Limit cycle analysis of a class of hybrid gene regulatory networks

Honglu Sun (1) , Maxime Folschette (2) , Morgan Magnin (1)

1 LS2N - équipe MéForBio - Méthodes Formelles pour la Bioinformatique
2 BioComputing

Our objective: Find limit cycles and analyze their stability in a hybrid modeling framework of gene regulatory networks [Cornillon et al. 2016] [Behaegel, Comet, Bernot, et al. 2016] [Behaegel, Comet, and Folschette 2017] which extends René Thomas' discrete modeling. Our idea: Extend Poincaré map to this hybrid framework. Our contribution: We search for potential cycles by abstracting the continuous trajectory into a succession of visited discrete domains. Then we introduce transition matrices and stable zones to analyze the concrete continuous dynamics and find the actual cycles that are stable.

Domaines: Bio-informatique [q-bio.QM]

Honglu Sun, Maxime Folschette, Morgan Magnin. Limit cycle analysis of a class of hybrid gene regulatory networks. Journées Nationales de l’Informatique Mathématique (JNIM 2022), Mar 2022, Lille, France. ⟨hal-03700402⟩