Qualitative petri net modelling of genetic networks
Transactions on Computational Systems Biology VI
Transactions on Computational Systems Biology VII
Modeling of Genetic Regulatory Network in Stochastic π-Calculus
BICoB '09 Proceedings of the 1st International Conference on Bioinformatics and Computational Biology
Quantitative Pathway Logic for Computational Biology
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Discrete Semantics for Hybrid Automata
Discrete Event Dynamic Systems
Petri nets for modelling metabolic pathways: a survey
Natural Computing: an international journal
Petri net representation of multi-valued logical regulatory graphs
Natural Computing: an international journal
An abstraction theory for qualitative models of biological systems
Theoretical Computer Science
Mean square stability of stochastic impulsive genetic regulatory networks with mixed time-delays
ISNN'12 Proceedings of the 9th international conference on Advances in Neural Networks - Volume Part I
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The complexity of biological regulatory networks often defies the intuition of the biologist and calls for the development of proper mathematical methods to model their structures and to delineate their dynamical properties. One qualitative approach consists in modelling regulatory networks in terms of logical equations (using either Boolean or multi-level discretisations). The Petri Net (PN) formalism offers a complementary framework to analyse the dynamical behaviour of large systems, either from a qualitative or from a quantitative point of view. Our proposal consists in articulating the logical approach with the PN formalism. In a previous work, we have already defined a systematic re-writing of Boolean regulatory models into a standard PN formalism. In this paper, we propose a rigorous and systematic mapping of multi-level logical regulatory models into specific standard Petri nets, called Multi-level Regulatory Petri Nets (MRPNs). We further propose some reduction strategies. Consequently, the resulting models become amenable to the algebraic and computational analyses used by the PN community. To illustrate our approach, we apply it to a multi-level logical model of the genetic switch controlling the lysis-lysogeny decision in the lambda bacteriophage.