9:90

    Article  Google Scholar 

  • Heiner M, Gilbert D, Donaldson R (2008) Petri nets for systems and synthetic biology. Lect Notes Comput Sci 5016:215–264

    Article  Google Scholar 

  • INA, Integrated Net Analyzer, tool for the analysis of (Coloured) PNs: http://www.informatik.hu-berlin.de/~starke/ina.html

  • Kam T, Villa T, Brayton RK, Sangiovanni-Vincentelli AL (1998) Multi-valued decision diagrams: theory and applications. Int J Multiple-Valued Logic 4:9–62

    MathSciNet  MATH  Google Scholar 

  • Kauffman S (1993) The origins of order: self-organization and selection in evolution. Oxford University Press, New York

    Google Scholar 

  • 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 7:56

    Article  Google Scholar 

  • 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 32:113–127

    Article  Google Scholar 

  • Marsan MA, Balbo G, Conte G, Donatelli S, Franceschinis G (1994) Modelling with generalized stochastic Petri nets. Wiley, New York

    Google Scholar 

  • Mendoza L (2006) A network model for the control of the differentiation process in Th cells. Biosystems 84:101–114

    Article  Google Scholar 

  • Mura I, Csikasz-Nagy A (2008) Stochastic Petri net extension of a yeast cell cycle model. J Theor Biol 254(4):850–860

    Article  Google Scholar 

  • 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 15:180–197

    Google Scholar 

  • Naldi A, Thieffry D, Chaouiya C (2007) Decision diagrams for the representation of logical models of regulatory networks. Lect Notes Bioinform 4695:233–247

    Google Scholar 

  • 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):134–139

    Article  Google Scholar 

  • Naldi A, Remy E, Thieffry D, Chaouiya C (2009b) A reduction method for logical regulatory graphs preserving essential dynamical properties. Lect Notes Bioinform 5688:266–280

    Google Scholar 

  • Remy E, Ruet P, Thieffry D (2006a) Positive or negative regulatory circuit inference from multilevel dynamics. Lect Notes Control Inf Sci 341:263–270

    Article  MathSciNet  Google Scholar 

  • 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 4230:55–72

    MathSciNet  Google Scholar 

  • Richard A, Comet J-P (2007) Necessary conditions for multistationarity in discrete dynamical systems. Discret Appl Math 155(18):2403–2413

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • 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):1059–1075

    Article  Google Scholar 

  • Schlitt T, Brazma A (2007) Current approaches to gene regulatory network modelling. BMC Bioinformatics 8:S9

    Article  Google Scholar 

  • Siebert H, Bockmayr A (2006) Incorporating time delays into the logical analysis of gene regulatory networks. Lect Notes Comput Sci 4210:169–183

    Article  MathSciNet  Google Scholar 

  • Siebert H, Bockmayr A (2007) Context sensitivity in logical modeling with time delays. Lect Notes Comput Sci 4695:64–79

    Article  Google Scholar 

  • 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–ii196

    Article  Google Scholar 

  • Soulé C (2006) Mathematical approaches to gene regulation and differentiation. CR Acad Sci Paris (Biol) 329:13–20

    Google Scholar 

  • Srivastava R, Peterson MS, Bentley WE (2001) Stochastic kinetic analysis of the Escherichia coli stress circuit using σ32-targeted antisense. Biotechnol Bioeng 75:120–129

    Article  Google Scholar 

  • Steggles LJ, Banks R, Shaw O, Wipat A (2007) Qualitatively modelling and analysing genetic regulatory networks: a Petri net approach. Bioinformatics 23:336–343

    Article  Google Scholar 

  • Thieffry D (2007) Dynamical roles of biological regulatory circuits. Brief Bioinform 8:220–225

    Article  Google Scholar 

  • Thomas R (1991) Regulatory networks seen as asynchronous automata: a logical description. J Theor Biol 153(1):1–23

    Article  Google Scholar 

  • Thomas R, D’Ari R (1990) Biological feedback. CRC Press, Boca Raton

    MATH  Google Scholar 

  • 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):247–276

    MATH  Google Scholar 

Download references

Acknowledgments

A.N. has been supported by a PhD grant from the French Ministry of Research and Technology. C.C. acknowledges the support provided by the Calouste Gulbenkian Foundation. This work was further supported by research grants from the French National Agency (projects ANR-06-BYOS-0006 and ANR-08-SYSC-003), and from the Belgian Science Policy Office (IAP BioMaGNet).

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Authors and Affiliations

  1. Instituto Gulbenkian de Ciência, Oeiras, Portugal

    C. Chaouiya

  2. INSERM U928—TAGC, Marseille, France

    C. Chaouiya, A. Naldi & D. Thieffry

  3. Université de la Méditerranée, Marseille, France

    A. Naldi & D. Thieffry

  4. Institut de Mathématiques de Luminy, Marseille, France

    E. Remy

  5. CONTRAINTES Project, INRIA-Paris-Rocquencourt, Le Chesnay, France

    D. Thieffry

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  1. C. Chaouiya
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  2. A. Naldi
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  4. D. Thieffry
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Correspondence to C. Chaouiya.

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Chaouiya, C., Naldi, A., Remy, E. et al. Petri net representation of multi-valued logical regulatory graphs. Nat Comput 10, 727–750 (2011). https://doi.org/10.1007/s11047-010-9178-0

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