Natural Computing

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

Petri net representation of multi-valued logical regulatory graphs

  • C. Chaouiya
  • A. Naldi
  • E. Remy
  • D. Thieffry


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.


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



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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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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