Correlated Neuronal Activity: High- and Low-Level Views - Computational Neuroscience: A Comprehensive Approach - page 360

m = 0 s = 0.35

100 100

m = 0.5

s = 1.0

s = 0.7

m = 0.25

s = 0.45

m = 0

s = 0.2

m = −0.2

0 0

4 3

0 0

0 80 0 80

t

corr (ms)

t

corr (ms)

Figure 12.7
Responses of the nonleaky integrate-and-fire neuron as functions of input correlation
time t corr . Only analytic results are shown. As the correlation time increases, the
firing rate always tends to an asymptotic value. In contrast, the CV ISI diverges always,
except when m s; this case corresponds to the thickest line in the plots on the right.

(Adapted from [69].)

>

The key to obtain all the analytic expressions was the use of a binary input. One
may wonder, however, whether the results are valid with a more realistic input sig-
nal. It turns out that, for this model, the mean firing rate and the CV ISI obtained using
correlated Gaussian noise are very similar to those obtained with binary noise. This
is not entirely unexpected, first, because the neuron essentially adds its inputs, and
second, because Gaussian noise can be properly approximated as the sum of mul-
tiple binary random samples, as a consequence of the central limit theorem. This
is strictly true when all binary and Gaussian samples are independent, that is, when
the autocorrelation functions are everywhere flat, but the approximation works quite
well even when there is a correlation time. For example, the rate and the CV ISI still
increase as functions of correlation time, and the same asymptotic behaviors are seen
[69].

12.7 Correlations and neuronal variability

The spike trains of neurons recorded in awake animals are highly variable [25, 75-
78]. However, spike generation mechanisms themselves seem to be highly reliable
[20, 49, 56]. The contrast between these two observations stirred a fair amount of