XPP model

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

# Markovian model for Human I(Ks) in heart cells which is responsible for cardiac repolarization
# Mutations in this channel will be susceptible to induction of early after-depolarizations
# Silva J, Rudy Y. Circulation 2005;112:1384-1391

# Constants
Rk=8314
Fara=96485
Temp=310

# Initial values
init c1=1, c2=0, c3=0, c4=0, c5=0, c6=0, c7=0
init c8=0, c9=0, c10=0, c11=0, c12=0, c13=0, c14=0, c15=0
init o1=0, o2=0

# Values of the model parameters
par ko=4.5, ki=136.89149
par nao=140, nai=15
par vhold=-80, vtest_1=40, vtest_2=-50
par cai=7.9e-5
par scale=120

# Voltage clamp protocols
par ton=100, toff=4100, toff_r=5000
v = vhold+heav(t-ton)*heav(toff-t)*(vtest_1-vhold)+heav(t-toff)*heav(toff_r-t)*(vtest_2-vhold)

# Expressions
Eks = ((Rk*Temp)/Fara)*log((ko+0.01833*nao)/(ki+0.01833*nai))
gksbar = 0.779*(1+0.6/(1+(3.8e-5/cai)^1.4))
a = 3.98e-4*exp(3.61e-1*v*Fara/(Rk*Temp))
b = 5.74e-5*exp(-9.23e-2*v*Fara/(Rk*Temp))
r = 3.41e-3*exp(8.68e-1*v*Fara/(Rk*Temp))
d = 1.2e-3*exp(-3.3e-1*v*Fara/(Rk*Temp))
theta = 6.47e-3
eta = 1.25e-2*exp(-4.81e-1*v*Fara/(Rk*Temp))
psi = 6.33e-3*exp(1.27*v*Fara/(Rk*Temp))
omega = 4.91e-3*exp(-6.79e-1*Fara/(Rk*Temp))

# Gating functions
c1' = c2*b - c1*4*a
c2' = c1*4*a + c3*2*b + c6*d - c2*(b + 3*a + r)
c3' = c2*3*a +c4*3*b + c7*d  - c3*(2*b + a + 2*r)
c4' = c3*2*a + c5*4*b + c8*d - c4*(3*b + a + 3*r)
c5' = c4*a + c9*d - c5*(4*b + 4*r)
c6' = c2*r + c7*2*b - c6*(d + 3*a)
c7' = c6*3*a + c8* 3*b + c3*2*r  + c10*2*d- c7*(2*b + 2*a + d + r)
c8' = c7*2*a + c9*4*b + c4*3*r + c11*2*d - c8*(3*b + a + d + 2*r) 
c9' = c8*a + c5*4*r + c12*2*d - c9*(4*b + d + 3*r)
c10' = c11*3*b + c7*r - c10*(2*a + 2*d) 
c11' = c10*2*a + c12*4*b + c8*2*r + c13*3*d - c11*(3*b + a + 2*d + r)
c12' = c11*a + c9**3*r + c14*3*d - c12*(4*b + 2*d + 3*d)
c13' = c14*4*b + c11*r - c13*(a + 3*d)
c14' = c13*a + c12*2*r + c15*4*d - c14*(4*b + 3*d + r)
c15' = c14*r + o1*eta - c15*(4*d + theta)
o1' = c15*theta + o2*omega - o1*(eta + psi)
o2' = o1*psi - o2*omega

aux iks = Gksbar*(o1+o2)/(c1+c2+c3+c4+c5+c6+c7+c8+c9+c10+c11+c12+c13+c14+c15+o1+o2)*(v-Eks)/scale

@ meth=Euler, dt=.5, total=4550
@ yp=iks, yhi=1.1, ylo=-.1, xlo=0, xhi=4550

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 [45] name constant value unit derived unit sbo cvterm
c1 c1 = 1 1.0 None
c2 c2 = 0 0.0 None
c3 c3 = 0 0.0 None
c4 c4 = 0 0.0 None
c5 c5 = 0 0.0 None
c6 c6 = 0 0.0 None
c7 c7 = 0 0.0 None
c8 c8 = 0 0.0 None
c9 c9 = 0 0.0 None
c10 c10 = 0 0.0 None
c11 c11 = 0 0.0 None
c12 c12 = 0 0.0 None
c13 c13 = 0 0.0 None
c14 c14 = 0 0.0 None
c15 c15 = 0 0.0 None
o1 o1 = 0 0.0 None
o2 o2 = 0 0.0 None
ko ko = 4.5 4.5 None
ki ki = 136.89149 136.89149 None
nao nao = 140 140.0 None
nai nai = 15 15.0 None
vhold vhold = -80 -80.0 None
vtest_1 vtest_1 = 40 40.0 None
vtest_2 vtest_2 = -50 -50.0 None
cai cai = 7.9e-5 7.9e-05 None
scale scale = 120 120.0 None
ton ton = 100 100.0 None
toff toff = 4100 4100.0 None
toff_r toff_r = 5000 5000.0 None
rk 0.0 dimensionless None
fara 0.0 dimensionless None
temp 0.0 dimensionless None
v 0.0 dimensionless None
eks 0.0 dimensionless None
gksbar 0.0 dimensionless None
a 0.0 dimensionless None
b 0.0 dimensionless None
r 0.0 dimensionless None
d 0.0 dimensionless None
theta 0.0 dimensionless None
eta 0.0 dimensionless None
psi 0.0 dimensionless None
omega 0.0 dimensionless None
iks 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [33]   assignment name derived units sbo cvterm
d c1/dt = c2 b c1 4 a None
d c2/dt = c1 4 a c3 2 b c6 d c2 b 3 a r None
d c3/dt = c2 3 a c4 3 b c7 d c3 2 b a 2 r None
d c4/dt = c3 2 a c5 4 b c8 d c4 3 b a 3 r None
d c5/dt = c4 a c9 d c5 4 b 4 r None
d c6/dt = c2 r c7 2 b c6 d 3 a None
d c7/dt = c6 3 a c8 3 b c3 2 r c10 2 d c7 2 b 2 a d r None
d c8/dt = c7 2 a c9 4 b c4 3 r c11 2 d c8 3 b a d 2 r None
d c9/dt = c8 a c5 4 r c12 2 d c9 4 b d 3 r None
d c10/dt = c11 3 b c7 r c10 2 a 2 d None
d c11/dt = c10 2 a c12 4 b c8 2 r c13 3 d c11 3 b a 2 d r None
d c12/dt = c11 a c9 3 r c14 3 d c12 4 b 2 d 3 d None
d c13/dt = c14 4 b c11 r c13 a 3 d None
d c14/dt = c13 a c12 2 r c15 4 d c14 4 b 3 d r None
d c15/dt = c14 r o1 eta c15 4 d theta None
d o1/dt = c15 theta o2 omega o1 eta psi None
d o2/dt = o1 psi o2 omega None
rk = 8314 None
fara = 96485 None
temp = 310 None
v = vhold heav t ton heav toff t vtest_1 vhold heav t toff heav toff_r t vtest_2 vhold None
eks = rk temp fara 10 ko 0.01833 nao ki 0.01833 nai None
gksbar = 0.779 1 0.6 1 3.8 -5 cai 1.4 None
a = 3.98 -4 3.61 -1 v fara rk temp None
b = 5.74 -5 9.23 -2 v fara rk temp None
r = 3.41 -3 8.68 -1 v fara rk temp None
d = 1.2 -3 3.3 -1 v fara rk temp None
theta = 6.47 -3 None
eta = 1.25 -2 4.81 -1 v fara rk temp None
psi = 6.33 -3 1.27 v fara rk temp None
omega = 4.91 -3 6.79 -1 fara rk temp None
iks = gksbar o1 o2 c1 c2 c3 c4 c5 c6 c7 c8 c9 c10 c11 c12 c13 c14 c15 o1 o2 v eks scale None
t = time None