Skip to main content
  • Poster presentation
  • Open access
  • Published:

Representation of dynamical stimuli in threshold neuron models

A vital function of the mammalian cortex is the processing of dynamical stimuli. These stimuli are encoded in cortical neurons as modifications of the input current, which can be brief, prolonged or periodic, all depending on the type of the sensory stimulus, e.g. [1, 2]. While experimental findings can increasingly link sensory stimulation to specific input current modulations, the representation of current stimuli by populations of cortical neurons currently lacks a comprehensive theoretical understanding. In particular, few theories can analytically describe the numerous phenomena related to the processing of dynamical current stimuli, such as pairwise spike correlations and spike triggered average currents (Fig. 1). Even in the simplest integrate and fire model, the complexity of the coupled differential equations allows for tractable analytical results only in specific limiting cases [3, 4]. Here, we show how a modified threshold model framework can accurately describe many important features of cortical neurons and provide set of tractable analytical expressions for all quantities of interest shown in Fig.1, such as spike triggered average current, pairwise spike correlations [4, 5] and response to dynamical input changes [3, 4]. Using this novel model framework, we study how populations of cortical neurons represent dynamical stimuli encoded in the input current and place many important, yet disparate, observations into a common conceptual scheme.

Figure 1
figure 1

Illustrating the role of the linear frequency response function ν1(ω) for the population firing response ν(t) to periodic or step changes of the mean current, the spike triggered average and the pairwise spike correlations νcond(τ) in a pair with a weak input correlation strength r. The dashed red line indicates the presence of ν1(ω), CI(τ) is the input current correlation function and F denotes the Fourier transform and ν is the stationary firing rate.


  1. Buzsáki G, Draguhn A: Neuronal Oscillations in Cortical Networks. Science. 2004, 304: 1926-1929. 10.1126/science.1099745.

    Article  PubMed  Google Scholar 

  2. Volgushev M, Pernberg J, Eysel UT: γ-frequency fluctuations of the membrane potential and response selectivity in visual cortical neurons. Eur J Neurosci. 2003, 17 (9): 1768-1776. 10.1046/j.1460-9568.2003.02609.x.

    Article  PubMed  Google Scholar 

  3. Brunel N, Chance F, Fourcaud N, Abbott LF: Effects of synaptic noise and filtering on the frequency response of spiking neurons. Phys Rev Lett. 2001, 86: 2186-2189. 10.1103/PhysRevLett.86.2186.

    Article  CAS  PubMed  Google Scholar 

  4. Ostojic S, Brunel N, Hakim V: How connectivity, background activity, and synaptic properties shape the cross-correlation between spike trains. J Neurosci. 2009, 29 (33): 10234-10253. 10.1523/JNEUROSCI.1275-09.2009.

    Article  CAS  PubMed  Google Scholar 

  5. Tchumatchenko T, Malyshev A, Volgushev M, Wolf F: Correlations and synchrony in threshold neuron models. Phys Rev Lett. 2010, 104 (5): 058102-10.1103/PhysRevLett.104.058102.

    Article  PubMed  Google Scholar 

Download references


We wish to thank Bundesministerium für Bildung und Forschung (#01GQ0430,01GQ07113), German-Israeli Foundation (#I-906-17.1/2006), Deutsche Forschungsgemeinschaft and Max Planck Society for financial support.

Author information

Authors and Affiliations


Corresponding author

Correspondence to Tatjana Tchumatchenko.

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

Tchumatchenko, T., Geisel, T. & Wolf, F. Representation of dynamical stimuli in threshold neuron models. BMC Neurosci 12 (Suppl 1), P376 (2011).

Download citation

  • Published:

  • DOI: