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Reproducibility of the computational model of induced pluripotent stem-cell derived cardiomyocytes
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Model Mathematics
Component based math viewer is available
Component: main
k_fca
=
0
if
x_fca_inf_inact
>
X_fca_inact
∧
v
>
-
60
1
otherwise
v_clamp
=
v
E_K
=
R
T
F
ln
Ko
Ki
g_k1
=
var_1
i_k1
=
g_k1
Ko
5.4
x_inf_act_Ik1
v
-
E_K
d
d
t
X_kr_act
=
x_inf_act
-
X_kr_act
tau_kr_act
d
d
t
X_kr_inact
=
x_inf_inact
-
X_kr_inact
tau_kr_inact
g_Kr
=
Xr1_0
i_Kr
=
g_Kr
Ko
5.4
X_kr_act
X_kr_inact
v
-
E_K
d
d
t
X_ks_act
=
x_ks_inf_act
-
X_ks_act
tau_ks_act
g_Ks
=
ks_0
i_Ks
=
g_Ks
X_ks_act
2
v
-
E_K
d
d
t
X_to_act
=
x_to_inf_act
-
X_to_act
tau_to_act
d
d
t
X_to_inact
=
x_to_inf_inact
-
X_to_inact
tau_to_inact
g_to
=
r_0
i_to
=
g_to
X_to_act
X_to_inact
v
-
E_K
d
d
t
X_ca_act
=
x_ca_inf_act
-
X_ca_act
tau_ca_act
d
d
t
X_ca_inact
=
x_ca_inf_inact
-
X_ca_inact
tau_ca_inact
d
d
t
X_fca_inact
=
k_fca
x_fca_inf_inact
-
X_fca_inact
tau_fca
p_CaL
=
d_0
p_CaL_shannonTot
=
p_CaL_shannonCa
+
p_CaL_shannonNa
+
p_CaL_shannonK
p_CaL_shannonCap
=
p_CaL_shannonCa
p_CaL_shannonTot
p_CaL_shannonNap
=
p_CaL_shannonNa
p_CaL_shannonTot
p_CaL_shannonKp
=
p_CaL_shannonK
p_CaL_shannonTot
p_CaL_Ca
=
p_CaL_shannonCap
p_CaL
p_CaL_Na
=
p_CaL_shannonNap
p_CaL
p_CaL_K
=
p_CaL_shannonKp
p_CaL
ibarca
=
p_CaL_Ca
4.0
v
F
2
R
T
0.341
ca_i
ⅇ
2.0
v
F
R
T
-
0.341
Cao
ⅇ
2.0
v
F
R
T
-
1.0
i_CaL_Ca
=
ibarca
X_ca_act
X_ca_inact
X_fca_inact
ibarna
=
p_CaL_Na
v
F
2
R
T
0.75
Na_i
ⅇ
2.0
v
F
R
T
-
0.75
Nao
ⅇ
2.0
v
F
R
T
-
1.0
i_CaL_Na
=
ibarna
X_ca_act
X_ca_inact
X_fca_inact
ibark
=
p_CaL_K
v
F
2
R
T
0.75
Ki
ⅇ
2.0
v
F
R
T
-
0.75
Ko
ⅇ
2.0
v
F
R
T
-
1.0
i_CaL_K
=
ibark
X_ca_act
X_ca_inact
X_fca_inact
i_CaL
=
i_CaL_Ca
+
i_CaL_Na
+
i_CaL_K
d
d
t
X_cat_act
=
x_cat_inf_act
-
X_cat_act
tau_cat_act
d
d
t
X_cat_inact
=
x_cat_inf_inact
-
X_cat_inact
tau_cat_inact
i_cat
=
g_cat
X_cat_act
X_cat_inact
v
-
E_Ca
E_Ca
=
0.5
R
T
F
ln
Cao
ca_i
E_Na
=
R
T
F
ln
Nao
Na_i
d
d
t
X_na_h_inact
=
x_na_h_inf_inact
-
X_na_h_inact
tau_na_h_inact
d
d
t
X_na_m_act
=
x_na_m_inf_act
-
X_na_m_act
tau_na_m_act
d
d
t
X_na_j_inact
=
x_na_j_inf_inact
-
X_na_j_inact
tau_na_j_inact
i_na
=
g_Na
X_na_m_act
3
X_na_h_inact
X_na_j_inact
v
-
E_Na
d
d
t
X_f_act
=
x_f_inf_act
-
X_f_act
tau_f_act
Na_frac
=
NatoK_ratio
NatoK_ratio
+
1
i_fNa
=
Na_frac
g_f
X_f_act
v
-
E_Na
i_fK
=
1
-
Na_frac
g_f
X_f_act
v
-
E_K
i_f
=
i_fNa
+
i_fK
i_naca
=
kNaCa
ⅇ
gamma
v
F
R
T
Na_i
3.0
Cao
-
ⅇ
gamma
-
1.0
v
F
R
T
Nao
3
ca_i
alpha
KmNai
3.0
+
Nao
3
KmCa
+
Cao
1.0
+
Ksat
ⅇ
gamma
-
1.0
v
F
R
T
i_nak
=
PNaK
Ko
Na_i
Ko
+
Km_K
Na_i
+
Km_Na
1.0
+
0.1245
ⅇ
-
0.1
v
F
R
T
+
0.0353
ⅇ
-
v
F
R
T
i_up
=
VmaxUp
1.0
+
Kup
2
ca_i
2
j_leak
=
ca_SR
-
ca_i
V_leak
kCaSR
=
MaxSR
-
MaxSR
-
MinSR
1
+
ec50SR
ca_SR
2.5
koSRCa
=
koCa
kCaSR
kiSRCa
=
kiCa
kCaSR
CI
=
1
-
C
-
O
-
I
d
d
t
C
=
kim
CI
-
kiSRCa
ca_i
C
-
koSRCa
ca_i
2
C
-
kom
O
d
d
t
O
=
koSRCa
ca_i
2
C
-
kom
O
-
kiSRCa
ca_i
O
-
kim
I
d
d
t
I
=
kiSRCa
ca_i
O
-
kim
I
-
kom
I
-
koSRCa
ca_i
2
CI
j_rel
=
ks
O
ca_SR
-
ca_i
V_SR
Vc
i_b_Na
=
g_b_Na
v
-
E_Na
i_b_Ca
=
g_b_Ca
v
-
E_Ca
i_PCa
=
g_PCa
ca_i
ca_i
+
KPCa
Ca_SR_bufSR
=
1
1
+
Buf_SR
Kbuf_SR
ca_SR
+
Kbuf_SR
2
d
d
t
ca_SR
=
Ca_SR_bufSR
Vc
V_SR
i_up
-
j_rel
+
j_leak
Cai_buf
=
1
1.0
+
Buf_C
Kbuf_C
ca_i
+
Kbuf_C
2
d
d
t
ca_ligand
=
0
d
d
t
ca_i
=
Cai_buf
j_leak
-
i_up
+
j_rel
-
ca_ligand
-
i_CaL_Ca
+
i_cat
+
i_b_Ca
+
i_PCa
-
2
i_naca
1
Cm
2
Vc
F
d
d
t
Na_i
=
-
Cm
i_na
+
i_b_Na
+
i_fNa
+
3
i_nak
+
3
i_naca
+
i_CaL_Na
F
Vc
d
d
t
Ki
=
-
Cm
i_k1
+
i_to
+
i_Kr
+
i_Ks
+
i_fK
-
2
i_nak
+
i_CaL_K
F
Vc
i_voltageclamp
=
v_clamp
-
v
R_clamp
d
d
t
v
=
-
i_k1
+
i_to
+
i_Kr
+
i_Ks
+
i_CaL
+
i_cat
+
i_nak
+
i_na
+
i_naca
+
i_PCa
+
i_f
+
i_b_Na
+
i_b_Ca
-
i_stim
-
i_voltageclamp
Component: parameter
V_tot_tenT
=
Vc_tenT
+
VSR_tenT
Vc
=
V_tot
Vc_tenT
V_tot_tenT
V_SR
=
V_tot
VSR_tenT
V_tot_tenT
Component: parameter_Ik1
Component: gating_Ik1
alpha_act
=
var_2
ⅇ
v
+
var_4
var_3
beta_act
=
ⅇ
v
+
var_6
var_5
x_inf_act_Ik1
=
alpha_act
alpha_act
+
beta_act
Component: parameter_Ikr
Component: gating_Ikr
Xr1_3
=
Xr1_5
Xr1_1
Xr2_3
=
Xr2_5
Xr2_1
Xr1_4
=
1
1
Xr1_2
+
1
Xr1_6
Xr2_4
=
1
1
Xr2_2
+
1
Xr2_6
alpha_act
=
Xr1_1
ⅇ
v
Xr1_2
beta_act
=
Xr1_3
ⅇ
v
Xr1_4
x_inf_act
=
alpha_act
alpha_act
+
beta_act
tau_kr_act
=
1
alpha_act
+
beta_act
+
Xr1_7
alpha_inact
=
Xr2_1
ⅇ
v
Xr2_2
beta_inact
=
Xr2_3
ⅇ
v
Xr2_4
x_inf_inact
=
alpha_inact
alpha_inact
+
beta_inact
tau_kr_inact
=
1
alpha_inact
+
beta_inact
+
Xr2_7
Component: parameter_Iks
Component: gating_Iks
ks_3
=
ks_5
ks_1
ks_4
=
1
1
ks_2
+
1
ks_6
alpha_act
=
ks_1
ⅇ
v
ks_2
beta_act
=
ks_3
ⅇ
v
ks_4
x_ks_inf_act
=
alpha_act
alpha_act
+
beta_act
tau_ks_act
=
1
alpha_act
+
beta_act
+
tau_ks_const
Component: parameter_Ito
Component: gating_Ito
r_3
=
r_5
r_1
s_3
=
s_5
s_1
r_4
=
1
1
r_2
+
1
r_6
s_4
=
1
1
s_2
+
1
s_6
alpha_act
=
r_1
ⅇ
v
r_2
beta_act
=
r_3
ⅇ
v
r_4
x_to_inf_act
=
alpha_act
alpha_act
+
beta_act
tau_to_act
=
1
alpha_act
+
beta_act
+
tau_r_const
alpha_inact
=
s_1
ⅇ
v
s_2
beta_inact
=
s_3
ⅇ
v
s_4
x_to_inf_inact
=
alpha_inact
alpha_inact
+
beta_inact
tau_to_inact
=
1
alpha_inact
+
beta_inact
+
tau_s_const
Component: parameter_Ica
Component: gating_Ica
d_3
=
d_5
d_1
f_3
=
f_5
f_1
d_4
=
1
1
d_2
+
1
d_6
f_4
=
1
1
f_2
+
1
f_6
alpha_act
=
d_1
ⅇ
v
d_2
beta_act
=
d_3
ⅇ
v
d_4
x_ca_inf_act
=
alpha_act
alpha_act
+
beta_act
tau_ca_act
=
1
alpha_act
+
beta_act
+
tau_d_const
alpha_inact
=
f_1
ⅇ
v
f_2
beta_inact
=
f_3
ⅇ
v
f_4
x_ca_inf_inact
=
alpha_inact
alpha_inact
+
beta_inact
tau_ca_inact
=
1
alpha_inact
+
beta_inact
+
tau_f_const
scale_Ical_Fca_Cadep
=
1.2
alpha_fCa
=
1.0
1.0
+
scale_Ical_Fca_Cadep
ca_i
.000325
8
beta_fCa
=
0.1
1.0
+
ⅇ
scale_Ical_Fca_Cadep
ca_i
-
.0005
0.0001
gamma_fCa
=
0.2
1.0
+
ⅇ
scale_Ical_Fca_Cadep
ca_i
-
0.00075
0.0008
x_fca_inf_inact
=
alpha_fCa
+
beta_fCa
+
gamma_fCa
+
0.23
1.46
Component: gating_Icat
x_cat_inf_act
=
1
1
+
ⅇ
-
v
+
26.3
6
tau_cat_act
=
1
1.068
ⅇ
v
+
26.3
30
+
1.068
ⅇ
-
v
+
26.3
30
x_cat_inf_inact
=
1
1
+
ⅇ
v
+
61.7
5.6
tau_cat_inact
=
1
0.0153
ⅇ
-
v
+
61.7
83.3
+
0.015
ⅇ
v
+
61.7
15.38
Component: parameter_Ina
Component: gating_Ina
m_3
=
m_5
m_1
h_3
=
h_5
h_1
j_3
=
j_5
j_1
m_4
=
1
1
m_2
+
1
m_6
h_4
=
1
1
h_2
+
1
h_6
j_4
=
1
1
j_2
+
1
j_6
j_5
=
h_5
j_6
=
h_6
alpha_m_act
=
m_1
ⅇ
v
m_2
beta_m_act
=
m_3
ⅇ
v
m_4
x_na_m_inf_act
=
alpha_m_act
alpha_m_act
+
beta_m_act
tau_na_m_act
=
1
alpha_m_act
+
beta_m_act
+
tau_m_const
alpha_h_inact
=
h_1
ⅇ
v
h_2
beta_h_inact
=
h_3
ⅇ
v
h_4
x_na_h_inf_inact
=
alpha_h_inact
alpha_h_inact
+
beta_h_inact
tau_na_h_inact
=
1
alpha_h_inact
+
beta_h_inact
+
tau_h_const
alpha_j_inact
=
j_1
ⅇ
v
j_2
beta_j_inact
=
j_3
ⅇ
v
j_4
x_na_j_inf_inact
=
alpha_j_inact
alpha_j_inact
+
beta_j_inact
tau_na_j_inact
=
1
alpha_j_inact
+
beta_j_inact
+
tau_j_const
Component: parameter_If
Component: gating_If
xf_3
=
xf_5
xf_1
xf_4
=
1
1
xf_2
+
1
xf_6
alpha_act
=
xf_1
ⅇ
v
xf_2
beta_act
=
xf_3
ⅇ
v
xf_4
x_f_inf_act
=
alpha_act
alpha_act
+
beta_act
tau_f_act
=
1
alpha_act
+
beta_act
+
xf_const
Source
Derived from workspace
Reproducibility of the computational model of induced pluripotent stem-cell derived cardiomyocytes
at changeset
013a1f6b6681
.
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Channels.cellml
Current_Ica.cellml
Current_If.cellml
Current_Ik1.cellml
Current_Ikr.cellml
Current_Iks.cellml
Current_Ina.cellml
Current_Ito.cellml