A Balance Equation Determines a Switch in Neuronal Excitability

TL;DR

This paper presents a mathematical condition based on a planar phase portrait that predicts a switch in neuronal excitability through a transcritical bifurcation, applicable across various conductance-based models.

Contribution

It introduces a simple mathematical criterion for excitability switches in neurons, linking geometry and bifurcation analysis to physiological mechanisms.

Findings

The condition predicts excitability switches in all tested models.

A transcritical bifurcation underlies the excitability change.

The mechanism is likely relevant across many neuron types.

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.