Biomedical Engineering Reference
In-Depth Information
1
0.8
Poisson
Regular
0.6
0.4
0.2
0
0
20
40
60
80
Pre-synaptic Firing Rate (Hz)
Figure 15.3
Average fraction of open NMDA channels as a function of the pre-synaptic firing
rate. The solid (dashed) line, calculated with Equation (15.43) (Equation (15.42)),
corresponds to the case when the spike train at the synapse is Poisson (periodic).
If the spike train is Poisson, the expression for ¯
s
is [25]
1
•
Â
n
at
rise
n
T
n
nt
1
(
−
)
s
=
+
≡
y
(
n
)
+
+
(
+
)
1
nt
1
n
n
1
!
=
1
k
n
k
Â
k
t
rise
(
+
)
1
nt
T
n
=
0
(
−
1
)
k
t
decay
.
(15.43)
t
rise
(
1
+
nt
)+
=
We will use this description for NMDAR-mediated transmission, with parameters
t
decay
NMDA
100 ms, t
rise
NMDA
=
=
2ms,anda
=
0
.
5 KHz.
The effective NMDA time
constant is thus
100 ms. In Figure 15.3, the average gating variable of an
NMDA synapse is plotted as a function of the average pre-synaptic firing rate n,for
the case of a regular and a Poisson input spike train. Note that, due to the saturation
term on the right of Equation (15.40), the gating variable starts to saturate when the
pre-synaptic rate becomes larger than
t
NMDA
=
∼
1
/
t
NMDA
∼
10 Hz.
15.2.6.3
Voltage-dependence of the post-synaptic currents
A post-synaptic current is voltage-dependent because of its driving force; in addition
the maximal conductance can also be voltage-dependent, as in the case of the NMDA
channels [87].
In general, even if the maximal conductance does not depend on the voltage, the
voltage dependence induced by the driving force term in the unitary synaptic current
(15.38) modifies the previous framework for calculating the output firing rate of the
cell in several ways.
Let us separate the time course of the gating variable into a deterministic compo-
nent, associated to its temporal average (we assume stationary inputs, in which case
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