Biomedical Engineering Reference
In-Depth Information
12.8.2 Postsynaptic Neurons
Once the neurotransmitter is released from the presynaptic neuron, it diffuses across the
synaptic gap and binds to the receptors on the postsynaptic neuron's dendrite. Once bound
to the dendrite, the neurotransmitter moves into the cytosol by carrier-mediated transport,
where once in the cytosol, an ion channel opens. If the neurotransmitter is excitatory,
Na
þ
flows into the open channel, and the membrane depolarizes. If the neurotransmitter is
inhibitory,
Cl
flows into the open channel, and the membrane hyperpolarizes. This process
takes less than 1 ms. The change in membrane potential lasts up to 15 ms due to the capaci-
tive nature of the membrane, thus allowing for temporal summation of all the neurotrans-
mitter secreted by the many presynaptic terminals.
Consider the neurotransmitter ACh and its carrier-mediated transport into the cytosol of
the postsynaptic neuron. ACh binds to the enzyme choline acetyltransferase,
, that trans-
ports it across the membrane, allowing it to pass into the cytosol. Using the model illus-
trated in Figure 8.21, we have
C
K
2
K
1
K
3
ACh
0
þ
C
0
!
P
o
!
P
i
!
ACh
i
þ
C
i
K
2
K
4
ð
12
:
56
Þ
ACh
i
!
A
i
þ
Ch
i
K
2
C
o
!
C
i
K
2
where
P
is the bound substrate and carrier complex,
A
is acetyl coenzyme A, and
Ch
is
choline. As before,
i
and
o
subscripts refer to the inside and outside of the cell. We assume
that
A
and
Ch
are moved from the cytosol into the synaptic gap by diffusion and that the
flow of
ACh
into the synaptic gap from the presynaptic neuron is given by
N
o
(now called
ACh
o
) from Eq. (12.55). The equations that describe this system are given by
q
ACh
o
¼
K
1
q
ACh
o
q
C
o
þ
nB
7
q
V
o
q
C
o
¼
K
q
C
o
q
P
o
¼
K
1
q
ACh
o
q
C
o
þ
K
2
q
P
i
K
2
q
P
o
q
P
i
¼
K
q
ACh
o
q
C
o
þ
K
q
C
i
K
1
2
2
q
P
i
q
ACh
i
¼
K
1
q
P
i
K
4
q
ACh
i
q
C
i
¼
K
q
P
o
K
2
1
ð
12
:
57
Þ
q
P
i
þ
K
q
C
o
K
q
C
i
1
2
2
q
A
i
¼
K
q
ACh
i
D
A
q
A
i
q
Ch
i
¼
K
4
q
ACh
i
D
Ch
q
Ch
i
4
and its impact on the mem-
brane potential, we introduce another channel in the dendritic membrane section, as shown
in Figure 12.40, where the stimulus current,
To capture the change in conductance as a function of
ACh
i
,
I
s
, from the neurotransmitter is
I
s
¼
V
m
V
TH
R ACh
ð Þ
ð
12
:
58
Þ
where
R ACh
ð Þ
is the channel resistance that depends on the quantity of
ACh
i
.
