XPP model

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

# Markovian model for human hKv4.3-2 in heart cells which is responsible for the early phase of cardiac repolarization
# Greenstein JL et al., Role of the calcium-independent tranisent outward current Ito1 in shaping action 
#  potential morphology and duration.  Circ Res 2000;87:1026-1033
# The results are similar to figure 3A of the paper.
# Notably, current traces shown in figure 2A were displaced for the the sake of clarity. 
# Model parameters appears in http://circres.ahajournals.org/cgi/data/87/11/1026/DC1/1.
# The model was implemented by Dr. Sheng-Nan Wu, Dr. Ruey J. Sung, Ya-Jean Wang and Jiun-Shian Wu

# Initial values
init c0=1, c1=0, c2=0, c3=0
init ci0=0, ci1=0, ci2=0, ci3=0
init o=0, oi=0

# Voltage clamp protocols (double-pulse protocol)
par vhold=-80, vtest_1=20, vtest_2=-80
par ton=10, toff=160, toff_r=170
v = vhold+heav(t-ton)*heav(toff-t)*(vtest_1-vhold)+heav(t-toff)*heav(toff_r-t)*(vtest_2-vhold)

# Values of the model parameters
par aa0=0.6347, aa=0.02912, ba0=0.1243, ba=0.0323, ai0=0.05388, ai=4.944e-6, bi0=2.825e-4, bi=4.096e-8
par f1=2.303, f2=16.4, f3=265.833, f4=259.12, b1=1.1653, b2=1.5137, b3=13.072, b4=529.125
par scale=1

# Expressions
Ek=-80.0
par gkbar=0.0075
aaa = aa0*exp(aa*v)
baa = ba0*exp(-ba*v)
aia = ai0*exp(-ai*v)
bia = bi0*exp(bi*v)

# Gating functions
c0' = c1*baa + ci0*aia -c0*(4*aaa + bia)
c1' = c0*4*aaa + c2*2*baa + ci1*aia/b1 - c1*(baa + 3*aaa + f1*bia)
c2' = c1*3*aaa +c3*3*baa + ci2*aia/b2  - c2*(2*baa +2*aaa + f2*bia)
c3' = c2*2*aaa + o*4*baa + ci3*aia/b3 - c3*(3*baa + aaa + f3*bia)
o' = c3*aaa + oi*aia/b4 - o*(4*baa + f4*bia)
ci0' = c0*bia + ci1*baa/f1 - ci0*(aia + b1*4*aaa)
ci1' = c1*f1*bia + ci0* b1*4*aaa +ci2*f1*2*baa/f2 - ci1*(baa/f1 + aia/b1 + b2*3*aaa/b1)
ci2' = c2*f2*bia + ci1*b2*3*aaa/b1 + ci3*f2*3*baa/f3  - ci2*(f1*2**baa/f2 + aia/b2 +b3*2*aaa/b2) 
ci3' = c3*f3*bia + ci2*b3*2*aaa/b2 + oi*f3*4*baa/f4 -ci3*(f2*3*baa/f3 + aia/b3 +b4*aaa/b3)
oi' = o*f4*bia  - oi*f3*4*baa/f4

aux ika = gkbar*(o+oi)*(v-Ek)/scale
aux prop = o+oi

# XPP parameters
@ meth=Euler, dt=.01, total=170
@ xplot=t, yplot=ika, yhi=1.1, ylo=-0.1, xlo=-0, xhi=170, bound=500

done
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Copyright © 2017 Matthias Koenig

Redistribution and use of any part of this model, with or without modification, are permitted provided that the following conditions are met:

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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 [43] name constant value unit derived unit sbo cvterm
c0 c0 = 1 1.0 None
c1 c1 = 0 0.0 None
c2 c2 = 0 0.0 None
c3 c3 = 0 0.0 None
ci0 ci0 = 0 0.0 None
ci1 ci1 = 0 0.0 None
ci2 ci2 = 0 0.0 None
ci3 ci3 = 0 0.0 None
o o = 0 0.0 None
oi oi = 0 0.0 None
vhold vhold = -80 -80.0 None
vtest_1 vtest_1 = 20 20.0 None
vtest_2 vtest_2 = -80 -80.0 None
ton ton = 10 10.0 None
toff toff = 160 160.0 None
toff_r toff_r = 170 170.0 None
aa0 aa0 = 0.6347 0.6347 None
aa aa = 0.02912 0.02912 None
ba0 ba0 = 0.1243 0.1243 None
ba ba = 0.0323 0.0323 None
ai0 ai0 = 0.05388 0.05388 None
ai ai = 4.944e-6 4.944e-06 None
bi0 bi0 = 2.825e-4 0.0002825 None
bi bi = 4.096e-8 4.096e-08 None
f1 f1 = 2.303 2.303 None
f2 f2 = 16.4 16.4 None
f3 f3 = 265.833 265.833 None
f4 f4 = 259.12 259.12 None
b1 b1 = 1.1653 1.1653 None
b2 b2 = 1.5137 1.5137 None
b3 b3 = 13.072 13.072 None
b4 b4 = 529.125 529.125 None
scale scale = 1 1.0 None
gkbar gkbar = 0.0075 0.0075 None
v 0.0 dimensionless None
ek 0.0 dimensionless None
aaa 0.0 dimensionless None
baa 0.0 dimensionless None
aia 0.0 dimensionless None
bia 0.0 dimensionless None
ika 0.0 dimensionless None
prop 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [19]   assignment name derived units sbo cvterm
d c0/dt = c1 baa ci0 aia c0 4 aaa bia None
d c1/dt = c0 4 aaa c2 2 baa ci1 aia b1 c1 baa 3 aaa f1 bia None
d c2/dt = c1 3 aaa c3 3 baa ci2 aia b2 c2 2 baa 2 aaa f2 bia None
d c3/dt = c2 2 aaa o 4 baa ci3 aia b3 c3 3 baa aaa f3 bia None
d o/dt = c3 aaa oi aia b4 o 4 baa f4 bia None
d ci0/dt = c0 bia ci1 baa f1 ci0 aia b1 4 aaa None
d ci1/dt = c1 f1 bia ci0 b1 4 aaa ci2 f1 2 baa f2 ci1 baa f1 aia b1 b2 3 aaa b1 None
d ci2/dt = c2 f2 bia ci1 b2 3 aaa b1 ci3 f2 3 baa f3 ci2 f1 2 baa f2 aia b2 b3 2 aaa b2 None
d ci3/dt = c3 f3 bia ci2 b3 2 aaa b2 oi f3 4 baa f4 ci3 f2 3 baa f3 aia b3 b4 aaa b3 None
d oi/dt = o f4 bia oi f3 4 baa f4 None
v = vhold heav t ton heav toff t vtest_1 vhold heav t toff heav toff_r t vtest_2 vhold None
ek = 80 None
aaa = aa0 aa v None
baa = ba0 ba v None
aia = ai0 ai v None
bia = bi0 bi v None
ika = gkbar o oi v ek scale None
prop = o oi None
t = time None