Modelling with Generalized Stochastic Petri Nets
Modelling with Generalized Stochastic Petri Nets
Necessary conditions for multistationarity in discrete dynamical systems
Discrete Applied Mathematics
Petri net modelling of biological regulatory networks
Journal of Discrete Algorithms
A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
RECOMB'07 Proceedings of the 11th annual international conference on Research in computational molecular biology
Context sensitivity in logical modeling with time delays
CMSB'07 Proceedings of the 2007 international conference on Computational methods in systems biology
Decision diagrams for the representation and analysis of logical models of genetic networks
CMSB'07 Proceedings of the 2007 international conference on Computational methods in systems biology
Petri nets for systems and synthetic biology
SFM'08 Proceedings of the Formal methods for the design of computer, communication, and software systems 8th international conference on Formal methods for computational systems biology
Incorporating time delays into the logical analysis of gene regulatory networks
CMSB'06 Proceedings of the 2006 international conference on Computational Methods in Systems Biology
Qualitative petri net modelling of genetic networks
Transactions on Computational Systems Biology VI
Modeling multi-valued genetic regulatory networks using high-level petri nets
ICATPN'05 Proceedings of the 26th international conference on Applications and Theory of Petri Nets
Delays in biological regulatory networks (BRN)
ICCS'06 Proceedings of the 6th international conference on Computational Science - Volume Part II
Transactions on Computational Systems Biology VII
Dynamically consistent reduction of logical regulatory graphs
Theoretical Computer Science
Integrated regulatory networks (IRNs): Spatially organized biochemical modules
Theoretical Computer Science
Control Flow Analysis of Generalised Boolean Networks
Electronic Notes in Theoretical Computer Science (ENTCS)
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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.