XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6.

# Luo-Rudy phase 1 kinetics for cardiac action potential
# Ref: Luo CH, Rudy T. Circ Res 1991;68:1501-1526
# Ref: Wu SN, Chinese J Physiol 2004;47:15-22

#Constant:
number R=8314.0, Fara=96484.6, Temp=310.0, C=1.0

# Initial values
initial V=-81.0, m=0.0, h=0.98, j=0.99, d=0.0, f=1.0, X=0.0, Cai=0.0002

# Value sof the model parameters
param  Nao=140.0, Nai=18.0, Ko=5.4, Ki=145.0, Cao=1.8
param  g_Na=23.0, g_Kmax=0.282, g_Kp=0.0183, g_bl=0.03921, g_b=0.03921
param E_Na=54.4, E_b=-59.87, E_b1=-59.87, PR_NaK=0.01833
param period=500, iStim_mag=8.0, iStim_beg=20.0,  iStim_dur=5.0

# Stimulus
i_Stim=  iStim_mag*(heav(mod(t,period)-iStim_beg)*heav((iStim_beg+iStim_dur)-mod(t,period)))

# Expressions
E_K1= (ln((Ko / Ki)) * R * Temp / Fara)
E_Kp= E_K1
E_K= (ln(((Ko + (PR_NaK * Nao)) / (Ki + (PR_NaK * Nai)))) * R * Temp / Fara)
E_si= (7.7 - (13.0287 * ln(Cai)))
alpha_m= (0.32 * (47.13 + V) / (1.0 - exp( - (0.1 * (47.13 + V)))))
alpha_j= heav(-V-40)*(( - (127140.0 * exp((0.2444 * V))) - (3.474E-5 * exp( - (0.04391 * V)))) * (37.78 + V) / (1.0 + exp((0.311 * (79.23 + V)))))
alpha_h=heav(-V-40)*(0.135 * exp( - (0.14705882352941177 * (80.0 + V))))
alpha_K1= (1.02 / (1.0 + exp((0.2385 * (-59.215 + V - E_K1)))))
alpha_f= (0.012 * exp( - (0.0080 * (28.0 + V))) / (1.0 + exp((0.15 * (28.0 + V)))))
alpha_d= (0.095 * exp( - (0.01 * (-5.0 + V))) / (1.0 + exp( - (0.072 * (-5.0 + V)))))
alpha_X= (5.0E-4 * exp((0.083 * (50.0 + V))) / (1.0 + exp((0.057 * (50.0 + V)))))
Xi=heav(V+100)*((2.837 * (-1.0 + exp((0.04 * (77.0 + V)))) / ((77.0 + V) * exp((0.04 * (35.0 + V))))))
beta_m= (0.08 * exp( - (0.09090909090909091 * V)))
beta_j= heav(-V-40)*((0.1212  * exp( - (0.01052 * V)) / (1.0 + exp( - (0.1378 * (40.14 + V)))))) + heav(V+40)*((0.3 * exp( - (2.535E-7 * V)) / (1.0 + exp( - (0.1 * (32.0 + V))))))
beta_h= heav(-V-40)*((((3.56 * exp((0.079 * V))) + (310000.0 * exp((0.35 * V)))))) + heav(V+40)*((1 / (0.13 * (1.0 + exp( - (0.0900900900900901 * (10.66 + V)))))))
beta_f= (0.0065 * exp( - (0.02 * (30.0 + V))) / (1.0 + exp( - (0.2 * (30.0 + V)))))
Kp= (1.0 / (1.0 + exp((0.16722408026755853 * (7.488 - V)))))
beta_d= (0.07 * exp( - (0.017 * (44.0 + V))) / (1.0 + exp((0.05 * (44.0 + V)))))
beta_K1= (((0.49124 * exp((0.08032 * (5.476 - E_K1 + V)))) + exp((0.06175 * (V - (594.31 + E_K1))))) / (1.0 + exp( - (0.5143 * (4.753 + V - E_K1)))))
K1_inf= (alpha_K1 / (alpha_K1 + beta_K1))
beta_X= (0.0013 * exp( - (0.06 * (20.0 + V))) / (1.0 + exp( - (0.04 * (20.0 + V)))))
g_K= (g_Kmax *(0.18518518518518517 * Ko)^0.5)
g_K1= (0.6047 * (0.18518518518518517 * Ko)^0.5)

i_Na= (g_Na * m^3 * h * j * (V - E_Na))
i_si= (0.09 * d * f * (V - E_si))
i_K= (g_K * X * Xi * (V - E_K))
i_K1= (g_K1 * K1_inf * (V - E_K1))
i_Kp= (g_Kp * Kp * (V - E_Kp))
i_b= (g_b * (V - E_b))

# Differential equations
V'= - ((-i_Stim + i_Na + i_si + i_K + i_K1 + i_Kp + i_b) / C)
m'= ((alpha_m * (1.0 - m)) - (beta_m * m))
h'= ((alpha_h * (1.0 - h)) - (beta_h * h))
j'= ((alpha_j * (1.0 - j)) - (beta_j * j))
d'= ((alpha_d * (1.0 - d)) - (beta_d * d))
f'= ((alpha_f * (1.0 - f)) - (beta_f * f))
X'= ((alpha_X * (1.0 - X)) - (beta_X * X))
Cai'= ( - (1.0E-4 * i_si) + (0.07 * (1.0E-4 - Cai)))

aux iapp=i_Stim
aux ina=I_Na
aux isi=i_si
aux ik=i_K
aux ik1=i_K1
aux ikp=i_Kp
aux iktot=i_K+i_K1+i_Kp

# Numerical and plotting parameters for xpp
@ maxstor=1000000, total=1000, bounds=100000, total=2000, xp=t, yp=V, xlo=0, xhi=2000, ylo=-100, yhi=60
@ meth=Euler, dt=0.01     

done
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Copyright © 2017 Matthias Koenig

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This model is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.


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Access SBML model  L3V1

FunctionDefinitions [4] name math sbo cvterm
max minimum x y x x y y
min maximum x y x x y y
heav heavyside x 0 x 0 0.5 x 0 1 x 0 0
mod modulo x y x y x y x 0 y 0 x y x y

Parameters [68] name constant value unit derived unit sbo cvterm
r r = 8314.0 8314.0 None
fara fara = 96484.6 96484.6 None
temp temp = 310.0 310.0 None
c c = 1.0 1.0 None
v v = -81.0 -81.0 None
m m = 0.0 0.0 None
h h = 0.98 0.98 None
j j = 0.99 0.99 None
d d = 0.0 0.0 None
f f = 1.0 1.0 None
x x = 0.0 0.0 None
cai cai = 0.0002 0.0002 None
nao nao = 140.0 140.0 None
nai nai = 18.0 18.0 None
ko ko = 5.4 5.4 None
ki ki = 145.0 145.0 None
cao cao = 1.8 1.8 None
g_na g_na = 23.0 23.0 None
g_kmax g_kmax = 0.282 0.282 None
g_kp g_kp = 0.0183 0.0183 None
g_bl g_bl = 0.03921 0.03921 None
g_b g_b = 0.03921 0.03921 None
e_na e_na = 54.4 54.4 None
e_b e_b = -59.87 -59.87 None
e_b1 e_b1 = -59.87 -59.87 None
pr_nak pr_nak = 0.01833 0.01833 None
period period = 500 500.0 None
istim_mag istim_mag = 8.0 8.0 None
istim_beg istim_beg = 20.0 20.0 None
istim_dur istim_dur = 5.0 5.0 None
i_stim 0.0 dimensionless None
e_k1 0.0 dimensionless None
e_kp 0.0 dimensionless None
e_k 0.0 dimensionless None
e_si 0.0 dimensionless None
alpha_m 0.0 dimensionless None
alpha_j 0.0 dimensionless None
alpha_h 0.0 dimensionless None
alpha_k1 0.0 dimensionless None
alpha_f 0.0 dimensionless None
alpha_d 0.0 dimensionless None
alpha_x 0.0 dimensionless None
xi 0.0 dimensionless None
beta_m 0.0 dimensionless None
beta_j 0.0 dimensionless None
beta_h 0.0 dimensionless None
beta_f 0.0 dimensionless None
kp 0.0 dimensionless None
beta_d 0.0 dimensionless None
beta_k1 0.0 dimensionless None
k1_inf 0.0 dimensionless None
beta_x 0.0 dimensionless None
g_k 0.0 dimensionless None
g_k1 0.0 dimensionless None
i_na 0.0 dimensionless None
i_si 0.0 dimensionless None
i_k 0.0 dimensionless None
i_k1 0.0 dimensionless None
i_kp 0.0 dimensionless None
i_b 0.0 dimensionless None
iapp 0.0 dimensionless None
ina 0.0 dimensionless None
isi 0.0 dimensionless None
ik 0.0 dimensionless None
ik1 0.0 dimensionless None
ikp 0.0 dimensionless None
iktot 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [46]   assignment name derived units sbo cvterm
d v/dt = i_stim i_na i_si i_k i_k1 i_kp i_b c None
d m/dt = alpha_m 1 m beta_m m None
d h/dt = alpha_h 1 h beta_h h None
d j/dt = alpha_j 1 j beta_j j None
d d/dt = alpha_d 1 d beta_d d None
d f/dt = alpha_f 1 f beta_f f None
d x/dt = alpha_x 1 x beta_x x None
d cai/dt = 1 -4 i_si 0.07 1 -4 cai None
i_stim = istim_mag heav mod t period istim_beg heav istim_beg istim_dur mod t period None
e_k1 = ko ki r temp fara None
e_kp = e_k1 None
e_k = ko pr_nak nao ki pr_nak nai r temp fara None
e_si = 7.7 13.0287 cai None
alpha_m = 0.32 47.13 v 1 0.1 47.13 v None
alpha_j = heav v 40 127140 0.2444 v 3.474 -5 0.04391 v 37.78 v 1 0.311 79.23 v None
alpha_h = heav v 40 0.135 0.147058823529412 80 v None
alpha_k1 = 1.02 1 0.2385 59.215 v e_k1 None
alpha_f = 0.012 0.008 28 v 1 0.15 28 v None
alpha_d = 0.095 0.01 5 v 1 0.072 5 v None
alpha_x = 5 -4 0.083 50 v 1 0.057 50 v None
xi = heav v 100 2.837 1 0.04 77 v 77 v 0.04 35 v None
beta_m = 0.08 0.0909090909090909 v None
beta_j = heav v 40 0.1212 0.01052 v 1 0.1378 40.14 v heav v 40 0.3 2.535 -7 v 1 0.1 32 v None
beta_h = heav v 40 3.56 0.079 v 310000 0.35 v heav v 40 1 0.13 1 0.0900900900900901 10.66 v None
beta_f = 0.0065 0.02 30 v 1 0.2 30 v None
kp = 1 1 0.167224080267559 7.488 v None
beta_d = 0.07 0.017 44 v 1 0.05 44 v None
beta_k1 = 0.49124 0.08032 5.476 e_k1 v 0.06175 v 594.31 e_k1 1 0.5143 4.753 v e_k1 None
k1_inf = alpha_k1 alpha_k1 beta_k1 None
beta_x = 0.0013 0.06 20 v 1 0.04 20 v None
g_k = g_kmax 0.185185185185185 ko 0.5 None
g_k1 = 0.6047 0.185185185185185 ko 0.5 None
i_na = g_na m 3 h j v e_na None
i_si = 0.09 d f v e_si None
i_k = g_k x xi v e_k None
i_k1 = g_k1 k1_inf v e_k1 None
i_kp = g_kp kp v e_kp None
i_b = g_b v e_b None
iapp = i_stim None
ina = i_na None
isi = i_si None
ik = i_k None
ik1 = i_k1 None
ikp = i_kp None
iktot = i_k i_k1 i_kp None
t = time None