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Inferring oscillatory modulation in neural spike trains

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  • Kensuke Arai
  • Robert E Kass

Abstract

Oscillations are observed at various frequency bands in continuous-valued neural recordings like the electroencephalogram (EEG) and local field potential (LFP) in bulk brain matter, and analysis of spike-field coherence reveals that spiking of single neurons often occurs at certain phases of the global oscillation. Oscillatory modulation has been examined in relation to continuous-valued oscillatory signals, and independently from the spike train alone, but behavior or stimulus triggered firing-rate modulation, spiking sparseness, presence of slow modulation not locked to stimuli and irregular oscillations with large variability in oscillatory periods, present challenges to searching for temporal structures present in the spike train. In order to study oscillatory modulation in real data collected under a variety of experimental conditions, we describe a flexible point-process framework we call the Latent Oscillatory Spike Train (LOST) model to decompose the instantaneous firing rate in biologically and behaviorally relevant factors: spiking refractoriness, event-locked firing rate non-stationarity, and trial-to-trial variability accounted for by baseline offset and a stochastic oscillatory modulation. We also extend the LOST model to accommodate changes in the modulatory structure over the duration of the experiment, and thereby discover trial-to-trial variability in the spike-field coherence of a rat primary motor cortical neuron to the LFP theta rhythm. Because LOST incorporates a latent stochastic auto-regressive term, LOST is able to detect oscillations when the firing rate is low, the modulation is weak, and when the modulating oscillation has a broad spectral peak.Author summary: Oscillatory modulation of neural activity in the brain is widely observed under conditions associated with a variety of cognitive tasks and mental states. Within individual neurons, oscillations may be uncovered in the moment-to-moment variation in neural firing rate. This, however, is often challenging because many factors may affect fluctuations in neural firing rate and, in addition, neurons fire irregular sets of action potentials, or spike trains, due to an unknown combination of meaningful signals and extraneous noise. We have devised a statistical Latent Oscillatory Spike Train (LOST) model with accompanying model-fitting technology, that is able to detect subtle oscillations in spike trains by taking into account both spiking noise and temporal variation in the oscillation itself. The method couples two techniques developed for other purposes in the literature on Bayesian analysis. Using data simulated from theoretical neurons and real data recorded from cortical motor neurons, we demonstrate the method’s ability to track changes in the modulatory structure of the oscillation across experimental trials.

Suggested Citation

  • Kensuke Arai & Robert E Kass, 2017. "Inferring oscillatory modulation in neural spike trains," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
  • Handle: RePEc:plo:pcbi00:1005596
    DOI: 10.1371/journal.pcbi.1005596
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    References listed on IDEAS

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    1. Michael M. Yartsev & Menno P. Witter & Nachum Ulanovsky, 2011. "Grid cells without theta oscillations in the entorhinal cortex of bats," Nature, Nature, vol. 479(7371), pages 103-107, November.
    2. Ayala Matzner & Izhar Bar-Gad, 2015. "Quantifying Spike Train Oscillations: Biases, Distortions and Solutions," PLOS Computational Biology, Public Library of Science, vol. 11(4), pages 1-21, April.
    3. Nicholas G. Polson & James G. Scott & Jesse Windle, 2013. "Bayesian Inference for Logistic Models Using Pólya--Gamma Latent Variables," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(504), pages 1339-1349, December.
    4. G. Huerta & M. West, 1999. "Priors and component structures in autoregressive time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 881-899.
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