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2.2
Synaptic Coupling
The excitatory synaptic coupling among pyramidal cells is assumed to be all-to-
all. The excitatory synaptic current acting on the
j
th
pyramidal cell is defined
−
by
1
k
=
j
1
N
PY
−
I
PP,j
=
g
e
s
PP,k
(
t
)(
V
j
−
V
PP
)
(10)
−
where
g
e
=0
.
5
mS/cm
2
represents the maximal amplitude of the excitatory
coupling, the function
s
PP,k
(
t
) describes the time evolution of the postsynaptic
current and
V
PP
is the corresponding reversal potential. According to [8] the
time evolution of
s
PP,k
(
t
) is described by
ds
PP,k
(
t
)
dt
=
T
(
V
k
)(1
s
PP,k
)
s
PP,k
/τ
e
(11)
−
−
where
T
(
V
k
)=5(1+
tanh
(
V
k
/
4) and
τ
e
=2
ms
is the decay time constant.
Similarly the inhibitory synaptic coupling among FS interneurons is assumed
to be all-to-all and the synaptic current on the
j
th
interneuron reads
−
1
k
=
j
1
N
FS
−
I
FF,j
=
g
i
s
FF,k
(
t
)(
V
j
−
V
FF
)
(12)
−
where
g
i
=0
.
25
mS/cm
2
represents the maximal amplitude of the inhibitory
coupling and
V
FF
is the corresponding reversal potential. The time evolution of
s
FF,k
(
t
) is described by
ds
FF,k
(
t
)
dt
=
T
(
V
k
)(1
s
FF,k
)
s
FF,k
/τ
i
(13)
−
−
where
T
(
V
k
)=2(1+
tanh
(
V
k
/
4) and
τ
1
=10
ms
is the decay time constant.
The pyramidal cells excite the network of FS cells and the corresponding
excitatory current acting on the
j
th
interneuron is defined as
−
1
k
=
j
1
N
PY
−
I
PF,j
=
g
PF
s
PF,k
(
t
)(
V
j
−
V
PF
)
−
(14)
where
g
PF
represents the maximal amplitude of the excitatory coupling and
V
PF
=
V
PP
is the corresponding reversal potential. The time evolution of
s
PF,k
(
t
)isdrivenby
ds
PF,k
(
t
)
dt
=
T
(
V
k
)(1
s
PF,k
)
s
PF,k
/τ
e
(15)
−
−
where
T
(
V
k
)=5(1+
tanh
(
V
k
/
4) and
τ
e
=2
ms
is the decay time constant.
The network of FS interneurons feedback inhibition to the pyramidal neurons
and the inhibitory current of the
j
th
cell is given by
−
1
k
1
N
FS
−
I
FP,j
=
g
FP
s
FP,k
(
t
)(
V
j
−
V
FP
)
−
(16)
=
j
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