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Eskandari, Wright, Loo 2005
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Renal SGLT1 model
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Model Mathematics
Component based math viewer is available
Component: environment
Component: parameters
k0_65
=
k0_65_r
if
Na_o
<
100
e
-3
k0_65_f
otherwise
k0_61
=
k0_61_r
if
Na_o
<
100
e
-3
k0_61_f
otherwise
k0_16
=
k0_16_r
if
Na_o
<
100
e
-3
k0_16_f
otherwise
alpha_p
=
1
-
delta
-
alpha_pp
C_T
=
1
e
6
N_C
N_Avo
mu
=
F
V
R
T
Component: ion_concentrations
d
d
time
V
=
200
e
-3
Component: rate_constants
ks_12
=
k0_12
ⅇ
-
n
alpha_p
mu
2
k_12
=
ks_12
Na_o
n
k_21
=
k0_21
ⅇ
n
z_Na
alpha_p
mu
2
k_23
=
k0_23
glucose_o
k_32
=
k0_32
k_34
=
k0_34
ⅇ
-
z_c
+
n
delta
mu
2
k_43
=
k0_43
ⅇ
z_c
+
n
delta
mu
2
k_45
=
k0_45
k_54
=
k0_54_temp
glucose_i
k_25
=
k0_25
ⅇ
-
z_c
+
n
delta
mu
2
k_52_temp
=
k0_52
ⅇ
z_c
+
n
delta
mu
2
k_56
=
k0_56
ⅇ
-
n
z_Na
alpha_pp
mu
2
k_65
=
k0_65
Na_i
n
ⅇ
n
z_Na
alpha_pp
mu
2
k_61
=
k0_61
ⅇ
z_c
delta
mu
2
k_16
=
k0_16
ⅇ
-
z_c
delta
mu
2
k_52
=
k0_12
k_25
k0_56
k0_61
k0_21
k0_16
k0_65
k0_54_temp
=
k0_23
k_34
k_45
k_52
k_43
k_32
k_25
Component: kinetic_equations
d
d
time
C_1
=
k_21
C_2
+
k_61
C_6
-
k_12
+
k_16
C_1
d
d
time
C_2
=
k_12
C_1
+
k_32
C_3
+
k_52
C_5
-
k_21
+
k_23
+
k_25
C_2
d
d
time
C_3
=
k_23
C_2
+
k_43
C_4
-
k_32
+
k_34
C_3
d
d
time
C_4
=
k_34
C_3
+
k_54
C_5
-
k_45
+
k_43
C_4
d
d
time
C_5
=
k_45
C_4
+
k_65
C_6
+
k_25
C_2
-
k_54
+
k_52
+
k_56
C_5
d
d
time
C_6_temp
=
k_16
C_1
+
k_56
C_5
-
k_61
+
k_65
C_6_temp
C_6
=
C_T
-
C_1
+
C_2
+
C_3
+
C_4
+
C_5
Component: king_altman_states
C1_sum
=
k_21
k_32
k_43
k_54
k_65
+
k_21
k_34
k_45
k_52
k_65
+
k_21
k_32
k_45
k_52
k_65
+
k_21
k_32
k_43
k_52
k_65
+
k_25
k_34
k_45
k_56
k_61
+
k_23
k_34
k_45
k_56
k_61
+
k_21
k_34
k_45
k_56
k_61
+
k_25
k_32
k_45
k_56
k_61
+
k_21
k_32
k_45
k_56
k_61
+
k_25
k_32
k_43
k_56
k_61
+
k_21
k_32
k_43
k_56
k_61
+
k_21
k_32
k_43
k_54
k_61
+
k_21
k_34
k_45
k_52
k_61
+
k_21
k_32
k_45
k_52
k_61
+
k_21
k_32
k_43
k_52
k_61
C2_sum
=
k_16
k_32
k_43
k_54
k_65
+
k_12
k_32
k_43
k_54
k_65
+
k_16
k_34
k_45
k_52
k_65
+
k_12
k_34
k_45
k_52
k_65
+
k_16
k_32
k_45
k_52
k_65
+
k_12
k_32
k_45
k_52
k_65
+
k_16
k_32
k_43
k_52
k_65
+
k_12
k_32
k_43
k_52
k_65
+
k_12
k_34
k_45
k_56
k_61
+
k_12
k_32
k_45
k_56
k_61
+
k_12
k_32
k_43
k_56
k_61
+
k_12
k_32
k_43
k_54
k_61
+
k_12
k_34
k_45
k_52
k_61
+
k_12
k_32
k_45
k_52
k_61
+
k_12
k_32
k_43
k_52
k_61
C3_sum
=
k_16
k_25
k_43
k_54
k_65
+
k_12
k_25
k_43
k_54
k_65
+
k_16
k_23
k_43
k_54
k_65
+
k_12
k_23
k_43
k_54
k_65
+
k_16
k_21
k_43
k_54
k_65
+
k_16
k_23
k_45
k_52
k_65
+
k_12
k_23
k_45
k_52
k_65
+
k_16
k_23
k_43
k_52
k_65
+
k_12
k_23
k_43
k_52
k_65
+
k_12
k_23
k_45
k_56
k_61
+
k_12
k_23
k_43
k_56
k_61
+
k_12
k_25
k_43
k_54
k_61
+
k_12
k_23
k_43
k_54
k_61
+
k_12
k_23
k_45
k_52
k_61
+
k_12
k_23
k_43
k_52
k_61
C4_sum
=
k_16
k_25
k_34
k_54
k_65
+
k_12
k_25
k_34
k_54
k_65
+
k_16
k_23
k_34
k_54
k_65
+
k_12
k_23
k_34
k_54
k_65
+
k_16
k_21
k_34
k_54
k_65
+
k_16
k_25
k_32
k_54
k_65
+
k_12
k_25
k_32
k_54
k_65
+
k_16
k_21
k_32
k_54
k_65
+
k_16
k_23
k_34
k_52
k_65
+
k_12
k_23
k_34
k_52
k_65
+
k_12
k_23
k_34
k_56
k_61
+
k_12
k_25
k_34
k_54
k_61
+
k_12
k_23
k_34
k_54
k_61
+
k_12
k_25
k_32
k_54
k_61
+
k_12
k_23
k_34
k_52
k_61
C5_sum
=
k_16
k_25
k_34
k_45
k_65
+
k_12
k_25
k_34
k_45
k_65
+
k_16
k_23
k_34
k_45
k_65
+
k_12
k_23
k_34
k_45
k_65
+
k_16
k_21
k_34
k_45
k_65
+
k_16
k_25
k_32
k_45
k_65
+
k_12
k_25
k_32
k_45
k_65
+
k_16
k_21
k_32
k_45
k_65
+
k_16
k_25
k_32
k_43
k_65
+
k_12
k_25
k_32
k_43
k_65
+
k_16
k_21
k_32
k_43
k_65
+
k_12
k_25
k_34
k_45
k_61
+
k_12
k_23
k_34
k_45
k_61
+
k_12
k_25
k_32
k_45
k_61
+
k_12
k_25
k_32
k_43
k_61
C6_sum
=
k_16
k_25
k_34
k_45
k_56
+
k_12
k_25
k_34
k_45
k_56
+
k_16
k_23
k_34
k_45
k_56
+
k_12
k_23
k_34
k_45
k_56
+
k_16
k_21
k_34
k_45
k_56
+
k_16
k_25
k_32
k_45
k_56
+
k_12
k_25
k_32
k_45
k_56
+
k_16
k_21
k_32
k_45
k_56
+
k_16
k_25
k_32
k_43
k_56
+
k_12
k_25
k_32
k_43
k_56
+
k_16
k_21
k_32
k_43
k_56
+
k_16
k_21
k_32
k_43
k_54
+
k_16
k_21
k_34
k_45
k_52
+
k_16
k_21
k_32
k_45
k_52
+
k_16
k_21
k_32
k_43
k_52
C_sum
=
C1_sum
+
C2_sum
+
C3_sum
+
C4_sum
+
C5_sum
+
C6_sum
C1
=
C_T
C1_sum
C_sum
C2
=
C_T
C2_sum
C_sum
C3
=
C_T
C3_sum
C_sum
C4
=
C_T
C4_sum
C_sum
C5
=
C_T
C5_sum
C_sum
C6
=
C_T
C6_sum
C_sum
Component: NBC_current
I_NaGl_pSS
=
-
F
n
z_Na
alpha_p
k_12
C_1
-
k_21
C_2
+
z_c
delta
k_16
C_1
-
k_61
C_6
+
n
z_Na
alpha_pp
k_56
C_5
-
k_65
C_6
I_NaGl_SS
=
-
F
z_c
k_16
C1
-
k_61
C6
+
z_c
+
z_Na
n
k_25
C2
-
k_52
C5
+
z_c
+
z_Na
n
k_34
C3
-
k_43
C4
Component: phenomonological_constants
lambda
=
ks_12
k0_23
k_43
k_54
k_65
+
ks_12
k0_23
k_34
k_54
k_65
+
ks_12
k0_23
k_45
k_52
k_65
+
ks_12
k0_23
k_43
k_52
k_65
+
ks_12
k0_23
k_34
k_52
k_65
+
ks_12
k0_23
k_34
k_45
k_65
+
ks_12
k0_23
k_45
k_56
k_61
+
ks_12
k0_23
k_43
k_56
k_61
+
ks_12
k0_23
k_34
k_56
k_61
+
ks_12
k0_23
k_43
k_54
k_61
+
ks_12
k0_23
k_34
k_54
k_61
+
ks_12
k0_23
k_45
k_52
k_61
+
ks_12
k0_23
k_43
k_52
k_61
+
ks_12
k0_23
k_34
k_52
k_61
+
ks_12
k0_23
k_34
k_45
k_61
+
ks_12
k0_23
k_34
k_45
k_56
chi
=
1
lambda
ks_12
k_32
k_43
k_54
k_65
+
ks_12
k_25
k_43
k_54
k_65
+
ks_12
k_25
k_34
k_54
k_65
+
ks_12
k_25
k_32
k_54
k_65
+
ks_12
k_34
k_45
k_52
k_65
+
ks_12
k_32
k_45
k_52
k_65
+
ks_12
k_32
k_43
k_52
k_65
+
ks_12
k_25
k_34
k_45
k_65
+
ks_12
k_25
k_32
k_45
k_65
+
ks_12
k_25
k_32
k_43
k_65
+
ks_12
k_34
k_45
k_56
k_61
+
ks_12
k_32
k_45
k_56
k_61
+
ks_12
k_32
k_43
k_56
k_61
+
ks_12
k_32
k_43
k_54
k_61
+
ks_12
k_25
k_43
k_54
k_61
+
ks_12
k_25
k_34
k_54
k_61
+
ks_12
k_25
k_32
k_54
k_61
+
ks_12
k_34
k_45
k_52
k_61
+
ks_12
k_32
k_45
k_52
k_61
+
ks_12
k_32
k_43
k_52
k_61
+
ks_12
k_25
k_34
k_45
k_61
+
ks_12
k_25
k_32
k_45
k_61
+
ks_12
k_25
k_32
k_43
k_61
+
ks_12
k_25
k_34
k_45
k_56
+
ks_12
k_25
k_32
k_45
k_56
+
ks_12
k_25
k_32
k_43
k_56
beta
=
1
lambda
k0_23
k_16
k_43
k_54
k_65
+
k0_23
k_16
k_34
k_54
k_65
+
k0_23
k_16
k_45
k_52
k_65
+
k0_23
k_16
k_43
k_52
k_65
+
k0_23
k_16
k_34
k_52
k_65
+
k0_23
k_16
k_34
k_45
k_65
+
k0_23
k_34
k_45
k_56
k_61
+
k0_23
k_16
k_34
k_45
k_56
alpha
=
1
lambda
k_21
k_32
k_43
k_54
k_65
+
k_16
k_32
k_43
k_54
k_65
+
k_16
k_25
k_43
k_54
k_65
+
k_16
k_21
k_43
k_54
k_65
+
k_16
k_25
k_34
k_54
k_65
+
k_16
k_21
k_34
k_54
k_65
+
k_16
k_25
k_32
k_54
k_65
+
k_16
k_21
k_32
k_54
k_65
+
k_21
k_34
k_45
k_52
k_65
+
k_16
k_34
k_45
k_52
k_65
+
k_21
k_32
k_45
k_52
k_65
+
k_16
k_32
k_45
k_52
k_65
+
k_21
k_32
k_43
k_52
k_65
+
k_16
k_32
k_43
k_52
k_65
+
k_16
k_25
k_34
k_45
k_65
+
k_16
k_21
k_34
k_45
k_65
+
k_16
k_25
k_32
k_45
k_65
+
k_16
k_21
k_32
k_45
k_65
+
k_16
k_25
k_32
k_43
k_65
+
k_16
k_21
k_32
k_43
k_65
+
k_25
k_34
k_45
k_56
k_61
+
k_21
k_34
k_45
k_56
k_61
+
k_25
k_32
k_45
k_56
k_61
+
k_21
k_32
k_45
k_56
k_61
+
k_25
k_32
k_43
k_56
k_61
+
k_21
k_32
k_43
k_56
k_61
+
k_21
k_32
k_43
k_54
k_61
+
k_21
k_34
k_45
k_52
k_61
+
k_21
k_32
k_45
k_52
k_61
+
k_21
k_32
k_43
k_52
k_61
+
k_16
k_25
k_34
k_45
k_56
+
k_16
k_21
k_34
k_45
k_56
+
k_16
k_25
k_32
k_45
k_56
+
k_16
k_21
k_32
k_45
k_56
+
k_16
k_25
k_32
k_43
k_56
+
k_16
k_21
k_32
k_43
k_56
+
k_16
k_21
k_32
k_43
k_54
+
k_16
k_21
k_34
k_45
k_52
+
k_16
k_21
k_32
k_45
k_52
+
k_16
k_21
k_32
k_43
k_52
gamma
=
1
lambda
k_16
k_21
k_32
k_43
k_54
k_65
+
k_16
k_21
k_34
k_45
k_52
k_65
+
k_16
k_21
k_32
k_45
k_52
k_65
+
k_16
k_21
k_32
k_43
k_52
k_65
phi
=
1
lambda
-
ks_12
k_25
k_34
k_45
k_56
k_61
-
ks_12
k_25
k_32
k_45
k_56
k_61
-
ks_12
k_25
k_32
k_43
k_56
k_61
epsilon
=
1
lambda
-
ks_12
k0_23
k_34
k_45
k_56
k_61
Imax_gluc
=
2
F
C_T
epsilon
Na_o
2
beta
+
Na_o
2
Imax_Na
=
2
F
C_T
phi
+
epsilon
glucose_o
chi
+
glucose_o
Khalf_gluc
=
alpha
+
chi
Na_o
2
beta
+
Na_o
2
Khalf_Na_sq
=
alpha
+
beta
glucose_o
chi
+
glucose_o
Khalf_Na
=
Khalf_Na_sq
Source
Derived from workspace
Eskandari, Wright, Loo 2005
at changeset
5d9d9d818d66
.
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Renal SGLT1 model