Biomedical Engineering Reference
In-Depth Information
where
G
H
L
is the constant conductance for the leak current. The voltage-
dependent sodium and potassium conductances are given by
G
H
Na
=
g
Na
m
3
HI
h
HI
,
(8.19)
G
H
K
=
g
K
n
4
HI
,
(8.20)
where the dynamics of the activation and inactivation variables
m
HI
,
n
HI
and
h
HI
are given by (8.11). The last term on the right of (8.15) represents
the input to the inhibitory unit from all the excitatory HVC units in the
model. It is a sum of synaptic currents and is given by
N
HVC
I
HI
V
HI
)
g
HI
HE
=(
E
E
−
S
(
V
Hj
)
.
(8.21)
HE
j
=1
The resting potential of the isolated inhibitory HVC neuron is
65 mV.
Equations (8.5)-(8.21) describe a set of excitatory HVC neurons which are
connected in a feed-forward fashion (so that activation of neuron
j
= 1 excites
j
= 2 and so forth to
j
=
N
HV C
, with
S
(
V
H
0
) = 0), plus an inhibitory neuron
connected to each of them. We use constants guaranteeing that an initial
excitation of the first unit will excite the remaining units sequentially. When
g
HI
∼−
= 0, the inhibitory neuron receives excitatory input in a global fashion
from the excitatory HVC neurons, and each excitatory HVC neuron receives
inhibition as well as sequential excitation. The parameters of the system are
adjusted so that the activity of an RA-projecting HVC unit consists of 4 to
7 spikes [Hahnloser et al. 2002].
8.4.2 Simulating the Activity of RA Neurons
A similar procedure can be carried out for the simulation of the activities of
the RA neurons. The
k
th excitatory RA neuron also satisfies an HH equation,
with the addition of input synaptic currents from the HVC population and
from the inhibitory RA interneuron, as well as excitatory connections from
other excitatory neurons within RA. The membrane voltage of the
k
th RA
excitatory neuron,
V
Rk
(
t
), where
k
=1
,
2
,...,N
RA
, satisfies
C
M
dV
Rk
dt
=
I
L
+
I
Na
+
I
K
+
I
RI
+
I
RE
+
I
HE
+
I
DC
,
(8.22)
where, again, we have the usual leak, sodium and potassium currents, as
well as the synaptic currents
I
RI
from the single inhibitory RA neuron and
I
RE
from several other RA excitatory neurons. In addition, HVC
RA
connections are considered: input from several excitatory HVC neurons is
represented by the synaptic current
I
HE
. With the constant current
I
DC
also present, these excitatory units in RA display, before HVC activity starts,
spontaneous spiking at approximately 20 Hz.
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