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arXiv · 1209.6445

A Balance Equation Determines a Switch in Neuronal Excitability

Alessio Franci·Guillaume Drion·Vincent Seutin·Rodolphe Sepulchre
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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.

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Alessio Franci, Guillaume Drion, Vincent Seutin, Rodolphe Sepulchre. 2013-03-07. A Balance Equation Determines a Switch in Neuronal Excitability. https://doi.org/10.1371/journal.pcbi.1003040

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