Biomedical Engineering Reference
In-Depth Information
Ca
þ2
in the
cytosol appears to be proportional to the number of action potentials, and in turn, the
amount of neurotransmitter released.
Keener and Sneyd [2] provide an excellent summary in Chapter 7 of the various theories
involving the role of
Ca
þ2
terminal, the concentration of
in the cytosol quickly rises. The amount of
Ca
þ2
in the release of neurotransmitter into the synaptic gap. Two current
models involve different roles for the change in membrane potential, one indicating that it has
a direct effect on the amount of neurotransmitter released, and the other acting directly on the
Ca
þ2
entering the cytosol.
For illustrative purposes, consider a model for the movement of the neurotransmitter
vesicles that involves the transport of
Ca
þ2
across the cell membrane using a carrier-
mediated transport process as described in Section 8.4.3.
2
When an action potential depo-
larizes the presynaptic terminal, a voltage-gated channel in the membrane is activated that
allows up to four
Ca
þ2
to bind to a binding protein,
R,
on the outside of the cell membrane
.
Ca
þ2
,
When totally bound, the protein joined by four
P
, moves to the interior of the cell
membrane, where it binds with a vesicle,
V
. A carrier,
C
, is then joined with
PV
, forming
Ca
þ2
and the binding protein
the bound carrier
W
. This reaction releases the four
R.
The
bound carrier
then moves to the outside of the cell membrane through the opened volt-
age-gated channel, where vesicle releases
W
n
packets of the neurotransmitter
N.
The overall
reaction is given by
B
2
B
1
Ca
þ2
4
o
þ
R
o
!
P
o
!
P
i
B
2
B
3
P
i
þ
V
i
!
P
i
V
i
B
4
Ca
þ2
C
i
þ
P
i
V
i
!
W
i
þ
4
o
þ
R
i
ð
12
:
53
Þ
B
5
B
6
W
i
!
W
o
!
V
o
þ
C
o
B
5
B
7
V
o
!
nN
B
8
R
i
!
R
o
B
9
C
o
!
C
i
where the subscript
are the inside and outside. Figure 12.39 shows a model of the four
stages of the binding protein with
i
and
o
Ca
þ2
, which are described by the following equations.
K
12
q
Ca
+2
K
34
q
Ca
+2
K
23
q
Ca
+2
K
01
q
Ca
+2
q
R
0
q
R
1
q
R
2
q
R
3
q
R
4
K
21
K
32
K
43
FIGURE 12.39
Carrier-mediated transport of calcium ions into the presynaptic terminal that initiates the move-
ment of the neurotransmitter out of the cell.
K
10
2
A more complex model is given in Section 7.1.3 of Keener and Sneyd that involves probabilistic
considerations.
