Journal of Computational Neuroscience

, Volume 37, Issue 1, pp 181–191 | Cite as

A simple Markov model of sodium channels with a dynamic threshold

  • A. V. Chizhov
  • E. Yu. Smirnova
  • K. Kh. Kim
  • A. V. Zaitsev


Characteristics of action potential generation are important to understanding brain functioning and, thus, must be understood and modeled. It is still an open question what model can describe concurrently the phenomena of sharp spike shape, the spike threshold variability, and the divisive effect of shunting on the gain of frequency-current dependence. We reproduced these three effects experimentally by patch-clamp recordings in cortical slices, but we failed to simulate them by any of 11 known neuron models, including one- and multi-compartment, with Hodgkin-Huxley and Markov equation-based sodium channel approximations, and those taking into account sodium channel subtype heterogeneity. Basing on our voltage-clamp data characterizing the dependence of sodium channel activation threshold on history of depolarization, we propose a 3-state Markov model with a closed-to-open state transition threshold dependent on slow inactivation. This model reproduces the all three phenomena. As a reduction of this model, a leaky integrate-and-fire model with a dynamic threshold also shows the effect of gain reduction by shunt. These results argue for the mechanism of gain reduction through threshold dynamics determined by the slow inactivation of sodium channels.


Divisive effect Spike shape Spike threshold Sodium channels Conductance-based neurons Dynamic patch-clamp 



The reported study was supported by RFBR, research projects 11-04-01281a and 13-04-01835a.

Conflict of interest

The authors declare that they have no conflict of interest.

Supplementary material

10827_2014_496_MOESM1_ESM.doc (1.4 mb)
ESM 1 (DOC 1387 kb)


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • A. V. Chizhov
    • 1
  • E. Yu. Smirnova
    • 1
  • K. Kh. Kim
    • 2
  • A. V. Zaitsev
    • 2
  1. 1.A.F. Ioffe Physical-Technical Institute of the Russian Academy of SciencesSaint-PetersburgRussia
  2. 2.Sechenov Institute of Evolutionary Physiology and Biochemistry of the Russian Academy of SciencesSaint-PetersburgRussia

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