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Related Experiment Videos

Relation between single neuron and population spiking statistics and effects on network activity.

Hideyuki Câteau1, Alex D Reyes

  • 1Center for Neural Science, New York University, 4 Washington Place, New York, New York 10003, USA.

Physical Review Letters
|February 21, 2006
PubMed
Summary

The assumption that summing neural network spike trains results in a Poisson process is incorrect. Accurate feedforward network analysis requires incorporating neuronal periodic firing tendencies using specific colored noise.

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Area of Science:

  • Computational Neuroscience
  • Theoretical Neuroscience
  • Neural Network Modeling

Background:

  • Individual neurons are frequently modeled as Poisson processes to simplify theoretical analyses of neural networks.
  • A common implicit assumption is that the composite activity of summed spike trains approximates a Poisson process, even with non-Poissonian individual neuron activity.

Purpose of the Study:

  • To challenge the validity of the assumption that summed spike trains from individual neurons approximate a Poisson process.
  • To determine the necessary conditions for accurately reproducing feedforward neural network behavior in theoretical models.

Main Methods:

  • Analytical derivations were employed to investigate the statistical properties of summed spike trains.
  • Numerical simulations were conducted to validate theoretical predictions.

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  • Fokker-Planck equations were utilized to model the dynamics of feedforward networks.

    • Main Results:

    • The study analytically and computationally demonstrates that the assumption of composite activity limiting to a Poisson process is invalid.
    • Feedforward network behavior is accurately reproduced only when neuronal periodic firing tendencies are accounted for.
    • Incorporating colored noise with a negative autocorrelation component is shown to be crucial for accurate modeling.

    Conclusions:

    • The simplification of neural network analysis using Poisson process assumptions for summed spike trains is fundamentally flawed.
    • Accurate theoretical analysis of feedforward networks necessitates the inclusion of neuronal periodicity.
    • The use of specific colored noise models is essential for capturing the dynamics of neural systems.