Skip to main content

The shaping of the coherence function of resonate-and-fire neuron models

It is known that integrate-and-fire neurons act as low-pass filters on information [1], i.e. they preferentially encode information at low frequencies. However, many neurons cannot be described by such integrators, even qualitatively. Experiments show that in several areas of the mammalian brain single neurons display a resonance property in their subthreshold voltage dynamics, see for example [2, 3]. Here, we study the information transmission of a current-based resonate-and-fire neuron model [4] by means of the spectral coherence function. We use a stochastic input current (the Ornstein-Uhlenbeck process from statistical physics) to model a complex dynamical stimulus. We show by numerical simulations that resonate-and-fire neurons encode time-dependent stimuli preferentially at moderate frequencies, including their resonance frequency, i.e. the coherence function of this model shows a clear maximum as a function of frequency. This is in marked contrast to the low-pass coherence that is found for the pure subthreshold dynamics (in the absence of spiking) in spite of resonant filter properties. We discuss dynamical mechanisms that lead to the band-pass filtering of information in the spiking resonate-and-fire model.


  1. Vilela RD, Lindner B: A comparative study of different integrate fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation. Phys Rev E. 2009, 80:

    Google Scholar 

  2. Hutcheon B, Yarom Y: Resonance, oscillation and the intrinsic frequency preferences of neurons. TINS. 2000, 23: 216-222.

    CAS  PubMed  Google Scholar 

  3. Erchova I, Kreck G, Heinemann U, Herz AVM: Dynamics of rat entorhinal cortex layer II/III cells: characteristics of membrane potential resonance at rest predict oscillation properties near threshold. Journal of Physiology. 2004, 560: 89-110. 10.1113/jphysiol.2004.069930.

    Article  PubMed Central  CAS  PubMed  Google Scholar 

  4. Engel TA, Schimansky-Geier L, Herz AVM, Schreiber S, Erchova I: Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex. J Neurophysiology. 2008, 100: 1576-1589. 10.1152/jn.01282.2007.

    Article  CAS  PubMed  Google Scholar 

Download references


This work was supported by grants from the BMBF (01GQ0901,01GQ1001A) and Deutsche orschungsgemeinschaft (SFB 618).

Author information

Authors and Affiliations


Corresponding author

Correspondence to Sven Blankenburg.

Rights and permissions

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.

Reprints and permissions

About this article

Cite this article

Blankenburg, S., Lindner, B. & Schreiber, S. The shaping of the coherence function of resonate-and-fire neuron models. BMC Neurosci 14 (Suppl 1), P346 (2013).

Download citation

  • Published:

  • DOI: