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Magnus, Keizer, 1997
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Minimal Model of beta-cell mitochondrial Ca2+ handling
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Model Mathematics
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Component: environment
Component: membrane
d
d
time
V
=
-1.0
Cmito
JH_F1
+
J_ant
+
JH_leak
+
J_uni
2.0
-
JH_res
delta_pH
=
pH_i
-
pH_m
proton_motive_force
=
V
-
2.303
R
T
F
delta_pH
Component: proton_pump
JH_res
=
360.0
rho_res
ra
10.0
6.0
delta_pH
ⅇ
F
A_res
R
T
+
rb
10.0
6.0
delta_pH
-
ra
+
rb
ⅇ
g
6.0
F
V
R
T
1.0
+
r1
ⅇ
F
A_res
R
T
ⅇ
6.0
F
V_B
R
T
+
r2
+
r3
ⅇ
F
A_res
R
T
ⅇ
g
6.0
F
V
R
T
Jo
=
30.0
rho_res
ra
10.0
6.0
delta_pH
+
rc1
ⅇ
6.0
F
V_B
R
T
ⅇ
F
A_res
R
T
-
ra
ⅇ
g
6.0
F
V
R
T
+
rc2
ⅇ
F
A_res
R
T
ⅇ
g
6.0
F
V
R
T
1.0
+
r1
ⅇ
F
A_res
R
T
ⅇ
6.0
F
V_B
R
T
+
r2
+
r3
ⅇ
F
A_res
R
T
ⅇ
g
6.0
F
V
R
T
A_res
=
R
T
F
ln
K_res
NADH_m
NAD_m
total_NAD_m
=
NADH_m
+
NAD_m
Component: proton_leak
JH_leak
=
g_H
proton_motive_force
Component: F0_F1_ATPase
JH_F1
=
-180.0
rho_F1
pa
10.0
3.0
delta_pH
ⅇ
F
A_F1
R
T
+
pb
10.0
3.0
delta_pH
-
pa
+
pb
ⅇ
3.0
F
V
R
T
1.0
+
p1
ⅇ
F
A_F1
R
T
ⅇ
3.0
F
V_B
R
T
+
p2
+
p3
ⅇ
F
A_F1
R
T
ⅇ
3.0
F
V
R
T
Jp_F1
=
-60.0
rho_F1
pa
10.0
3.0
delta_pH
+
pc1
ⅇ
3.0
F
V_B
R
T
ⅇ
F
A_F1
R
T
-
pa
ⅇ
3.0
F
V
R
T
+
pc2
ⅇ
F
A_F1
R
T
ⅇ
3.0
F
V
R
T
1.0
+
p1
ⅇ
F
A_F1
R
T
ⅇ
3.0
F
V_B
R
T
+
p2
+
p3
ⅇ
F
A_F1
R
T
ⅇ
3.0
F
V
R
T
A_F1
=
R
T
F
ln
K_F1
ATP_m
ADP_m_free
Pi_m
total_mitochondrial_adenosine_phosphate
=
ATP_m
+
ADP_m
ADP_m_free
=
0.8
ADP_m
Component: ATP_ADP_exchange
J_ant
=
Jmax_ant
1.0
-
ATP4_i
ADP3_m
ADP3_i
ATP4_m
ⅇ
-
F
V
R
T
1.0
+
ATP4_i
ADP3_i
ⅇ
-
f
F
V
R
T
1.0
+
ADP3_m
ATP4_m
d
d
time
ADP_m
=
J_ant
-
Jp_F1
ADP3_m
=
0.45
0.8
ADP_m
ADP3_i
=
0.45
1.0
ADP_i
ATP4_m
=
0.05
ATP_m
ATP4_i
=
0.05
ATP_i
Component: Ca_uniporter
J_uni
=
Jmax_uni
Ca_i
K_trans
1.0
+
Ca_i
K_trans
3.0
1.0
+
Ca_i
K_trans
4.0
+
L
1.0
+
Ca_i
K_act
na
2.0
F
V
-
V_offset
R
T
1.0
-
ⅇ
-2.0
F
V
-
V_offset
R
T
Component: Na_Ca_exchanger
J_Na_Ca
=
Jmax_Na_Ca
ⅇ
b
F
V
-
V_offset
R
T
1.0
+
K_Na
Na_i
n
1.0
+
K_Ca
Ca_m
d
d
time
Ca_m
=
fm
J_uni
-
J_Na_Ca
Source
Derived from workspace
Magnus, Keizer, 1997
at changeset
dfde5c8c8f2f
.
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This work is licensed under a
Creative Commons Attribution 3.0 Unported License
.
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Minimal Model of beta-cell mitochondrial Ca2+ handling