XPP model

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

# The model consists of one DA neuron and one GABA neuron
# for a reduced model set spike-producing currents (fast sodium and delayed rectifier  potassium currents) to 0

# Injected currents to DA and GABA neurons
par I=0, Iapp=0

# ===============DA neuron=====================

# Synaptic conductances
par gbarnmda=0, ggaba=0,gampa=0

# Reversal potentials
par ECa=50., EK=-90., ENa=55., ENMDA=0., EAMPA=0., Egaba=-90.,Eh=-20.

# Leak current
par gL=0.18, EL=-35
IL=gL*(EL-v)

# H-current
par vhh=-95, slh=8, th0=625, vtauh=-112, gbarh=2
hinf(v)=1/(1+exp((v-vhh)/slh))
tauh(v)=th0*exp(0.075*(v-vtauh))/(1+exp(0.083*(v-vtauh)))
Ih=gbarh*q*(Eh-v)

# subthreshold Na current
par gSNa=0.13, vhna=-50, slna=5
na(v)=1/(1+exp(-(v-vhna)/slna))
Isna=gSNa*na(v)*(Ena-v)

# SK current
par gbarKCa=7.8, k=160
gKCa(x)=gbarKCa*(x**4)/((x**4) + (k**4))
IKCa=gKCa(u)*(EK-v)

# Instantaneous K+ current
par gbarK=1., vHk=-10, vSk=7 
gK(x)=gbarK/(1. + exp(-(x-vHk)/vSk))
IK=gK(v)*(EK-v)

# Ca2+ balance parameters & constants
par caLeak=0.1, caNMDA=0, buf=0.00023, r=0.2, tc=0.52, zF=.019298

# Ca2+ current
par gbarCa=2.5, Vcah=-52, Sca=3., CaConst=0.016
alphac(V)=if (abs(V-Vcah)>0.00001) then (-0.0032*(V-Vcah)/(exp(-(V-Vcah)/Sca) - 1.)) else (-0.0032*0.00001/(exp(-0.00001/Sca)-1.))
betac(V)=0.05*exp(-(V-Vcah+5.)/40.)
csinf(V)=alphac(V)/(alphac(V)+betac(V)) 
gCa(V)=gbarCa*(csinf(V)**4)
Ica=gCa(v)*(ECa-v)

# Na+ current
par th=0.05, gbarNa=50;
alpham(V)=-0.32*(V+31.)/(exp(-(V+31.)/4.) - 1.)
betam(V)=0.28*(V+4.)/(exp((V+4.)/5.) - 1.)
minf(v)=alpham(v)/(alpham(v)+betam(v))
alphah(V)=0.2*th*exp(-((V+47.)/18.))
betah(V)=25.*th/(1.+(exp(-(V+24.)/5.)))
gNa(v,h)=gbarNa*(minf(v)**3)*h
Ina=gNa(v,h)*(ENa-v)

# Delayed rectifier K+ current
par Vdrh=-5, tk=1, gbarDR=2
alphan(V)=-0.0032*tk*(V+5.)/(exp(-(V-Vdrh)/10.) - 1.)
betan(V)=0.05*tk*exp(-((V-Vdrh+5.)/16.))
Idr=gbarDR*(n**4)*(EK-v)

# NMDA current
par Mg=0.5, me=0.062
gnmda(v)=gbarnmda/(1+0.28*Mg*exp(-me*v))
aux nmda=gnmda(v)
#nmdasig=1/(1+exp(-(-nmdathresh)/nmdasl));
Inmda=gnmda(v)*(ENMDA-v)

# AMPA current
Iampa=gampa*(EAMPA-v)
#ampasig=1/(1+exp(-(y[2]*y[6]-ampathresh)/ampasl));

v'=Ica + IKCa + IK + IsNa + IL + Ih + Idr + Ina + Inmda +Iampa + ggaba*gaba*(Egaba-v) + I
u'= 2.*buf*((gCa(v)+gL*caLeak+gnmda(v)*caNMDA)*(ECa - v)/zF - u/tc)/r
h'= alphah(v)*(1.-h)-betah(v)*h
n'= alphan(v)*(1.-n)-betan(v)*n
q'= (hinf(v)-q)/tauh(v)

# =================GABA neuron==========================================
par glg=0.05, gbarnag=22, gbardrg=7, tng=1, thg=5, tbn=0.7, as=12, bs=0.1, vgnz=0, dg=0
par gampag=0, gnmdabarg=0;

# N+ on GABA neuron
amg(vgaba)=0.1*(vgaba+30.0)/(1.0-exp(-(vgaba+30.0)/10.0))
bmg(vgaba)=4.0*exp(-(vgaba+55.0)/18.0)
minfgg(vgaba)=amg(vgaba)/(amg(vgaba)+bmg(vgaba))
ahg(vgaba)=0.07*exp(-(vgaba+53.0)/20.0)
bhg(vgaba)=1.0/(1.0+exp(-(vgaba+23.0)/10.0))
gnag(vgaba,hg)=gbarnag*(minfgg(vgaba)**3)*hg
Inag = gnag(vgaba,hg)*(55-vgaba) 

# K+ on GABA neuron
ang(vgaba)=0.01*(vgaba+29.0)/(1.0-exp(-(vgaba+29.0)/10.0))
bng(vgaba)=tbn*0.125*exp(-(vgaba+39.0)/80.0)
gdrg(vgaba,ng)=gbardrg*(ng**4)
gnmdagg(vgaba)=gnmdabarg/(1+0.28*Mg*exp(-me*vgaba))
gspikeg(vgaba)=1/(1+exp(-vgaba/2))
Idrg = gdrg(vgaba,ng)*(-90-vgaba)

# Leak current on GABA neuron
ILg=glg*(-51-vgaba)

vgaba' = ILg + Inag + Idrg + gnmdagg(vgaba)*(eNMDA-vgaba) + gampag*(eAMPA-vgaba) + Iapp
ng'=tng*(ang(vgaba)*(1-ng))-bng(vgaba)*ng
hg'=thg*(ahg(vgaba)*(1-hg))-bhg(vgaba)*hg
gaba'=as*gspikeg(vgaba)*(1-gaba)-bs*(1-gspikeg(vgaba))*gaba

init v=-60, u=50, vgaba=-40, ng=0, hg=0, gaba=0

@ MAXSTOR=40000,TOTAL=1000,bell=0,XP=v,YP=u
@ BOUND=10000,DT=0.05,METH=stiff,YLO=40,YHI=130,XLO=-80,XHI=0

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 [33] 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
hinf v slh vhh 1 1 v vhh slh
tauh v th0 vtauh th0 0.075 v vtauh 1 0.083 v vtauh
na v slna vhna 1 1 v vhna slna
gkca x gbarkca k gbarkca x 4 x 4 k 4
gk x gbark vhk vsk gbark 1 x vhk vsk
alphac v sca vcah 0.0032 v vcah v vcah sca 1 v vcah 1 -5 0.0032 1 -5 1 -5 sca 1
betac v vcah 0.05 v vcah 5 40
csinf v sca vcah alphac v vcah sca alphac v vcah sca betac v vcah
gca v gbarca sca vcah gbarca csinf v sca vcah 4
alpham v 0.32 v 31 v 31 4 1
betam v 0.28 v 4 v 4 5 1
minf v alpham v alpham v betam v
alphah v th 0.2 th v 47 18
betah v th 25 th 1 v 24 5
gna v h gbarna gbarna minf v 3 h
alphan v tk vdrh 0.0032 tk v 5 v vdrh 10 1
betan v tk vdrh 0.05 tk v vdrh 5 16
gnmda v gbarnmda me mg gbarnmda 1 0.28 mg me v
amg vgaba 0.1 vgaba 30 1 vgaba 30 10
bmg vgaba 4 vgaba 55 18
minfgg vgaba amg vgaba amg vgaba bmg vgaba
ahg vgaba 0.07 vgaba 53 20
bhg vgaba 1 1 vgaba 23 10
gnag vgaba hg gbarnag gbarnag minfgg vgaba 3 hg
ang vgaba 0.01 vgaba 29 1 vgaba 29 10
bng vgaba tbn tbn 0.125 vgaba 39 80
gdrg vgaba ng gbardrg gbardrg ng 4
gnmdagg vgaba gnmdabarg me mg gnmdabarg 1 0.28 mg me vgaba
gspikeg vgaba 1 1 vgaba 2

Parameters [80] name constant value unit derived unit sbo cvterm
i i = 0 0.0 None
iapp iapp = 0 0.0 None
gbarnmda gbarnmda = 0 0.0 None
ggaba ggaba = 0 0.0 None
gampa gampa = 0 0.0 None
eca eca = 50. 50.0 None
ek ek = -90. -90.0 None
ena ena = 55. 55.0 None
enmda enmda = 0. 0.0 None
eampa eampa = 0. 0.0 None
egaba egaba = -90. -90.0 None
eh eh = -20. -20.0 None
gl gl = 0.18 0.18 None
el el = -35 -35.0 None
vhh vhh = -95 -95.0 None
slh slh = 8 8.0 None
th0 th0 = 625 625.0 None
vtauh vtauh = -112 -112.0 None
gbarh gbarh = 2 2.0 None
gsna gsna = 0.13 0.13 None
vhna vhna = -50 -50.0 None
slna slna = 5 5.0 None
gbarkca gbarkca = 7.8 7.8 None
k k = 160 160.0 None
gbark gbark = 1. 1.0 None
vhk vhk = -10 -10.0 None
vsk vsk = 7 7.0 None
caleak caleak = 0.1 0.1 None
canmda canmda = 0 0.0 None
buf buf = 0.00023 0.00023 None
r r = 0.2 0.2 None
tc tc = 0.52 0.52 None
zf zf = .019298 0.019298 None
gbarca gbarca = 2.5 2.5 None
vcah vcah = -52 -52.0 None
sca sca = 3. 3.0 None
caconst caconst = 0.016 0.016 None
th th = 0.05 0.05 None
gbarna gbarna = 50 50.0 None
vdrh vdrh = -5 -5.0 None
tk tk = 1 1.0 None
gbardr gbardr = 2 2.0 None
mg mg = 0.5 0.5 None
me me = 0.062 0.062 None
glg glg = 0.05 0.05 None
gbarnag gbarnag = 22 22.0 None
gbardrg gbardrg = 7 7.0 None
tng tng = 1 1.0 None
thg thg = 5 5.0 None
tbn tbn = 0.7 0.7 None
as as = 12 12.0 None
bs bs = 0.1 0.1 None
vgnz vgnz = 0 0.0 None
dg dg = 0 0.0 None
gampag gampag = 0 0.0 None
gnmdabarg gnmdabarg = 0 0.0 None
v v = -60 -60.0 None
u u = 50 50.0 None
vgaba vgaba = -40 -40.0 None
ng ng = 0 0.0 None
hg hg = 0 0.0 None
gaba gaba = 0 0.0 None
h 0.0 dimensionless None
n 0.0 dimensionless None
q 0.0 dimensionless None
il 0.0 dimensionless None
ih 0.0 dimensionless None
isna 0.0 dimensionless None
ikca 0.0 dimensionless None
ik 0.0 dimensionless None
ica 0.0 dimensionless None
ina 0.0 dimensionless None
idr 0.0 dimensionless None
nmda 0.0 dimensionless None
inmda 0.0 dimensionless None
iampa 0.0 dimensionless None
inag 0.0 dimensionless None
idrg 0.0 dimensionless None
ilg 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [24]   assignment name derived units sbo cvterm
d v/dt = ica ikca ik isna il ih idr ina inmda iampa ggaba gaba egaba v i None
d u/dt = 2 buf gca v gbarca sca vcah gl caleak gnmda v gbarnmda me mg canmda eca v zf u tc r None
d h/dt = alphah v th 1 h betah v th h None
d n/dt = alphan v tk vdrh 1 n betan v tk vdrh n None
d q/dt = hinf v slh vhh q tauh v th0 vtauh None
d vgaba/dt = ilg inag idrg gnmdagg vgaba gnmdabarg me mg enmda vgaba gampag eampa vgaba iapp None
d ng/dt = tng ang vgaba 1 ng bng vgaba tbn ng None
d hg/dt = thg ahg vgaba 1 hg bhg vgaba hg None
d gaba/dt = as gspikeg vgaba 1 gaba bs 1 gspikeg vgaba gaba None
il = gl el v None
ih = gbarh q eh v None
isna = gsna na v slna vhna ena v None
ikca = gkca u gbarkca k ek v None
ik = gk v gbark vhk vsk ek v None
ica = gca v gbarca sca vcah eca v None
ina = gna v h gbarna ena v None
idr = gbardr n 4 ek v None
nmda = gnmda v gbarnmda me mg None
inmda = gnmda v gbarnmda me mg enmda v None
iampa = gampa eampa v None
inag = gnag vgaba hg gbarnag 55 vgaba None
idrg = gdrg vgaba ng gbardrg 90 vgaba None
ilg = glg 51 vgaba None
t = time None