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.
Cite
@article{arxiv.1209.6445,
title = {A Balance Equation Determines a Switch in Neuronal Excitability},
author = {Alessio Franci and Guillaume Drion and Vincent Seutin and Rodolphe Sepulchre},
journal= {arXiv preprint arXiv:1209.6445},
year = {2015}
}