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The Poisson process with dead time captures important statistical features of neural activity

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Poster presentation

Stochastic point processes are widely used in computational neuroscience to model the spiking of single neurons and neuronal populations. The choice of a particular point process is critical for statistical measures of neural activity and has impact on the subthreshold dynamics of neuron models.

Here we show that the Poisson process with dead time, a particular simple point process, captures important features of the spiking statistics of neurons [1, 2] (Fig. 1). On the level of single neurons, we apply a step change to the rate of a Poisson process with dead time, keeping the dead time constant. The expected PSTH is computed by numerically solving the partial differential equation of the corresponding non-homogeneous renewal process [3] and we also give an analytical approximation. We observe a very sharp transient in the firing-rate (Fig. 2) that resembles experimental results of [4].

figure1

Figure 1

figure2

Figure 2

On the level of neuronal populations, we employ the superposition of many Poisson processes with dead time as a model of the population activity in a network. We compute the explicit form of the inter-spike-interval (ISI) distribution and the coefficient of variation for superimposed processes and compare them to direct simulations. The ISIs of the superimposed spike trains show negative serial correlations that correspond to those we observe in population recordings of simulated integrate-and-fire neurons (Fig 3).

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Figure 3

For the single Poisson process with dead time and superpositions alike, we can determine the variance of shot noise driven by them with the associated spike count in a certain time window or the free membrane potential of an IF neuron. This enables us to show how empirical approximations of the Fano factor depend on the width of the counting window, and how the statistical properties of the driving point-process influence the variance of the subthreshold dynamics of neurons.

References

  1. 1.

    Johnson D, Swami A: The transmission of signals by auditory-nerve fiber discharge patterns. J Acoust Soc Am. 1983, 74.

  2. 2.

    Johnson D: Point process models of single-neuron discharges. J Computational Neuroscience. 1996, 275-299. 10.1007/BF00161089.

  3. 3.

    Gerstner W, Kistler M: Spiking neuron models. 2002, Cambridge University Press

  4. 4.

    Mainen Z, Sejnowski T: Reliability of spike timing in neocortical neurons. Science. 1995, 268.

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Acknowledgements

Partially funded by DIP F1.2 and BMBF Grant 01GQ0420 to the Bernstein Center for Computational Neuroscience Freiburg.

Author information

Correspondence to Moritz Deger.

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Open Access This article is published under license to BioMed Central Ltd. This is an Open Access article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Deger, M., Cardanobile, S., Helias, M. et al. The Poisson process with dead time captures important statistical features of neural activity. BMC Neurosci 10, P110 (2009) doi:10.1186/1471-2202-10-S1-P110

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Keywords

  • Poisson Process
  • Point Process
  • Spike Train
  • Neuronal Population
  • Dead Time