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A Novel Phase Portrait for Neuronal Excitability

Authors
Journal
PLoS ONE
1932-6203
Publisher
Public Library of Science
Publication Date
Volume
7
Issue
8
Identifiers
DOI: 10.1371/journal.pone.0041806
Keywords
  • Research Article
  • Biology
  • Anatomy And Physiology
  • Electrophysiology
  • Molecular Cell Biology
  • Cellular Types
  • Neurons
  • Signal Transduction
  • Signaling Cascades
  • Calcium Signaling Cascade
  • Neuroscience
  • Cellular Neuroscience
  • Ion Channels
  • Computational Neuroscience
  • Single Neuron Function
  • Mathematics
  • Nonlinear Dynamics
Disciplines
  • Biology

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.

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