XPP model

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

% Spike adaptation by erg-like K+ current.  If girbar is altered (0.5->0), 
% spike discharge will be changed.  
% Written by Dr. Sheng-Nan Wu, Dept Physiol, Natl Cheng Kung U Med Coll.
% Ref: Chiesa et al., J Physiol 1997;501:313-318

% Initial values of the variables
init v=-72.0, nK=0.288, hK=0.367, mNa=0.041,  hNa=0.844, nIR=0.003, rIR=0.282

% Values of the model parameters
params iapp=1.2, cm=1, gnabar=15, gkbar=2.5, girbar=0.5, gl=0.05, vna=50, vk=-80, vir=-80, vl=-80

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

% Apply current injection
par tpulse=610
par tfirst=10
istim = iapp*(heav(t-tfirst)-heav(t-tpulse))

% The differential equations
v' =  -(gnabar*mNa^3*hNa*(v-vna) + gkbar*nK^4*hK*(v-vk) + girbar*nIR*rIR*(v-vir) + gl*(v-vl) - istim)/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)

% Numerical and plotting parameters for xpp
@xlo=0, xhi=700, ylo=-90, yhi=+60, total=700, dt=0.05, method=Euler, LT=1
d
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Copyright © 2017 Matthias Koenig

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Access SBML model  L3V1

FunctionDefinitions [28] 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 0.09 1 0.11 v 100
betairn v 0.00035 0.07 v 25
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

Parameters [21] name constant value unit derived unit sbo cvterm
v v = -72.0 -72.0 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
iapp iapp = 1.2 1.2 None
cm cm = 1 1.0 None
gnabar gnabar = 15 15.0 None
gkbar gkbar = 2.5 2.5 None
girbar girbar = 0.5 0.5 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
tpulse tpulse = 610 610.0 None
tfirst tfirst = 10 10.0 None
istim 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [9]   assignment name derived units sbo cvterm
d v/dt = gnabar mna 3 hna v vna gkbar nk 4 hk v vk girbar nir rir v vir gl v vl istim 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
istim = iapp heav t tfirst heav t tpulse None
t = time None