A Balance Equation Determines a Switch in Neuronal Excitability

Alessio Franci (1) , Guillaume Drion (2) , Vincent Seutin (3) , Rodolphe Sepulchre (1, 2)

1 Orchestron - Orchestron : from neuronal rhythms to rhythmic brain functions
2 Institut Montefiore - Department of Electrical Engineering and Computer Science
3 Neurophysiology Unit, GIGA Neurosciences

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.

Domaines: Neurobiologie; Systèmes dynamiques [math.DS]; Neurosciences

Alessio Franci, Guillaume Drion, Vincent Seutin, Rodolphe Sepulchre. A Balance Equation Determines a Switch in Neuronal Excitability. PLoS Computational Biology, 2013, 9 (5), pp.e1003040. ⟨10.1371/journal.pcbi.1003040⟩. ⟨hal-00826259⟩