title: A balance equation determines a switch in neuronal excitability.
abstract: We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.
authors.affiliation: INRIA Lille-Nord Europe, Orchestron Project, Villeneuve d'Ascq, France.
authors.forename: Alessio
authors.initials: A
authors.lastname: Franci
authors.forename: Guillaume
authors.initials: G
authors.lastname: Drion
authors.forename: Vincent
authors.initials: V
authors.lastname: Seutin
authors.forename: Rodolphe
authors.initials: R
authors.lastname: Sepulchre
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D000818:Animals; D001369:Axons / Q000502:physiology; D049832:Decapodiformes; D025461:Feedback, Physiological; D007473:Ion Channels / Q000502:physiology; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology*; D051381:Rats
chemical_list: D007473:Ion Channels