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Firing frequency response to current and conductance periodic inputs in a Ih/INap biophysical neuron model

Various neurons exhibit membrane potential (or subthreshold) resonance [1], a peak in the subthreshold voltage amplitude response to oscillatory current inputs at a certain preferred (resonant) input frequency. Previous theoretical work using linear models has shown that subthreshold resonance can be communicated to the supra-threshold regime [2, 3]; i.e., the firing frequency (or signal gain) response to oscillatory input currents peaks at the subthreshold resonant frequency. Whether this property is maintained under more general conditions and for different types of inputs is still an open question.

In this work, we investigate the firing frequency patterns generated in response to both current and conductance sinusoidal inputs in a biophysical (conductance-based) neuron model that includes two ionic currents: h- (Ih) and persistent sodium (INap). This model is based on measurements for stellate cells (SCs) in layer II of the medial entorhinal cortex [4] and captures various phenomena observed in SCs such as membrane potential oscillations and membrane potential (subthreshold) resonance at theta frequencies (4 - 10 Hz)[2]. The Ih/INap model describes the cell's subthreshold dynamics and the onset of spikes [5]. Spikes were generated artificially as in integrate/resonate-and-fire models (see [5]).

We computed the firing rate and signal gain responses of the Ih/INap model to both current and conductance sinusoidal inputs for a wide range of frequencies and input amplitudes (Ain). The resulting patterns for current and conductance input are qualitatively different. For current inputs, the firing frequency (and signal gain) patterns show up to three prominent peaks with heights that differ only slightly. The number of peaks increases with increasing values of Ain. For small values of Ain, the peak input frequency coincides with the subthreshold resonant frequency. The voltage traces (voltage vs. time) corresponding different peaks for the same value of Ain have roughly the same number of spikes (and inter-spike intervals of similar size), and differ in the number of subthreshold oscillations interspersed in between two consecutive spikes. For conductance (excitatory) inputs, the firing rate patterns show multiple peaks with different heights. As Ain increases, the highest peak moves to the right. For input frequencies above 60 Hz, the firing rate and gain of the highest peak significantly increases relative to other peaks for the same value of Ain. This prominent peak reflects the fast time scale present in the model that has been shown to underlie hyper-excitable firing in SCs [6] observed in animal models of temporal lobe epilepsy.

We use dynamical systems tools to explain the mechanism that govern the generation of the firing frequency patterns described above. We show that the nonlinearities present in the model and the time scale separation between voltage and the h-current gating variables play an important role in determining these patterns.


  1. Hutcheon B, Yarom Y: Resonance, oscillations and the intrinsic frequency preferences in neurons. Trends in Neurosciences. 2000, 23: 216-222. 10.1016/S0166-2236(00)01547-2.

    Article  CAS  PubMed  Google Scholar 

  2. Richardson MJE, Brunel N, Hakim V: From subthreshold to firing-rate resonance. J. Neurophysiol. 2003, 89: 2538-2554. 10.1152/jn.00955.2002.

    Article  PubMed  Google Scholar 

  3. Engel TA, Schimansky-Geier L, Herz AV, Schreiber S, Erchova I: Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex. J. Neurophysiol. 2008, 100: 1576-1588. 10.1152/jn.01282.2007.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  4. Acker CD, Kopell N, White JA: Synchronization of strongly coupled excitatory neurons: Relating network behavior to biophysics. Journal of Comp Neurosci. 2003, 15: 71-90. 10.1023/A:1024474819512.

    Article  Google Scholar 

  5. Rotstein HG, Oppermann T, White JA, Kopell N: A reduced model for medial entorhinal cortex stellate cells: Subthreshold oscillations, spiking and synchronization. J Comp Neurosci. 2006, 21: 271-292. 10.1007/s10827-006-8096-8.

    Article  Google Scholar 

  6. Kispersky T, White JA, Rotstein HG: The mechanism of abrupt transition between theta and hyperexcitable spiking activity in medial entorhinal cortex layer II stellate cells. PLoS One. 2010, 5: e13697-10.1371/journal.pone.0013697.

    Article  PubMed Central  PubMed  Google Scholar 

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This work was partially supported by the National Science Foundation grant DMS-0817241 (HGR)

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Correspondence to Horacio G Rotstein.

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This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Kim, D., Rotstein, H.G. Firing frequency response to current and conductance periodic inputs in a Ih/INap biophysical neuron model. BMC Neurosci 12 (Suppl 1), P271 (2011).

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