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background noise current. The predictions of the model were later tested in
experimental system of two coupled cultured networks (Baruchi
et al
., in press).
12.8. Analyzing the SBEs Motifs
Identification of clusters of repeating burst motifs can serve as an important
tool for investigating the inter-neuronal relations in the neuronal network
(Baruchi
et al
., in press). Successful clustering of burst motifs based on different
measures of burst similarity has been previously achieved. For example, in the
works by Mukai
et al
. (2003) and Madhavan
et al
. (2005) SBEs were clustered
according to the firing intensity of individual neurons, with disregards to the
temporal delays between neurons. We have developed a novel measure of SBE
similarity that inspects the changes in the temporal delays between neuron
activation in the SBE (Raichman and Ben-Jacob, 2008). By applying a standard
clustering algorithm, one can determine the number of observed motifs in a
culture.
In our method, we reduce the image of the SBE motif to include only the first
spike of each neuron, and thus capture its initiation profile. Our assumption to
include only the first spike of the neuronal spike-train is in accordance with
results showing that spike timing is more accurate in the beginning of the spike-
train, both in spontaneous firing and in bursts generated as a response to electric
stimuli (Jimbo and
rL
2000; Bonifazi
et al.
2005; Luczak
et al.
2007).
In order to identify sets of SBE motifs of neuronal activation, we looked at
the first spike of each neuron during the activation time τ
act
for each burst (as
previously defined). We represented the activation of each SBE by an activation
matrix,
A
, where
A
(
i
,
j
) is the delay in milliseconds between the first spike of
neuron
i
and the first spike of neuron
j
in the SBE. Neurons that do not fire in the
SBE received a NULL value in the activation matrix. Obviously, the matrix is
anti-symmetric:
A
(
i
,
j
) = -
A
(
j
,
i
) and A(
i
,
i
) = 0.
We then defined the similarity,
S
(
A
p
,
A
q
), between SBEs
p
and
q
as:
where
H
is the Heaviside step function (
H
(
x
) = 0 if
x
< 0 and
H
(
x
) = 1if
x
≥ 0)
and
th
is a time-threshold parameter. According to this formula,
S
(
A
p
,
A
q
) is the
fraction of neuron pairs (
i
,
j
) that obey the condition that the accuracy in delays
between the two bursts is less than
th
: |
A
p
(
i
,
j
) -
A
q
(
i
,
j
)| <
th
. The summation is
made only on neuron pairs that did not receive NULL values in any of the two
SBEs (i.e. both neurons fired a spike in both SBEs). In our analysis we set
