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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Model :
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type | FunctionDefinitions [4] | name | math | sbo | cvterm |
---|---|---|---|---|---|
FunctionDefinition | max
|
minimum | |||
FunctionDefinition | min
|
maximum | |||
FunctionDefinition | heav
|
heavyside | |||
FunctionDefinition | mod
|
modulo |
type | Parameters [68] | name | constant | value | unit | derived unit | sbo | cvterm |
---|---|---|---|---|---|---|---|---|
Parameter | r
|
r = 8314.0 | F | 8314.0 | None | |||
Parameter | fara
|
fara = 96484.6 | F | 96484.6 | None | |||
Parameter | temp
|
temp = 310.0 | F | 310.0 | None | |||
Parameter | c
|
c = 1.0 | F | 1.0 | None | |||
Parameter | v
|
v = -81.0 | F | -81.0 | None | |||
Parameter | m
|
m = 0.0 | F | 0.0 | None | |||
Parameter | h
|
h = 0.98 | F | 0.98 | None | |||
Parameter | j
|
j = 0.99 | F | 0.99 | None | |||
Parameter | d
|
d = 0.0 | F | 0.0 | None | |||
Parameter | f
|
f = 1.0 | F | 1.0 | None | |||
Parameter | x
|
x = 0.0 | F | 0.0 | None | |||
Parameter | cai
|
cai = 0.0002 | F | 0.0002 | None | |||
Parameter | nao
|
nao = 140.0 | F | 140.0 | None | |||
Parameter | nai
|
nai = 18.0 | F | 18.0 | None | |||
Parameter | ko
|
ko = 5.4 | F | 5.4 | None | |||
Parameter | ki
|
ki = 145.0 | F | 145.0 | None | |||
Parameter | cao
|
cao = 1.8 | F | 1.8 | None | |||
Parameter | g_na
|
g_na = 23.0 | F | 23.0 | None | |||
Parameter | g_kmax
|
g_kmax = 0.282 | F | 0.282 | None | |||
Parameter | g_kp
|
g_kp = 0.0183 | F | 0.0183 | None | |||
Parameter | g_bl
|
g_bl = 0.03921 | F | 0.03921 | None | |||
Parameter | g_b
|
g_b = 0.03921 | F | 0.03921 | None | |||
Parameter | e_na
|
e_na = 54.4 | F | 54.4 | None | |||
Parameter | e_b
|
e_b = -59.87 | F | -59.87 | None | |||
Parameter | e_b1
|
e_b1 = -59.87 | F | -59.87 | None | |||
Parameter | pr_nak
|
pr_nak = 0.01833 | F | 0.01833 | None | |||
Parameter | period
|
period = 500 | F | 500.0 | None | |||
Parameter | istim_mag
|
istim_mag = 8.0 | F | 8.0 | None | |||
Parameter | istim_beg
|
istim_beg = 20.0 | F | 20.0 | None | |||
Parameter | istim_dur
|
istim_dur = 5.0 | F | 5.0 | None | |||
Parameter | i_stim
|
F | 0.0 | dimensionless | None | |||
Parameter | e_k1
|
F | 0.0 | dimensionless | None | |||
Parameter | e_kp
|
F | 0.0 | dimensionless | None | |||
Parameter | e_k
|
F | 0.0 | dimensionless | None | |||
Parameter | e_si
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_m
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_j
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_h
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_k1
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_f
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_d
|
F | 0.0 | dimensionless | None | |||
Parameter | alpha_x
|
F | 0.0 | dimensionless | None | |||
Parameter | xi
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_m
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_j
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_h
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_f
|
F | 0.0 | dimensionless | None | |||
Parameter | kp
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_d
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_k1
|
F | 0.0 | dimensionless | None | |||
Parameter | k1_inf
|
F | 0.0 | dimensionless | None | |||
Parameter | beta_x
|
F | 0.0 | dimensionless | None | |||
Parameter | g_k
|
F | 0.0 | dimensionless | None | |||
Parameter | g_k1
|
F | 0.0 | dimensionless | None | |||
Parameter | i_na
|
F | 0.0 | dimensionless | None | |||
Parameter | i_si
|
F | 0.0 | dimensionless | None | |||
Parameter | i_k
|
F | 0.0 | dimensionless | None | |||
Parameter | i_k1
|
F | 0.0 | dimensionless | None | |||
Parameter | i_kp
|
F | 0.0 | dimensionless | None | |||
Parameter | i_b
|
F | 0.0 | dimensionless | None | |||
Parameter | iapp
|
F | 0.0 | dimensionless | None | |||
Parameter | ina
|
F | 0.0 | dimensionless | None | |||
Parameter | isi
|
F | 0.0 | dimensionless | None | |||
Parameter | ik
|
F | 0.0 | dimensionless | None | |||
Parameter | ik1
|
F | 0.0 | dimensionless | None | |||
Parameter | ikp
|
F | 0.0 | dimensionless | None | |||
Parameter | iktot
|
F | 0.0 | dimensionless | None | |||
Parameter | t
|
model time | F | 0.0 | dimensionless | None |
type | Rules [46] | assignment | name | derived units | sbo | cvterm | |
---|---|---|---|---|---|---|---|
Rule | d v/dt
|
= | None | ||||
Rule | d m/dt
|
= | None | ||||
Rule | d h/dt
|
= | None | ||||
Rule | d j/dt
|
= | None | ||||
Rule | d d/dt
|
= | None | ||||
Rule | d f/dt
|
= | None | ||||
Rule | d x/dt
|
= | None | ||||
Rule | d cai/dt
|
= | None | ||||
Rule | i_stim
|
= | None | ||||
Rule | e_k1
|
= | None | ||||
Rule | e_kp
|
= | None | ||||
Rule | e_k
|
= | None | ||||
Rule | e_si
|
= | None | ||||
Rule | alpha_m
|
= | None | ||||
Rule | alpha_j
|
= | None | ||||
Rule | alpha_h
|
= | None | ||||
Rule | alpha_k1
|
= | None | ||||
Rule | alpha_f
|
= | None | ||||
Rule | alpha_d
|
= | None | ||||
Rule | alpha_x
|
= | None | ||||
Rule | xi
|
= | None | ||||
Rule | beta_m
|
= | None | ||||
Rule | beta_j
|
= | None | ||||
Rule | beta_h
|
= | None | ||||
Rule | beta_f
|
= | None | ||||
Rule | kp
|
= | None | ||||
Rule | beta_d
|
= | None | ||||
Rule | beta_k1
|
= | None | ||||
Rule | k1_inf
|
= | None | ||||
Rule | beta_x
|
= | None | ||||
Rule | g_k
|
= | None | ||||
Rule | g_k1
|
= | None | ||||
Rule | i_na
|
= | None | ||||
Rule | i_si
|
= | None | ||||
Rule | i_k
|
= | None | ||||
Rule | i_k1
|
= | None | ||||
Rule | i_kp
|
= | None | ||||
Rule | i_b
|
= | None | ||||
Rule | iapp
|
= | None | ||||
Rule | ina
|
= | None | ||||
Rule | isi
|
= | None | ||||
Rule | ik
|
= | None | ||||
Rule | ik1
|
= | None | ||||
Rule | ikp
|
= | None | ||||
Rule | iktot
|
= | None | ||||
Rule | t
|
= | None |