A balance equation determines a switch in neuronal excitability

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


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.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology
  • Algorithms
  • Animals
  • Axons / physiology
  • Decapodiformes
  • Feedback, Physiological
  • Ion Channels / physiology
  • Models, Neurological*
  • Neurons / physiology*
  • Rats


  • Ion Channels

Grant support

This paper presents research results of the Belgian Network DYSCO (Dynamical Systems, Control, and Optimization), funded by the Interuniversity Attraction Poles Programme, initiated by the Belgian State, Science Policy Oce. The scientific responsibility rests with its authors. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.