title: On circuit functionality in Boolean networks.
abstract: It has been proved, for several classes of continuous and discrete dynamical systems, that the presence of a positive (resp. negative) circuit in the interaction graph of a system is a necessary condition for the presence of multiple stable states (resp. a cyclic attractor). A positive (resp. negative) circuit is said to be functional when it "generates" several stable states (resp. a cyclic attractor). However, there are no definite mathematical frameworks translating the underlying meaning of "generates." Focusing on Boolean networks, we recall and propose some definitions concerning the notion of functionality along with associated mathematical results.
authors.affiliation: Lab. I3S UMR CNRS 7271, Université Nice-Sophia Antipolis, 2000 Route des Lucioles, 06903 Sophia Antipolis, France. comet@unice.fr
authors.forename: Jean-Paul
authors.initials: JP
authors.lastname: Comet
authors.forename: Mathilde
authors.initials: M
authors.lastname: Noual
authors.forename: Adrien
authors.initials: A
authors.lastname: Richard
authors.forename: Julio
authors.initials: J
authors.lastname: Aracena
authors.forename: Laurence
authors.initials: L
authors.lastname: Calzone
authors.forename: Jacques
authors.initials: J
authors.lastname: Demongeot
authors.forename: Marcelle
authors.initials: M
authors.lastname: Kaufman
authors.forename: Aurélien
authors.initials: A
authors.lastname: Naldi
authors.forename: El Houssine
authors.initials: el H
authors.lastname: Snoussi
authors.forename: Denis
authors.initials: D
authors.lastname: Thieffry
mesh_terms: D000818:Animals; D053263:Gene Regulatory Networks; D006801:Humans; D055641:Mathematical Concepts; D008957:Models, Genetic; D013598:Systems Theory