Friday evening, Poster II-29
Cosyne 2007
Correlation between neural spike trains increases with firing rate
Brent Doiron1,2 , Jaime de la Rocha1 , Eric Shea-Brown1,2 , Krešimir Josić3 & Alex Reyes1
1: Center for Neural Science, New York University, New York, NY 10003, USA
2: Courant Institute of Mathematical Sciences, New York University, NY 10012, USA
3: Department of Mathematics, University of Houston, Houston, TX 77204, USA
Populations of neurons in a variety of brain areas show temporal correlation between their spike trains.
Correlated firing has been linked to stimulus encoding, attention, stimulus discrimination, and motor behavior. Nevertheless, the mechanisms underlying correlated spiking are poorly understood, and its coding
implications are still debated. It is not clear, for instance, on whether correlations between the discharges of
two neurons simply reflect the correlation between their afferent currents or whether they depend on other
factors. We addressed this question by computing the spike train correlation coefficient (ρ) of unconnected
pairs of in vitro cortical neurons receiving correlated inputs (Fig. 1A). Remarkably, even when input correlation remained fixed, the spike train output correlation increased with the firing rate (ν), but was independent
of spike train variability (Fig. 1B). In the limit of white noise forcing and weak input correlation c we derive
the compact expression valid for any spiking neuron:
ρ=
2
dν
dμ
CV 2 ν
σ2
c.
(1)
Here μ and σ2 are the mean and variance of the driving current and CV is the coefficient of variation of
the ISI distribution. Our theory gives an excellent match to simulations of spiking LIF neurons (Fig. 1C) as
well as the cortical data. A functional consequence of our relation is that, if the firing rate of a population of
neurons is tuned to a stimulus feature, then so is the population correlation.
C
B
A
LIF theory
in vitro experiments
c
+
ξ2
-60
+
0.2
0
0
output correlation ρ
ξc
0.4
output correlation ρ
ξ1
0
10
output firing rate (Hz)
20
c
2
0
0
50
100
output firing rate ν [spks/sec]
Figure 1: Relationship between output spike correlation and output rate. A In vitro neurons were stimulated with Gaussian
currents having both common and independent components, evoking correlated trains of action potentials. B. The spike train
correlation coefficient (a normalized and zero mean corrected measure) increases with the dischrage rate of the neurons as the input
correlation remains fixed. C. Statistical theory (Eq. 1, curves) and simulations from pairs of LIF neuron models. Firing rate was
ranged by increasing the mean input current μ (red curve) or the current fluctuations σ2 (blue curve).
Acknowledgments
Funding was provided by the Spanish MEC (JR), HFSP (BD), Burroughs Welcome Fund (ESB), NSF (KJ,
ESB) and NIH (AR).
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