Interspike interval statistics in the stochastic Hodgkin-Huxley model: coexistence of gamma frequency bursts and highly irregular firing

Neural Comput. 2007 May;19(5):1215-50. doi: 10.1162/neco.2007.19.5.1215.


When the classical Hodgkin-Huxley equations are simulated with Na- and K-channel noise and constant applied current, the distribution of interspike intervals is bimodal: one part is an exponential tail, as often assumed, while the other is a narrow gaussian peak centered at a short interspike interval value. The gaussian arises from bursts of spikes in the gamma-frequency range, the tail from the interburst intervals, giving overall an extraordinarily high coefficient of variation--up to 2.5 for 180,000 Na channels when I approximately 7 microA/cm(2). Since neurons with a bimodal ISI distribution are common, it may be a useful model for any neuron with class 2 firing. The underlying mechanism is due to a subcritical Hopf bifurcation, together with a switching region in phase-space where a fixed point is very close to a system limit cycle. This mechanism may be present in many different classes of neurons and may contribute to widely observed highly irregular neural spiking.

MeSH terms

  • Action Potentials / physiology*
  • Action Potentials / radiation effects
  • Animals
  • Electric Stimulation / methods
  • Models, Neurological*
  • Neurons / physiology*
  • Neurons / radiation effects
  • Nonlinear Dynamics
  • Normal Distribution
  • Periodicity*
  • Probability
  • Sodium Channels / physiology
  • Stochastic Processes*
  • Time Factors


  • Sodium Channels