XPP model

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

# Adoped from Pinsky-Rinzel CA3 pyramidal cell model
# 
# Pinsky and Rinzel, J Comput Neurosci 1994;1:39-60.
# K(ATP) channel was inserted into the model.
# Parameters for K(ATP) channels were from Koyto model
# Matsuoka et al. Prog Biophys Mol Biol 2004;85:279-299.
# 
# stochastic simulation of flunctuations in intracellular ATP

# initial conditions
init Vs=-60, Vd=-60, s=0.185
wiener w

# Parameter values
par ip0=0.75
par gLs=0.1  gLd=0.1  gNa=30  gKdr=15  gCa=9  gKahp=0.8  gKC=15
par VNa=60  VCa=80  VK=-75  VL=-60  Vsyn=0
par gc=2.1 pp=0.5  Cm=3
par alphac=2 betac=0.1
par tstim=4.0e3 n=500
par gkatp=0.0236*(4^0.24)
par init_atp=0.1 final_atp=0.5
par natp=10
iatp=if(t<tstim)then(init_atp)else(final_atp)

# Pyramidal cell functions
ICad =  gCa*sd*sd*(Vd-VCa)
alphams(v) =  0.32*(-46.9-v)/(exp((-46.9-v)/4.0)-1.0)
betams(v) =  0.28*(v+19.9)/(exp((v+19.9)/5.0)-1.0)
Minfs(v) =  alphams(v)/(alphams(v)+betams(v))
alphans(v) =  0.016*(-24.9-v)/(exp((-24.9-v)/5.0)-1.0)
betans(v) =  0.25*exp(-1.0-0.025*v)
alphahs(v) =  0.128*exp((-43.0-v)/18.0)
betahs(v) =  4.0/(1.0+exp((-20.0-v)/5.0))
alphasd(v) = 1.6/(1.0+exp(-0.072*(v-5.0)))
betasd(v) =  0.02*(v+8.9)/(exp((v+8.9)/5.0)-1.0)
alphacd(v) = (1.0-heav(v+10.0))*exp((v+50.0)/11-(v+53.5)/27)/18.975+heav(v+10.0)*2.0*exp((-53.5-v)/27.0) 
betacd(v) =  (1.0-heav(v+10.0))*(2.0*exp((-53.5-v)/27.0)-alphacd(v))
alphaqd = min(0.00002*Cad,0.01)
betaqd = 0.001
chid = min(Cad/250.0,1.0)

# Level of intracellular ATP concentration
poatp = 0.8/(1+(iatp*s/0.023)^2)

# Stochastics
par alphas=1, taus=100, noise=1, s0=0.2
betas = alphas*(1/s0 - 1)
varnoise=sqrt((alphas*(1 - s)+betas*s)/(taus*natp))

# Output cols are t, ODEs, AUXs in order, here:
# t versus vd cad hs ns sd cd qd gqk gkc 
Vs'=(-gLs*(Vs-VL)-gNa*(Minfs(Vs)^2)*hs*(Vs-VNa)-gKdr*ns*(Vs-VK)-gkatp*natp*poatp*(Vs-VK)+(gc/pp)*(Vd-Vs)+Ip0/pp)/Cm
Vd'=(-gLd*(Vd-VL)-ICad-gKahp*qd*(Vd-VK)-gKC*cd*chid*(Vd-VK)-gkatp*natp*poatp*(Vd-VK)+(gc*(Vs-Vd))/(1.0-pp))/Cm
Cad'=  -0.13*ICad-0.075*Cad
hs'=  alphahs(Vs)-(alphahs(Vs)+betahs(Vs))*hs
ns'=  alphans(Vs)-(alphans(Vs)+betans(Vs))*ns
sd'=  alphasd(Vd)-(alphasd(Vd)+betasd(Vd))*sd
cd'=  alphacd(Vd)-(alphacd(Vd)+betacd(Vd))*cd
qd'=  alphaqd-(alphaqd+betaqd)*qd
s' = (alphas*(1-s)-betas*s)/taus + noise*w*varnoise

# auxiliary equationns
aux Ica=ICad
aux gkq = gKahp*qd
aux gkc = gKC*cd*chid
aux ikatp = gkatp*natp*poatp*(Vs-VK)
aux iatp=iatp*s

# For stochastics, CVODE can not be used.
@ maxstor=1000000, total=1.0e4, bounds=10000, xlo=0, xhi=1.0e4, ylo=-90, yhi=60
@ meth=Euler, atol=1e-10, toler=1e-10, dt=0.05
done
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Copyright © 2017 Matthias Koenig

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Access SBML model  L3V1

FunctionDefinitions [15] 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
alphams v 0.32 46.9 v 46.9 v 4 1
betams v 0.28 v 19.9 v 19.9 5 1
minfs v alphams v alphams v betams v
alphans v 0.016 24.9 v 24.9 v 5 1
betans v 0.25 1 0.025 v
alphahs v 0.128 43 v 18
betahs v 4 1 20 v 5
alphasd v 1.6 1 0.072 v 5
betasd v 0.02 v 8.9 v 8.9 5 1
alphacd v 1 heav v 10 v 50 11 v 53.5 27 18.975 heav v 10 2 53.5 v 27
betacd v 1 heav v 10 2 53.5 v 27 alphacd v

Parameters [50] name constant value unit derived unit sbo cvterm
vs vs = -60 -60.0 None
vd vd = -60 -60.0 None
s s = 0.185 0.185 None
w 0.0 None
ip0 ip0 = 0.75 0.75 None
gls gls = 0.1 0.1 None
gld gld = 0.1 0.1 None
gna gna = 30 30.0 None
gkdr gkdr = 15 15.0 None
gca gca = 9 9.0 None
gkahp gkahp = 0.8 0.8 None
gkc gkc = 15 15.0 None
vna vna = 60 60.0 None
vca vca = 80 80.0 None
vk vk = -75 -75.0 None
vl vl = -60 -60.0 None
vsyn vsyn = 0 0.0 None
gc gc = 2.1 2.1 None
pp pp = 0.5 0.5 None
cm cm = 3 3.0 None
alphac alphac = 2 2.0 None
betac betac = 0.1 0.1 None
tstim tstim = 4.0e3 4000.0 None
n n = 500 500.0 None
gkatp gkatp 0.0 None
init_atp init_atp = 0.1 0.1 None
final_atp final_atp = 0.5 0.5 None
natp natp = 10 10.0 None
alphas alphas = 1 1.0 None
taus taus = 100 100.0 None
noise noise = 1 1.0 None
s0 s0 = 0.2 0.2 None
cad 0.0 dimensionless None
hs 0.0 dimensionless None
ns 0.0 dimensionless None
sd 0.0 dimensionless None
cd 0.0 dimensionless None
qd 0.0 dimensionless None
iatp 0.0 dimensionless None
icad 0.0 dimensionless None
alphaqd 0.0 dimensionless None
betaqd 0.0 dimensionless None
chid 0.0 dimensionless None
poatp 0.0 dimensionless None
betas 0.0 dimensionless None
varnoise 0.0 dimensionless None
ica 0.0 dimensionless None
gkq 0.0 dimensionless None
ikatp 0.0 dimensionless None
t model time 0.0 dimensionless None

InitialAssignments [1] name assignment derived units sbo cvterm
gkatp = 0.0236 4 0.24 None

Rules [22]   assignment name derived units sbo cvterm
d vs/dt = gls vs vl gna minfs vs 2 hs vs vna gkdr ns vs vk gkatp natp poatp vs vk gc pp vd vs ip0 pp cm None
d vd/dt = gld vd vl icad gkahp qd vd vk gkc cd chid vd vk gkatp natp poatp vd vk gc vs vd 1 pp cm None
d cad/dt = 0.13 icad 0.075 cad None
d hs/dt = alphahs vs alphahs vs betahs vs hs None
d ns/dt = alphans vs alphans vs betans vs ns None
d sd/dt = alphasd vd alphasd vd betasd vd sd None
d cd/dt = alphacd vd alphacd vd betacd vd cd None
d qd/dt = alphaqd alphaqd betaqd qd None
d s/dt = alphas 1 s betas s taus noise w varnoise None
iatp = init_atp t tstim final_atp None
icad = gca sd sd vd vca None
alphaqd = min 2 -5 cad 0.01 None
betaqd = 0.001 None
chid = min cad 250 1 None
poatp = 0.8 1 iatp s 0.023 2 None
betas = alphas 1 s0 1 None
varnoise = 2 alphas 1 s betas s taus natp None
ica = icad None
gkq = gkahp qd None
gkc = gkc cd chid None
ikatp = gkatp natp poatp vs vk None
t = time None