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Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 461-481. doi: 10.3934/mbe.2016001
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The effect of positive interspike interval correlations on neuronal information transmission

  • 1.
    Bernstein Center for Computational Neuroscience Berlin, Berlin 10115
  • Received: 01 April 2015 Accepted: 29 June 2018 Published: 01 January 2016

  • MSC : 93E03, 93E11, 94A12, 94A15, 94A24, 60G10, 60G15, 60G35, 60G50, 60G55.

  • Experimentally it is known that some neurons encode preferentially information about low-frequency (slow) components of a time-dependent stimulus while others prefer intermediate or high-frequency (fast) components. Accordingly, neurons can be categorized as low-pass, band-pass or high-pass information filters. Mechanisms of information filtering at the cellular and the network levels have been suggested. Here we propose yet another mechanism, based on noise shaping due to spontaneous non-renewal spiking statistics. We compare two integrate-and-fire models with threshold noise that differ solely in their interspike interval (ISI) correlations: the renewal model generates independent ISIs, whereas the non-renewal model exhibits positive correlations between adjacent ISIs. For these simplified neuron models we analytically calculate ISI density and power spectrum of the spontaneous spike train as well as approximations for input-output cross-spectrum and spike-train power spectrum in the presence of a broad-band Gaussian stimulus. This yields the spectral coherence, an approximate frequency-resolved measure of information transmission. We demonstrate that for low spiking variability the renewal model acts as a low-pass filter of information (coherence has a global maximum at zero frequency), whereas the non-renewal model displays a pronounced maximum of the coherence at non-vanishing frequency and thus can be regarded as a band-pass filter of information.

    Citation: Sven Blankenburg, Benjamin Lindner. The effect of positive interspike interval correlations on neuronal information transmission[J]. Mathematical Biosciences and Engineering, 2016, 13(3): 461-481. doi: 10.3934/mbe.2016001

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  • Experimentally it is known that some neurons encode preferentially information about low-frequency (slow) components of a time-dependent stimulus while others prefer intermediate or high-frequency (fast) components. Accordingly, neurons can be categorized as low-pass, band-pass or high-pass information filters. Mechanisms of information filtering at the cellular and the network levels have been suggested. Here we propose yet another mechanism, based on noise shaping due to spontaneous non-renewal spiking statistics. We compare two integrate-and-fire models with threshold noise that differ solely in their interspike interval (ISI) correlations: the renewal model generates independent ISIs, whereas the non-renewal model exhibits positive correlations between adjacent ISIs. For these simplified neuron models we analytically calculate ISI density and power spectrum of the spontaneous spike train as well as approximations for input-output cross-spectrum and spike-train power spectrum in the presence of a broad-band Gaussian stimulus. This yields the spectral coherence, an approximate frequency-resolved measure of information transmission. We demonstrate that for low spiking variability the renewal model acts as a low-pass filter of information (coherence has a global maximum at zero frequency), whereas the non-renewal model displays a pronounced maximum of the coherence at non-vanishing frequency and thus can be regarded as a band-pass filter of information.


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