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Low-Pass Filtering of Information in the Leaky Integrate-and-Fire Neuron Driven by White Noise

  • Benjamin Lindner
Chapter
Part of the Understanding Complex Systems book series (UCS)

Abstract

The question of how noisy spiking neurons respond to external time-dependent stimuli is a central topic in computational neuroscience. An important aspect of the neural information transmission is, whether neurons encode preferentially information about slow or about fast components of the stimulus (signal). A convenient way to quantify this is the spectral coherence function, that in some experimental data shows a global maximum at low frequencies (low-pass information filter), in some other cases has a maximum at higher frequencies (band-pass or high-pass information filter); information-filtering defined in this way is related but not identical to the usual filtering of spectral power. Here I demonstrate numerically that the leaky integrate-and-fire neuron driven by white noise (a stimulus without temporal correlations) acts as a low-pass information filter irrespective of the dynamical regime (fluctuation-driven and irregular or mean-driven and regular firing).

Keywords

Firing Rate Spike Train Noise Intensity Firing Regime Coherence Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Notes

Acknowledgments

This research has been funded by the BMBF (FKZ: 01GQ1001A).

References

  1. 1.
    L. Badel, S. Lefort, R. Brette, C.C.H. Petersen, W. Gerstner, M.J.E. Richardson, Generalized integrate-and-fire models of neuronal activity approximate spike trains of a detailed model to a high degree of accuracy. J. Neurophysiol. 92, 959 (2004)CrossRefGoogle Scholar
  2. 2.
    L. Badel, S. Lefort, R. Brette, C.C.H. Petersen, W. Gerstner, M.J.E. Richardson, Dynamic I-V curves are reliable predictors of naturalistic pyramidal-neuron voltage traces. J. Neurophysiol. 99, 656 (2008)CrossRefGoogle Scholar
  3. 3.
    B. Lindner, L. Schimansky-Geier, A. Longtin, Maximizing spike train coherence or incoherence in the leaky integrate-and-fire model. Phys. Rev. E 66, 031916 (2002)CrossRefMathSciNetGoogle Scholar
  4. 4.
    A. N. Burkitt, A review of the integrate-and-fire neuron model: I. homogeneous synaptic input. Biol. Cyber. 95(1) (2006)Google Scholar
  5. 5.
    R.D. Vilela, B. Lindner, Are the input parameters of white-noise-driven integrate & fire neurons uniquely determined by rate and CV? J. Theor. Biol. 257, 90 (2009)CrossRefMathSciNetGoogle Scholar
  6. 6.
    N. Fourcaud-Trocmé, D. Hansel, C. van Vreeswijk, N. Brunel, How spike generation mechanisms determine the neuronal response to fluctuating inputs. J. Neurosci. 23, 11628 (2003)Google Scholar
  7. 7.
    R.D. Vilela, B. Lindner, A comparative study of three different integrate-and-fire neurons: spontaneous activity, dynamical response, and stimulus-induced correlation. Phys. Rev. E 80, 031909 (2009)CrossRefGoogle Scholar
  8. 8.
    R.B. Stein, A.S. French, A.V. Holden, The frequency response, coherence, and information capacity of two neuronal models. Biophys. J. 12, 295 (1972)CrossRefGoogle Scholar
  9. 9.
    B. Lindner, L. Schimansky-Geier, Transmission of noise coded versus additive signals through a neuronal ensemble. Phys. Rev. Lett. 86, 2934 (2001)CrossRefGoogle Scholar
  10. 10.
    B. Lindner, J. García-Ojalvo, A. Neiman, L. Schimansky-Geier, Effects of noise in excitable systems. Phys. Rep. 392, 321 (2004)CrossRefGoogle Scholar
  11. 11.
    M. Abramowitz, I.A. Stegun, Handbook of Mathematical Functions (Dover, New York, 1970)Google Scholar
  12. 12.
    N. Fourcaud, N. Brunel, Dynamics of the firing probability of noisy integrate-and-fire neurons. Neural Comp. 14, 2057 (2002)CrossRefzbMATHGoogle Scholar
  13. 13.
    M. J. E. Richardson, Spike-train spectra and network response functions for non-linear integrate-and-fire neurons. Biol. Cybern. (to appear) 99, 381–392 (2008)Google Scholar
  14. 14.
    J.W. Middleton, A. Longtin, J. Benda, L. Maler, Postsynaptic receptive field size and spike threshold determine encoding of high-frequency information via sensitivity to synchronous presynaptic activity. J. Neurophysiol. 101, 1160 (2009)CrossRefGoogle Scholar
  15. 15.
    N. Sharafi, J. Benda, B. Lindner, Information filtering by synchronous spikes in a neural population. J. Comp. Neurosci. 34, 285 (2013)Google Scholar
  16. 16.
    B. Lindner, D. Gangloff, A. Longtin, J.E. Lewis, Broadband coding with dynamic synapses. J. Neurosci. 29, 2076 (2009)CrossRefGoogle Scholar
  17. 17.
    R. Rosenbaum, J. Rubin, B. Doiron, Short term synaptic depression imposes a frequency dependent filter on synaptic information transfer. PLoS Comput. Biol. 8, e1002557 (2012)CrossRefMathSciNetGoogle Scholar
  18. 18.
    J. Benda, A.V.M. Herz, A universal model for spike-frequency adaptation. Neural Comp. 15, 2523 (2003)CrossRefzbMATHGoogle Scholar
  19. 19.
    M.J.E. Richardson, N. Brunel, V. Hakim, From subthreshold to firing-rate resonance. J. Neurophysiol. 89, 2538 (2003)CrossRefGoogle Scholar
  20. 20.
    T.A. Engel, L. Schimansky-Geier, A.V.M. Herz, S. Schreiber, I. Erchova, Subthreshold membrane-potential resonances shape spike-train patterns in the entorhinal cortex. J. Neurophysiol. 100(3), 1576 (2008)CrossRefGoogle Scholar
  21. 21.
    B. Lindner, Superposition of many independent spike trains is generally not a poisson process. Phys. Rev. E 73, 022901 (2006)CrossRefGoogle Scholar
  22. 22.
    N. Brunel, S. Sergi, Firing frequency of leaky integrate-and-fire neurons with synaptic current dynamics. J. Theor. Biol. 195, 87 (1998)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Bernstein Center for Computational Neuroscience BerlinBerlinGermany
  2. 2.Physics DepartmentHumboldt University BerlinBerlinGermany

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