Biomedical Engineering Reference
In-Depth Information
13.2.3.3
Stimulus-dependent spike patterns
A neuronal population can carry information by emitting patterns of spikes that
tag
each stimulus, without the differences in the patterns being expressed in the PSTHs
[6, 11, 32, 39, 41]. When the assumptions of the series expansion are satisfied, the
only types of spike pattern it is necessary to consider are spike pairs - higher order
interactions can be neglected. Patterns involving pairs of spikes are quantified, for
each stimulus, as the correlation between the number of spikes occurring in each of
two time bins. For within-cell patterns, the bins come from the same cell; for cross-
cell patterns, they come from different cells. This quantity is sometimes known as
the noise correlation. In the case of cross-cell synchrony, for example, the noise
correlation will be greater than expected from the PSTHs. In the case of within-cell
refractoriness, where the presence of a spike in one bin predicts the absence of a
spike in the next bin, the noise correlation will be less than that expected from the
PSTH.
The amount of information conveyed by stimulus-dependent spike patterns de-
pends, analogously to the PSTH information, on how much the noise correlations
(normalised by firing rate) vary across the stimulus set: the greater the diversity, the
greater the information available. This effect is quantified by Equation (13.6):
CN
aib js
s
CN
aib js
s
CN
aib js
log
2
ECN
aib js
÷
1
2
Â
I
ttc
=
(13.6)
ECN
aib js
s
a
,
b
,
i
,
j
CN
aib js
(noise correlation) is the
joint
PSTH of bin
i
of cell a and bin
j
of cell b
given stimulus
s
. It is equal to
n
ais
n
bjs
, unless
a
j
. In the latter case,
CN
aib js
is equal to zero if each bin contains at most one spike, or equal to
n
ais
−
=
b
and
i
=
n
ais
otherwise [28].
ECN
aib js
=
n
ais
n
bjs
is the expected value of
CN
aib js
for statistically
independent spikes.
I
ttc
is positive or zero.
13.2.3.4
Stimulus-independent spike patterns
Even if not stimulus-dependent, spike patterns can exert an effect on the neuronal
code through a subtle interaction between signal correlation and noise correlation.
In contrast to stimulus-dependent patterns, this less intuitive coding mechanism has
received little attention in experimental work - it has been noted in theoretical pa-
pers by [1, 17, 22, 36]. As shown schematically in
Figure 13.1,
correlated noise
can serve to sharpen the distinction in responses to different stimuli under certain
circumstances, and to blur those distinctions under other circumstances. In general,
this term - Equation (13.7) - is positive if signal correlations and noise correlations
have different signs, negative if they have the same signs. If signals are uncorrelated,
the term is zero.
CS
aib j
ECS
aib j
1
2ln2
Â
I
ttb
=
−
j
CN
aib js
−
ECN
aib js
s
ln
(13.7)
a
,
b
,
i
,
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