Correlation between neural spike trains increases with firing rate (original) (raw)

Nature volume 448, pages 802–806 (2007)Cite this article

Abstract

Populations of neurons in the retina1,2,3, olfactory system4, visual5 and somatosensory6 thalamus, and several cortical regions7,8,9,10 show temporal correlation between the discharge times of their action potentials (spike trains). Correlated firing has been linked to stimulus encoding9, attention11, stimulus discrimination4, and motor behaviour12. Nevertheless, the mechanisms underlying correlated spiking are poorly understood2,3,13,14,15,16,17,18,19,20, and its coding implications are still debated13,16,21,22. It is not clear, for instance, whether correlations between the discharges of two neurons are determined solely by the correlation between their afferent currents, or whether they also depend on the mean and variance of the input. We addressed this question by computing the spike train correlation coefficient of unconnected pairs of _in vitr_o cortical neurons receiving correlated inputs. Notably, even when the input correlation remained fixed, the spike train output correlation increased with the firing rate, but was largely independent of spike train variability. With a combination of analytical techniques and numerical simulations using ‘integrate-and-fire’ neuron models we show that this relationship between output correlation and firing rate is robust to input heterogeneities. Finally, this overlooked relationship is replicated by a standard threshold-linear model, demonstrating the universality of the result. This connection between the rate and correlation of spiking activity links two fundamental features of the neural code.

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Acknowledgements

We thank C. Colbert, A. Kohn, L. Maler, D. Nikolic, A.-M. Oswald and A. Renart for their critical reading of the manuscript, and R. Moreno-Bote, M. Schiff and J. Rinzel for insightful discussions. Funding was provided by the Spanish MEC (J.R.), HFSP (B.D.), a Burroughs Welcome Fund career award and an NSF postdoctoral fellowship (E.S.-B.), NSF (K.J.) and NIH (A.R.).

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Author notes

  1. Brent Doiron
    Present address: Present address: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.,
  2. Jaime de la Rocha and Brent Doiron: These authors contributed equally to this work.

Authors and Affiliations

  1. Center for Neural Science, New York University, New York 10003, USA
    Jaime de la Rocha, Brent Doiron, Eric Shea-Brown & Alex Reyes
  2. Courant Institute of Mathematical Sciences, New York University, New York 10012, USA
    Brent Doiron & Eric Shea-Brown
  3. Department of Mathematics, University of Houston, Houston, Texas 77204, USA,
    Krešimir Josić

Authors

  1. Jaime de la Rocha
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  2. Brent Doiron
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  3. Eric Shea-Brown
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  4. Krešimir Josić
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  5. Alex Reyes
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Corresponding authors

Correspondence toJaime de la Rocha or Brent Doiron.

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Reprints and permissions information is available at www.nature.com/reprints. The authors declare no competing financial interests.

Supplementary information

Supplementary Information

This file contains Supplementary Methods, Supplementary Figures S1-S6 with Legends illustrating additional analysis of the correlation-rate relation and a complete derivation of Eq. (3) presented in the main text. (PDF 1362 kb)

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de la Rocha, J., Doiron, B., Shea-Brown, E. et al. Correlation between neural spike trains increases with firing rate.Nature 448, 802–806 (2007). https://doi.org/10.1038/nature06028

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