Letter

Nature 448, 802-806 (16 August 2007) | doi:10.1038/nature06028; Received 16 April 2007; Accepted 18 June 2007

Correlation between neural spike trains increases with firing rate

Jaime de la Rocha1,4, Brent Doiron1,2,4,5, Eric Shea-Brown1,2, Kres caronimir Josic acute3 & Alex Reyes1

  1. Center for Neural Science, New York University, New York 10003, USA
  2. Courant Institute of Mathematical Sciences, New York University, New York 10012, USA
  3. Department of Mathematics, University of Houston, Houston, Texas 77204, USA
  4. These authors contributed equally to this work.
  5. Present address: Department of Mathematics, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA.

Correspondence to: Jaime de la Rocha1,4Brent Doiron1,2,4,5 Correspondence and requests for materials should be addressed to B.D. (Email: bdoiron@cns.nyu.edu) or J.R (Email: jrocha@cns.nyu.edu).

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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