A novel phase portrait for neuronal excitability

PLoS One. 2012;7(8):e41806. doi: 10.1371/journal.pone.0041806. Epub 2012 Aug 8.

Abstract

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons.

Publication types

  • Research Support, Non-U.S. Gov't

MeSH terms

  • Action Potentials / physiology
  • Algorithms
  • Calcium Channels / metabolism*
  • Cell Membrane / metabolism
  • Cerebral Cortex / metabolism
  • Humans
  • Membrane Potentials / physiology
  • Models, Biological
  • Models, Neurological
  • Models, Theoretical
  • Neurons / metabolism*
  • Neurophysiology / methods*
  • Thalamus / metabolism
  • Time Factors

Substances

  • Calcium Channels

Grants and funding

The research leading to these results has received funding from the European Union Seventh Framework Programme [FP7/2007–2013] under grant agreement n 257462 HYCON2 Network of excellence, from grant 9.4560.03 from the F.R.S.-FNRS (VS), from two grants from the Belgian Science Policy (IAP6/31 (VS) and IAP6/4 (RS)), and from the Fonds Léon Fredericq (GD). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.