XPP model

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

#Simulation of pituitary GH(3) cells, firing of action potentials with three slow variable
#IK(erg) was incorporated.  gkatp channels were regulated.
# Wu SN and Chang HD, Diethyl pyrocarbonate, a histidine-modifying agent,
# directly stimulate activity of ATP-sensitive potassium channels in pituitary GH(3) cells.
# Biochem Pharmacol 2005 Dec 19; [Epub ahead of print].

#units: V=mV; t=ms; g=pS; I=fA
#Reference:  Bertram and Sherman. 
#Calcium-based model for pituitary GH3 cells
#
#Ica- calcium current
#Ik- delayed rectifier K+ current
#Ik(Ca)- Ca2+ dependent K+ current
#Ik(ATP)- nucleotide-sensitive K+ current
#Iir- erg-like K+ current
#c - cytosolic free Ca2+ concentration
#cer - ER Ca2+ concentration

#initial conditions
init v=-60.0, c=0.10, n=0.01, cer=100, a=0.46, nIR=0.008, rIR=0.282

#parameters
par gca=1000, gkca=900, gk=1400, gir=5
par vca=50, vk=-75, vir=-75, cm=5300
par taun=16, alpha=4.5e-6
par fcyt=0.01, kpmca=0.2, kd=0.3
par vn=-16, vm=-20, sn=5, sm=12
par kserca=0.4, dact=0.35, dinact=0.4
par fer=0.01, pleak=0.0005, dip3=0.5, vcytver=5
par ip3=0, sa=0.1, r=0.14 taua=300000
par tstim=3e4

gkatp=if(t<tstim)then(500)else(530)

# Iir parameters
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))

#Iir activation and inactivation functions
nIR' = (nIRinf(v) - nIR)/tauIRn(v)
rIR' = (rIRinf(v) - rIR)/tauIRr(v)

# ionic currents
ica(v)=gca*minf(v)*(v-vca)
ik(v)=gk*n*(v-vk)
ikca(v)=gkca*w*(v-vk)
ikatp(v)=gkatp*a*(v-vk)
iir(v)=gir*nIR*rIR*(v-vir)

#activation functions
minf(v)=1.0/(1.0+exp((vm-v)/sm))
ninf(v)=1.0/(1.0+exp((vn-v)/sn))
ainf(c)=1.0/(1.0+exp((r-c)/sa))

#fraction of K(Ca) channels activated by cytosolic Ca2+
w=c^5/(c^5+kd^5)

#flux of Ca2+ through the membrane
jmem=-(alpha*Ica(v)+kpmca*c)

#Ca2+ influx into the ER via SERCA 
jserca=kserca*c

#efflux out of the ER has two components
# 1. Ca2+ leak is proportional to gradient between Ca2+ and ER
jleak=pleak*(cer-c)

# 2. Ca2+ efflux through the IP3R
jip3=oinf*(cer-c)

#fraction of open channels
oinf=(c/(dact+c))*(ip3/(dip3+ip3))*(dinact/(dinact+c))

#net Ca2+ efflux from the ER
jer=jleak+jip3-jserca

#differential equations
v'=-(ica(v)+ik(v)+ikca(v)+ikatp(v)+iir(v))/cm
n'=(ninf(v)-n)/taun
c'=fcyt*(jmem+jer)
cer'=-fer*(vcytver)*jer
a'=(ainf(c)-a)/taua

aux tsec=t/1000.0

@ meth=cvode, dtmax=1, dt=2, total=8e4, maxstor=80000
@ bounds=1000, xp=tsec,  yp=v, toler=1.0e-7, atoler=1.0e-7
@ xlo=0, xhi=80, ylo=-80, yhi=5

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 [20] 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
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
ica v gca sm vca vm gca minf v vm sm v vca
ik v gk n vk gk n v vk
ikca v gkca vk w gkca w v vk
ikatp v a gkatp vk gkatp a v vk
iir v gir nir rir vir gir nir rir v vir
minf v sm vm 1 1 vm v sm
ninf v sn vn 1 1 vn v sn
ainf c r sa 1 1 r c sa

Parameters [46] name constant value unit derived unit sbo cvterm
v v = -60.0 -60.0 None
c c = 0.10 0.1 None
n n = 0.01 0.01 None
cer cer = 100 100.0 None
a a = 0.46 0.46 None
nir nir = 0.008 0.008 None
rir rir = 0.282 0.282 None
gca gca = 1000 1000.0 None
gkca gkca = 900 900.0 None
gk gk = 1400 1400.0 None
gir gir = 5 5.0 None
vca vca = 50 50.0 None
vk vk = -75 -75.0 None
vir vir = -75 -75.0 None
cm cm = 5300 5300.0 None
taun taun = 16 16.0 None
alpha alpha = 4.5e-6 4.5e-06 None
fcyt fcyt = 0.01 0.01 None
kpmca kpmca = 0.2 0.2 None
kd kd = 0.3 0.3 None
vn vn = -16 -16.0 None
vm vm = -20 -20.0 None
sn sn = 5 5.0 None
sm sm = 12 12.0 None
kserca kserca = 0.4 0.4 None
dact dact = 0.35 0.35 None
dinact dinact = 0.4 0.4 None
fer fer = 0.01 0.01 None
pleak pleak = 0.0005 0.0005 None
dip3 dip3 = 0.5 0.5 None
vcytver vcytver = 5 5.0 None
ip3 ip3 = 0 0.0 None
sa sa = 0.1 0.1 None
r r = 0.14 0.14 None
taua taua = 300000 300000.0 None
tstim tstim = 3e4 30000.0 None
gkatp 0.0 dimensionless None
w 0.0 dimensionless None
jmem 0.0 dimensionless None
jserca 0.0 dimensionless None
jleak 0.0 dimensionless None
jip3 0.0 dimensionless None
oinf 0.0 dimensionless None
jer 0.0 dimensionless None
tsec 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [17]   assignment name derived units sbo cvterm
d nir/dt = nirinf v nir tauirn v None
d rir/dt = ririnf v rir tauirr v None
d v/dt = ica v gca sm vca vm ik v gk n vk ikca v gkca vk w ikatp v a gkatp vk iir v gir nir rir vir cm None
d n/dt = ninf v sn vn n taun None
d c/dt = fcyt jmem jer None
d cer/dt = fer vcytver jer None
d a/dt = ainf c r sa a taua None
gkatp = 500 t tstim 530 None
w = c 5 c 5 kd 5 None
jmem = alpha ica v gca sm vca vm kpmca c None
jserca = kserca c None
jleak = pleak cer c None
jip3 = oinf cer c None
oinf = c dact c ip3 dip3 ip3 dinact dinact c None
jer = jleak jip3 jserca None
tsec = t 1000 None
t = time None