XPP model

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

% JYBfig07.ode
% Ref: Wu et al., J Theor B2008;252:711-21

% Initial values of the variables
init v=-74.0, nK=0.288, hK=0.367, mNa=0.041,  hNa=0.844, nIR=0.003, rIR=0.282, ni=0.657

% Values of the model parameters
params cm=1, gnabar=15, gkbar=8, girbar=1.0, gl=0.05, vna=50, vk=-80, vir=-80, vl=-80
params koi=0.081, kio=0.001, f=0.9

% Gating functions
alphaNam(v) = 0.1*(v+40)/( 1 - exp(-0.09*(v+40)))
betaNam(v) =  4*exp(-0.055*(v+70))
mNainf(v) = 1/(1+betaNam(v)/alphaNam(v))
tauNam(v) = 1/(alphaNam(v) + betaNam(v))

alphaNah(v) =  0.07*exp(-0.05*(v+70))
betaNah(v) = 1/( 1 + exp(-0.09*(v+25)) )
hNainf(v) = 1/(1+betaNah(v)/alphaNah(v))
tauNah(v) = 1/(alphaNah(v) + betaNah(v))

alphaKn(v) = 0.01*(v + 60)/(1 - exp(-0.1*(V + 60)))
betaKn(v) = 0.125*exp(-0.0125*(V + 70))
nKinf(v) = 1/(1+betaKn(v)/alphaKn(v))
tauKn(v) = 1/(alphaKn(v) + betaKn(v))

alphaKh(v) = 0.001*exp(-0.04*(v+70))
betaKh(v) = 0.001*exp(-0.0195*(v+40))
hKinf(v) = 1/(1+betaKh(v)/alphaKh(v))
tauKh(v) = 1/(alphaKh(v) + betaKh(v))

alphaIRn(v) = 0.00035*exp(0.07*(v+25))
betaIRn(v) = 0.09/(1+exp(0.11*(v+100)))
nIRinf(v) = 1/(1+betaIRn(v)/alphaIRn(v))
tauIRn(v) = 1/(alphaIRn(v) + betaIRn(v))

alphaIRr(v) = 30/(1+exp(0.04*(v+230)))
betaIRr(v) = 0.15/(1+exp(-0.05*(v+120)))
rIRinf(v) = 1/(1+betaIRr(v)/alphaIRr(v))
tauIRr(v) = 1/(alphaIRr(v) + betaIRr(v))

alpha_n3(v)=-0.021*(v+8.3)/(exp(-(v+8.3)/9.8)-1)
beta_n3(v)=0.0002*exp(-(v+23.6)/20.7)

% Applied current pulse 
param ia1=1.4, t1=30, dt1=530
param ia2=0, t2=0, dt2=0
param ia3=0, t3=0, dt3=0
i(amp,t0,dt)=amp*(heav(t-t0)-heav(t-t0-dt))
ia=i(ia1,t1,dt1)+i(ia2,t2,dt2)+i(ia3,t3,dt3)

% Differential equations
v' =  -(gnabar*mNa^3*hNa*(v-vna) + (1-f)*gkbar*nK^4*hK*(v-vk) + girbar*nIR*rIR*(v-vir) + f*gkbar*(nK^4)*ni*(v-vk) + gl*(v-vl) - ia)/cm
mNa' =  (mNainf(v) - mNa)/tauNam(v)
hNa' =  (hNainf(v) - hNa)/tauNah(v)
nK' =  (nKinf(v) - nK)/tauKn(v)
hK' = (hKinf(v) - hK)/tauKh(v)
nIR' = (nIRinf(v) - nIR)/tauIRn(v)
rIR' = (rIRinf(v) - rIR)/tauIRr(v)
ni' = kio*(1-ni)-koi*nK^4*ni

aux ik=(1-f)*gkbar*(nK^4)*hK*(v-vk)+f*gkbar*(nK^4)*ni*(v-vk)

% Numerical and plotting parameters for xpp
@ xlo=0, xhi=700, ylo=-90, yhi=+60, total=700, dt=0.05, method=Euler
@ bounds=10000

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.


Model :

id
name
time
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volume
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length
Access SBML model  L3V1

FunctionDefinitions [31] 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
alphanam v 0.1 v 40 1 0.09 v 40
betanam v 4 0.055 v 70
mnainf v 1 1 betanam v alphanam v
taunam v 1 alphanam v betanam v
alphanah v 0.07 0.05 v 70
betanah v 1 1 0.09 v 25
hnainf v 1 1 betanah v alphanah v
taunah v 1 alphanah v betanah v
alphakn v 0.01 v 60 1 0.1 v 60
betakn v 0.125 0.0125 v 70
nkinf v 1 1 betakn v alphakn v
taukn v 1 alphakn v betakn v
alphakh v 0.001 0.04 v 70
betakh v 0.001 0.0195 v 40
hkinf v 1 1 betakh v alphakh v
taukh v 1 alphakh v betakh v
alphairn v 0.00035 0.07 v 25
betairn v 0.09 1 0.11 v 100
nirinf v 1 1 betairn v alphairn v
tauirn v 1 alphairn v betairn v
alphairr v 30 1 0.04 v 230
betairr v 0.15 1 0.05 v 120
ririnf v 1 1 betairr v alphairr v
tauirr v 1 alphairr v betairr v
alpha_n3 v 0.021 v 8.3 v 8.3 9.8 1
beta_n3 v 0.0002 v 23.6 20.7
i amp t0 dt t amp heav t t0 heav t t0 dt

Parameters [32] name constant value unit derived unit sbo cvterm
v v = -74.0 -74.0 None
nk nk = 0.288 0.288 None
hk hk = 0.367 0.367 None
mna mna = 0.041 0.041 None
hna hna = 0.844 0.844 None
nir nir = 0.003 0.003 None
rir rir = 0.282 0.282 None
ni ni = 0.657 0.657 None
cm cm = 1 1.0 None
gnabar gnabar = 15 15.0 None
gkbar gkbar = 8 8.0 None
girbar girbar = 1.0 1.0 None
gl gl = 0.05 0.05 None
vna vna = 50 50.0 None
vk vk = -80 -80.0 None
vir vir = -80 -80.0 None
vl vl = -80 -80.0 None
koi koi = 0.081 0.081 None
kio kio = 0.001 0.001 None
f f = 0.9 0.9 None
ia1 ia1 = 1.4 1.4 None
t1 t1 = 30 30.0 None
dt1 dt1 = 530 530.0 None
ia2 ia2 = 0 0.0 None
t2 t2 = 0 0.0 None
dt2 dt2 = 0 0.0 None
ia3 ia3 = 0 0.0 None
t3 t3 = 0 0.0 None
dt3 dt3 = 0 0.0 None
ia 0.0 dimensionless None
ik 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [11]   assignment name derived units sbo cvterm
d v/dt = gnabar mna 3 hna v vna 1 f gkbar nk 4 hk v vk girbar nir rir v vir f gkbar nk 4 ni v vk gl v vl ia cm None
d mna/dt = mnainf v mna taunam v None
d hna/dt = hnainf v hna taunah v None
d nk/dt = nkinf v nk taukn v None
d hk/dt = hkinf v hk taukh v None
d nir/dt = nirinf v nir tauirn v None
d rir/dt = ririnf v rir tauirr v None
d ni/dt = kio 1 ni koi nk 4 ni None
ia = i ia1 t1 dt1 t i ia2 t2 dt2 t i ia3 t3 dt3 t None
ik = 1 f gkbar nk 4 hk v vk f gkbar nk 4 ni v vk None
t = time None