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for t
0
<t<t
1
where
a
r
T
max
a
r
T
max
Ca
d
s
1
D
(4.9)
and
1
a
r
T
max
Ca
d
s
D
(4.10)
After the pulse of the transmitter has gone, s.t/ decays as
s.t/ D s.t
1
/e
a
d
.tt
1
/
(4.11)
A model about the concentration of the transmitter at the pre-synaptic neuron is
T
max
1Cexp..V
pre
V
T
=KCp//
ŒT.V
pre
/ D
(4.12)
4.4
Study of the Glutamate Neurotransmitter
Glutamate neurotransmitter activates two different types of receptors: (1)
AMPA/Kainate which is vary fast, (2) NMDA which is associated with memory.
Both receptors lead to activation of the post-synaptic neuron [
16
,
65
].
(a) AMPA/Kainate
The current associated with the neuro-transmitter is
I
AMPA
Dg
AMPA
.V V
AMPA
/
(4.13)
The responses of AMPA synapses can be very fast, for example in the case of
acoustic neurons they can have rise and decay times of the order of milliseconds.
Similarly, in the case of cortical neurons the rise and decay time can be of the
order of 0.4-0.8 ms. AMPA synapses exhibit intensive depression in case of
subsequent spikes. Each time that a spike is generated the amplitude of the
AMPA current at the post-synaptic neuron drops.
(b) NMDA
The NMDA receptor is also sensitive to glutamate with a response that lasts
longer than the one of AMPA. Under normal conditions the NMDA receptor
is partially found blocked by Mg
2C
ions. One of the basic types of ions that
is transferred by the NMDA current is Ca
2C
which is responsible for many
long-term changes in neurons. This ion is considered to affect significantly the
mechanism of short-term memory.
