Positive circuits and maximal number of fixed points in discrete dynamical systems
Discrete Applied Mathematics
A Reduction of Logical Regulatory Graphs Preserving Essential Dynamical Properties
CMSB '09 Proceedings of the 7th International Conference on Computational Methods in Systems Biology
Dynamically consistent reduction of logical regulatory graphs
Theoretical Computer Science
Logic programming for Boolean networks
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
Efficient handling of large signalling-regulatory networks by focusing on their core control
CMSB'12 Proceedings of the 10th international conference on Computational Methods in Systems Biology
From kernels in directed graphs to fixed points and negative cycles in Boolean networks
Discrete Applied Mathematics
Learning from interpretation transition
Machine Learning
Formal Analysis of Oscillatory Behaviors in Biological Regulatory Networks: An Alternative Approach
Electronic Notes in Theoretical Computer Science (ENTCS)
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It is acknowledged that the presence of positive or negative circuits in regulatory networks such as genetic networks is linked to the emergence of significant dynamical properties such as multistability (involved in differentiation) and periodic oscillations (involved in homeostasis). Rules proposed by the biologist R. Thomas assert that these circuits are necessary for such dynamical properties. These rules have been studied by several authors. Their obvious interest is that they relate the rather simple information contained in the structure of the network (signed circuits) to its much more complex dynamical behaviour. We prove in this article a nontrivial converse of these rules, namely that certain positive or negative circuits in a regulatory graph are actually sufficient for the observation of a restricted form of the corresponding dynamical property, differentiation or homeostasis. More precisely, the crucial property that we require is that the circuit be globally minimal. We then apply these results to the vertebrate immune system, and show that the two minimal functional positive circuits of the model indeed behave as modules which combine to explain the presence of the three stable states corresponding to the Th0, Th1 and Th2 cells. Contact: ruet@iml.univ-mrs.fr Supplementary information: Supplementary data are available at Bioinformatics online.