Search Advanced

Mathematical Biosciences and Engineering

2016, Volume 13, Issue 3: 461-481. doi: 10.3934/mbe.2016001
Previous Article Next Article

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

    Related Papers:

  • 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.


    加载中
    [1] Nature, 431 (2004), 796-803.
    [2] Proc. Nat. Acad. Sci., 97 (2000), 8110-8115.
    [3] J. Neurophysiol., 113 (2014), 1342-1357.
    [4] J. Comput. Neurosci., 39 (2015), 349-370.
    [5] Nat. Neurosci., 2 (1999), 947-957.
    [6] Phys. Rev. E, 66 (2002), 031907, 14pp.
    [7] Springer, 2009.
    [8] Phys. Rev. E, 67 (2003), 051916, 23pp.
    [9] J. Comput. Neurosci., 23 (2007), 301-311.
    [10] J. Neurosci., 21 (2001), 5328-5343.
    [11] Nature, 423 (2003), 77-81.
    [12] Phys. Rev. Lett., 93 (2004), 059904.
    [13] Wiley, New-York, 1991.
    [14] Chapman and Hall, London, 1966.
    [15] Front. Comp. Neurosci., 7 (2013), p86.
    [16] J. Neurophysiol., 100 (2008), 1576-1589.
    [17] J. Neurosci., 32 (2012), 17332-17344.
    [18] J. R. Statist. Soc. B, 40 (1978), 263-289.
    [19] Network Comp. Neural., 7 (1996), 61-85.
    [20] Biophys. J., 6 (1966), 53-69.
    [21] Biophys. J., 4 (1964), 41-68.
    [22] Cambridge University Press, Cambridge, 2002.
    [23] Princeton University Press, 1994.
    [24] Springer-Verlag, Berlin, 1976.
    [25] Neural. Netw., 14 (2001), 883-894.
    [26] Phys. Rev. E, 69 (2004), 022901.
    [27] in International Conference on Theory and Application in Nonlinear Dynamics (ICAND 2012) (eds. I. Visarath, A. Palacios and P. Longhini), Springer, 2012.
    [28] Phys. Rev. E, 72 (2005), p021911, 21pp.
    [29] J. Neurosci., 29 (2009), 2076-2087.
    [30] J. Acoust. Soc. Am., 92 (1992), 803-806.
    [31] Proc. Natl. Acad. Sci., 96 (1999), 10450-10455.
    [32] J. Neurophysiol., 92 (2004), 939-948.
    [33] J. Neurophysiol., 105 (2011), 1798-1814.
    [34] Phys. Rev. E, 81 (2010), 041921, 19pp.
    [35] J. Neurophysiol., 101 (2009), 1160-1170.
    [36] Chaos, 21 (2011), 047505.
    [37] Phys. Rev. Lett., 109 (2012), 238103.
    [38] J. Neurosci., 24 (2004), 4351-4362.
    [39] J. Neurosci., 28 (2008), 13649-13661.
    [40] Proc. Biol. Sci., 262 (1995), 259-265.
    [41] MIT Press, Cambridge, Massachusetts, 1999.
    [42] J. Comput. Neurosci., 8 (2000), 95-112.
    [43] J. Neurosci., 27 (2007), 771-781.
    [44] PLoS Comp. Biol., 6 (2010), e1001026, 25pp.
    [45] Bell Syst. Tech. J., 27 (1948), 379-423.
    [46] J. Comp. Neurosci., 34 (2013), 285-301.
    [47] J. Comp. Neurosci., 38 (2015), 589-600.
    [48] Neurocomp., 44 (2002), 167-175.
    [49] Int. J. Electronics, 74 (1993), 359-368.
    [50] Gordon and Breach, New York, 1967.
    [51] Phys. Rev. E, 80 (2009), 031909.
    [52] Ann. Rev. Physiol., 64 (2002), 355-405.
  • Reader Comments
  • © 2016 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索
Mathematical Biosciences and Engineering
4.4

Metrics

Article views(3359) PDF downloads(476) Cited by(10)

Preview PDF
Download XML
Export Citation
Article outline

Other Articles By Authors

Related pages

Tools

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog