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A dynamical system analysis of the adaptive spike threshold

BMC Neuroscience20078 (Suppl 2) :P119

  • Published:


  • Differential Equation
  • Animal Model
  • Dynamical System
  • Phase Space
  • Membrane Potential
Recent in vivo experiments have revealed that the action potential threshold depends on the rate of depolarization just preceding the spike. This phenomenon can be reproduced in the Hodgkin-Huxley model. We analyzed spike initiation in the (V, h) phase space, where h is the sodium inactivation variable, and found that the dynamical system exhibits a saddle equilibrium, whose stable manifold is the curve of the threshold. We derived an equation of this manifold, which relates the threshold to the sodium inactivation variable. It leads to a differential equation of the threshold depending on the membrane potential, which translates into an integrate-and-fire model with an adaptive threshold. The model accounts well for the variability of threshold and the slope-threshold relationship. See figure 1.
Figure 1
Figure 1

Sample trace of a noise-driven integrate-and-fire model with adaptive threshold. Blue: membrane potential, red: spike threshold.



This work was partially supported by the EC IP project FP6-015879, FACETS, and the EADS Corporate Research Foundation.

Authors’ Affiliations

Odyssee (INRIA/ENS/ENPC), Département d'Informatique, Ecole Normale Supérieure, 45, rue d'Ulm, 75230 Paris Cedex 05, France


© Platkiewicz and Brette; licensee BioMed Central Ltd. 2007

This article is published under license to BioMed Central Ltd.