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the coupling with the network of interneurons. These currents will be defined
in the next section. To reproduce the membrane potential fluctuations each
j
th
cell model is injected with the noisy current
η
P
ξ
P,j
(
t
),
ξ
P,j
being an
uncorrelated Gaussian random variable of zero mean and unit standard deviation
<ξ
P,i
,ξ
P,j
>
=
δ
ij
,i
−
=
j
=1
,
2
,
3
,,N
PY
). The adopted value of the parameter
η
P
was chosen to have a realistic amplitude of the fluctuations of membrane
potential.
The biophysical mathematical model of the
j
th
FS interneuron reads:
−
C
dV
j
dt
g
Na
m
j
h
j
(
V
j
−
g
K
n
j
(
V
j
−
=
I
F,j
−
V
Na
)
V
K
)
g
L
(
V
j
−
V
L
)
−
−
+
I
FF,j
+
J
FF,j
+
I
PF,j
+
η
F
ξ
F,j
(
t
)
(6)
dm
j
dt
=
α
m,j
(1
m
j
)
β
m,j
m
j
(7)
−
−
dh
j
dt
=
α
h,j
(1
h
j
)
β
h,j
h
j
,
(8)
−
−
dn
j
dt
=
α
n,j
(1
n
j
)
β
n,j
n
j
,
(9)
−
−
where
C
=1
μF/cm
2
,
I
F,j
=
I
F
(
j
=1
,
2
, ..N
) is the external stimulation
current. The maximal specific conductances,the reversal potentials and the rate
variables are equal to those adopted for the pyramidal cell model. In this model
the onset of periodic firing occurs through an Hopf bifurcation for
I
F
= 1
.
04
μA/cm
2
with a well defined frequency (
ν
= 2
Hz
).
The current
I
FF,j
arises from the inhibitory coupling of the
j
th
FS interneu-
ron with the other cells, while
J
FF,j
describes the current due to the electrical
coupling (gap-junction) among interneurons; lastly
I
PF,j
describes the excitatory
current due to the coupling with the network of pyramidal neurons. These cur-
rents will be defined in the next section. To reproduce the membrane potential
fluctuations each
j
−
th
cell model is injected with the noisy current
η
F
ξ
F,j
(
t
),
ξ
F,j
being an uncorrelated Gaussian random variable of zero mean and unit standard
deviation
<ξ
F,i
,ξ
F,j
−
=
j
=1
,
2
,
3
,,N
FS
)and
<ξ
P,i
,ξ
F,j
>
=0.The
value of the
η
F
was chosen in order to get realistic amplitude of the fluctuation
of membrane potential.
The reason of using a single compartment model of each cell is motivated
by computational constraints. The simulation will be performed by using up to
100 coupled neuron models, and this requires a high computational cost. There-
fore, for the aim of the present work, the choice of using a single compartment
biophysical model of each cell is a good compromise between two requirements:
computational advantages and realistic network of coupled neurons.
>
=
δ
ij
,i
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