Biomedical Engineering Reference
In-Depth Information
q
Ca
þ2
0
¼
J
Ca
þ2
þ
K
q
R
o
þ
K
q
R
o
þ
K
q
R
o
þ
K
q
R
10
1
21
2
32
3
43
4
o
K
01
q
Ca
þ2
0
q
R
o
K
12
q
Ca
þ2
0
q
R
o
K
23
q
Ca
þ2
0
q
R
o
K
34
q
Ca
þ2
0
q
R
0
1
2
3
o
ð
12
:
54
Þ
q
R
o
¼
B
8
q
R
i
þ
K
10
q
R
o
K
01
q
Ca
þ2
0
q
R
0
1
0
o
q
R
o
¼
K
q
R
o
þ
K
q
Ca
þ2
0
q
R
o
K
q
R
o
K
q
Ca
þ2
0
q
R
21
2
01
0
10
1
12
1
o
1
q
R
o
¼
K
32
q
R
o
þ
K
12
q
Ca
þ2
o
q
R
o
K
21
q
R
o
K
23
q
Ca
þ2
o
q
R
2
3
1
2
2
o
q
R
o
¼
K
43
q
R
o
þ
K
23
q
Ca
þ2
o
q
R
o
K
32
q
R
o
K
34
q
Ca
þ2
o
q
R
4
2
3
3
o
3
q
R
o
¼
K
q
Ca
þ2
o
q
R
o
K
q
R
o
B
q
R
34
3
43
4
1
4
o
4
R
i
o
iCa
þ2
o
where
has
bound to it, the transfer rates,
K
i
,
j
, are functions of membrane voltage,
Ca
þ2
out of the cell. Here, we assume that the quantity of
Ca
þ2
and
J
Ca
þ2
is the flow of
is
constant and given by g
¼
q
Ca
þ2
i
þ
q
Ca
þ2
o
q
R
o
q
R
o
q
R
o
q
R
o
q
R
o
:
The flow
J
Ca
þ2
is due
0
1
2
3
4
Ca
þ2
in the cytosol low, while the concen-
tration outside the cell is very high. One can imagine a similar process for the
to an active pump that keeps the concentration of
J
Ca
þ2
active
pump as given for the
pump described in Section 8.4.4. The transfer rates are zero
at resting potential and increase as the membrane depolarizes (Keener and Sneyd use expo-
nential functions for the transfer rates). Next, we have
q
P
o
¼
B
1
q
R
Na-K
o
þ
B
2
q
P
i
B
2
q
P
o
4
q
P
i
¼
B
q
P
o
B
2
q
P
i
B
q
P
i
q
V
i
2
3
q
P
i
q
V
i
q
V
o
¼
B
6
q
W
o
B
7
q
V
o
q
W
i
¼
B
q
V
i
¼
J
V
i
B
3
ð
12
:
55
Þ
q
C
i
q
P
i
V
i
þ
B
5
q
W
o
B
q
W
i
4
5
q
W
o
¼
B
q
W
i
B
5
q
W
o
B
q
W
o
5
6
q
C
i
¼
B
q
C
i
q
P
i
V
i
q
C
o
¼
B
6
q
W
o
B
9
q
C
o
q
N
o
¼
nB
q
C
o
B
9
4
q
V
o
7
where
J
V
i
is the rate of the creation of new vesicles.
It should be noted that the vesicles absorbed into the cell membrane during the move-
ment of the neurotransmitter out of the cell, after a period of time, leave the cell mem-
braneandreforminthecytosolwiththesamecharacteristicsasbefore.Thevesicle
then synthesizes the neurotransmitter using enzyme proteins in its membrane using
ATP from the mitochondria. For example, ACh is resupplied inside the vesicle using a
carrier-mediated enzyme choline acetyltransferase that binds acetyl coenzyme and cho-
line similar to the reaction described in Section 8.4.3. The entire process from receipt of
the action potential at the presynaptic terminal to release of the neurotransmitter takes
less than 1 ms.
