Petri net representation of multi-valued logical regulatory graphs |
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Authors: | C Chaouiya A Naldi E Remy D Thieffry |
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Affiliation: | (1) Instituto Gulbenkian de Ci?ncia, Oeiras, Portugal;(2) INSERM U928—TAGC, Marseille, France;(3) Universit? de la M?diterran?e, Marseille, France;(4) Institut de Math?matiques de Luminy, Marseille, France;(5) CONTRAINTES Project, INRIA-Paris-Rocquencourt, Le Chesnay, France |
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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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