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Local negative circuits and cyclic attractors in Boolean networks with at most five components

Tonello, Elisa; Farcot, Etienne; Chaouiya, Claudine

Local negative circuits and cyclic attractors in Boolean networks with at most five components Thumbnail


Authors

Elisa Tonello

Claudine Chaouiya



Abstract

We consider the following question on the relationship between the asymptotic behaviors of asynchronous dynamics of Boolean networks and their regulatory structures: Does the presence of a cyclic attractor imply the existence of a local negative circuit in the regulatory graph? When the number of model components n verifies n ≥ 6, the answer is known to be negative. We show that the question can be translated into a Boolean satisfiability problem on n · 2n variables. A Boolean formula expressing the absence of local negative circuits and a necessary condition for the existence of cyclic attractors is found to be unsatisfiable for n ≤ 5. In other words, for Boolean networks with up to 5 components, the presence of a cyclic attractor requires the existence of a local negative circuit.

Journal Article Type Article
Acceptance Date Oct 12, 2018
Online Publication Date Jan 15, 2019
Publication Date Jan 15, 2019
Deposit Date Jan 18, 2019
Publicly Available Date Jan 21, 2019
Journal SIAM Journal on Applied Dynamical Systems
Print ISSN 1536-0040
Electronic ISSN 1536-0040
Publisher Society for Industrial and Applied Mathematics
Peer Reviewed Peer Reviewed
Volume 18
Issue 1
Pages 68-79
DOI https://doi.org/10.1137/18m1173988
Keywords Modelling and Simulation; Analysis
Public URL https://nottingham-repository.worktribe.com/output/1481812
Publisher URL https://epubs.siam.org/doi/10.1137/18M1173988

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