A Novel Phase Portrait to Understand Neuronal Excitability
  Fifty years ago, Fitzugh 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 the 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 Fitzugh-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 complexication of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which the calcium conductance controls the two distinct firing modes of thalamocortical neurons. 
Alessio Franci, Guillaume Drion, Vincent Seutin, and Rodolphe   Sepulchre
math.DS q-bio.NC