Email updates

Keep up to date with the latest news and content from BMC Neuroscience and BioMed Central.

This article is part of the supplement: Eighteenth Annual Computational Neuroscience Meeting: CNS*2009

Open Access Poster presentation

Resonant response of a Hodgkin-Huxley neuron to a spike train input

Lech S Borkowski

Author Affiliations

Quantum Physics Division, Faculty of Physics, Adam Mickiewicz University, 61-614 Poznan, Poland

BMC Neuroscience 2009, 10(Suppl 1):P250  doi:10.1186/1471-2202-10-S1-P250

The electronic version of this article is the complete one and can be found online at:

Published:13 July 2009

© 2009 Borkowski; licensee BioMed Central Ltd.


Experiments show that neurons have a tendency to respond to signals tuned to a resonant frequency [1]. In order to understand the general properties of a resonant response of a neuron, we study the silent Hodgkin-Huxley neuron driven by periodic input. The current arriving through the synapse consists of a set of spikes Ip(t) ~ gsyn ∑(t/τ) exp(-t/τ) C(t) (Va-Vsyn), where gsyn is the synapse conductivity, τ is the time constant associated with the synapse conduction, Va is the maximum membrane potential and Vsyn is the reversal potential of the synapse.


See Figures 1 and 2.

thumbnailFigure 1. The phase diagram for typical HH model parameters [2]in the limit of small synaptic conductivity. There is a well-pronounced minimum at Ti = 17.5 ms. The resonant nature of the response can be seen also at multiples of this value, at Ti ≈ 34 ms and Ti ≈ 50 ms. Near the resonance the system has the tendency to mode locking with high values of k, where k = To/Ti is the ratio of the output ISI to the input ISI. For example near the main resonance frequency we find narrow regions with k = 5, 6 or 9. Areas with bistable solutions are shown in grey. We expect the resonance at Ti = 17.5 ms to survive in the presence of noise.

thumbnailFigure 2. In the limit of small Ti the distinction between the firing spikes and subthreshold oscillations disappears and the output signal decreases to 0 for sufficiently large gsyn. Broken line in the figure indicates a transition to nonfiring behavior. In the area below this transition the amplitude of the spikes gradually increases. Solid lines are borders of the mode-locked states with different values of k. Properties of this model are similar to the HH model with a sinusoidal driving current at intermediate values of input ISI Ti = 5–12 ms. However the results in both the high and the low frequency regime are qualitatively different. In the case of a sinusoidal input there is only one resonance frequency and reported values of k are lower [3].


Part of the numerical computation was performed in the Computer Center of the Tri-city Academic Computer Network in Gdansk, Poland.


  1. Hutcheon B, Yarom Y: Resonance, oscillation and the intrinsic frequency preference of neurons.

    Trends Neurosci 2000, 23:216-222. PubMed Abstract | Publisher Full Text OpenURL

  2. Hasegawa H: Responses of a Hodgkin-Huxley neuron to various types of spike-train inputs.

    Phys Rev E 2000, 61:718-726. Publisher Full Text OpenURL

  3. Lee SG, Kim S: Bifurcation analysis of mode-locking structure in a Hodgkin-Huxley neuron under sinusoidal current.

    Phys Rev E 2006, 73:041924. Publisher Full Text OpenURL