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PLoS Comput Biol. 2013;9(5):e1003040. doi: 10.1371/journal.pcbi.1003040. Epub 2013 May 23.

A balance equation determines a switch in neuronal excitability.

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INRIA Lille-Nord Europe, Orchestron Project, Villeneuve d'Ascq, France.


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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