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Correlation between neural spike trains increases with firing rate


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 vitro 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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Figure 1: Relationship between output spike correlation and rate in in vitro cells.
Figure 2: The correlation–rate relationship in an integrate-and-fire neuron model.
Figure 3: Correlation–rate relationship in a simple network.
Figure 4: Nonlinearities shape the correlation–rate relationship in a phenomenological neural model.


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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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Correspondence to Jaime de la Rocha or Brent Doiron.

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Reprints and permissions information is available at 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).

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