XPP model

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

# PLOS Computational Biology, Riz et al., 2013
# human beta-cell model including SK-channels and Ca2+ dynamics
# Default parameters as in Fig. 1A

# Differential equations
V'= -(ISK + IBK + IKv + IHERG + INa + ICaL + ICaPQ + ICaT + IKatp*(1+sigma*q) + Ileak + Igabar)

# use for stochastic simulation in Fig 1E
wiener q
par sigma=0

mkv'=(mkvinf-mkv)/taumkv
mBK'=(mBKinf-mBK)/taumBK
hNa'=(hNainf-hNa)/tauhNa
hCaL'=(hCaLinf-hCaL)/tauhCaL
hCaT'=(hCaTinf-hCaT)/tauhCaT
mHERG'=(mHERGinf-mHERG)/taumHERG
hHERG'=(hHERGinf-hHERG)/tauhHERG

# Differential equations for Ca2+ dynamics
Cam'=f*( (JCaL+JCaPQ+JCaT) - B*(Cam-Cac)/Volm*Volc - L/Volm*Volc )
Cac'=f*(B*(Cam-Cac)-Jserca+Jleak)

# Initial conditions
V(0)=-63
mkv(0)=0.02
mBK(0)=0.002
hNa(0)=0.97
hCaL(0)=0.98
hCaT(0)=0.52
mHERG(0)=0.1
hHERG(0)=0.7
Cam(0)=0.30
Cac(0)=0.17

## Nernst voltages
par VNa=70
par VCa=65
par VK=-75
par VCl=-40

## Leak current
par gleak=0.015
par vleak=-30

Ileak=gleak*(V-vleak)
aux Ileak=Ileak

## IKv
par taumkv0=2, Vmkv=0, nmkv=-10, gkv=1

mkvinf=1/(1+exp((V-Vmkv)/nmkv))
taumkv=taumkv0+10*exp(min(log(3),(-20-V)/6))
IKv=gkv*mkv*(V-VK)

## IBK
par taumBK=2, VmBK=0, nmBK=-10, BBK=20, gBK=0.02

mBKinf=1/( 1+exp((V-VmBK)/nmBK))
IBK = gBK*(-ICa+BBK)*mBK*(V-VK)
aux ibk=IBK

## hERG channels
par VmHERG=-30, nmHERG=-10, taumHERG=100
par VhHERG=-42, nhHERG=17.5, tauhHERG=50
par gHERG=0

mHERGinf=1/( 1+exp((V-VmHERG)/nmHERG) )
hHERGinf=1/( 1+exp((V-VhHERG)/nhHERG) )
IHERG = gHERG*mHERG*hHERG*(V-VK)

## Na current
par gNa=0.4, VmNa=-18, nmNa=-5, VhNa=-42, nhNa=6, tauhNa=2
hNainf=1/( 1+exp((V-VhNa)/nhNa) )
mNainf=1/( 1+exp((V-VmNa)/nmNa) )
INa=gNa*mNainf*hNa*(V-VNa)

## L-type Ca current
par gCaL=0.14, VmCaL=-25, nmCaL=-6, tauhCaL=20

mCaLinf=1/( 1+exp((V-VmCaL)/nmCaL) ) 
hCaLinf=max(0,min(1,1+mCaLinf*(V-VCa)/57))
ICaL = gCaL*mCaLinf*hCaL*(V-VCa)

## PQ-type Ca current
par gCaPQ=0.17, VmCaPQ=-10, nmCaPQ=-6

mCaPQinf=1/( 1+exp((V-VmCaPQ)/nmCaPQ) )
ICaPQ = gCaPQ*mCaPQinf*(V-VCa)

## T-type Ca current
par gCaT=0.05, VmCaT=-40, nmCaT=-4, VhCaT=-64, nhCaT=8, tauhCaT=7

mCaTinf=1/( 1+exp((V-VmCaT)/nmCaT) )
hCaTinf=1/( 1+exp((V-VhCaT)/nhCaT) )
ICaT = gCaT*mCaTinf*hCaT*(V-VCa)
ICa=ICaL+ICaPQ+ICaT

## Katp current
IKatp=gkatp*(V-VK)

par gkatp=0.01

## Gabar current
Igabar=ggabar*(V-VCl)

par ggabar=0


## ISK current
par gSK=0.1, kSK=0.57, nSK=5.2

ISK = gSK*(Cam^nSK/( kSK^nSK+Cam^nSK) )*(V-VK)
#aux ISK=ISK

## Ca diffusion
#definition of fluxes
par Cm=10

JCaL=-alpha*ICaL*Cm/Volm
JCaPQ=-alpha*ICaPQ*Cm/Volm
JCaT=-alpha*ICaT*Cm/Volm
Jserca=Jsercamax*Cac^2/(Kserca^2 + Cac^2)
Jpmca=Jpmcamax*Cam/(Kpmca + Cam)
Jncx=Jncx0*(Cam)
L=Jpmca+Jncx

# Calcium dynamics parameters

par f=0.01
par B=0.1
par Volc=1.15e-12, Volm=1e-13
 
# conversion to fluxes
par alpha=5.18e-15
 
# other fluxes
par Jsercamax=0.06, Kserca=0.27, Jpmcamax=0.021, Kpmca=0.5, Jleak=0.94e-3, Jncx0=0.01867

@ meth=cvode, toler=1.0e-10, atoler=1.0e-10, dt=.01, total=3000,
@ maxstor=2000000,bounds=10000000000000000000, xp=t, yp=v
@ xlo=0, xhi=3000, ylo=-80, yhi=10

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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  2. Redistributions in a different form must reproduce the above copyright notice, this list of conditions and the following disclaimer in the documentation and/or other materials provided with the distribution.
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 [4] 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
mod modulo x y x y x y x 0 y 0 x y x y

Parameters [103] name constant value unit derived unit sbo cvterm
q 0.0 None
sigma 0.0 None
V -63.0 None
mkv 0.02 None
mBK 0.002 None
hNa 0.97 None
hCaL 0.98 None
hCaT 0.52 None
mHERG 0.1 None
hHERG 0.7 None
Cam 0.3 None
Cac 0.17 None
VNa 70.0 None
VCa 65.0 None
VK -75.0 None
VCl -40.0 None
gleak 0.015 None
vleak -30.0 None
taumkv0 2.0 None
Vmkv 0.0 None
nmkv -10.0 None
gkv 1.0 None
taumBK 2.0 None
VmBK 0.0 None
nmBK -10.0 None
BBK 20.0 None
gBK 0.02 None
VmHERG -30.0 None
nmHERG -10.0 None
taumHERG 100.0 None
VhHERG -42.0 None
nhHERG 17.5 None
tauhHERG 50.0 None
gHERG 0.0 None
gNa 0.4 None
VmNa -18.0 None
nmNa -5.0 None
VhNa -42.0 None
nhNa 6.0 None
tauhNa 2.0 None
gCaL 0.14 None
VmCaL -25.0 None
nmCaL -6.0 None
tauhCaL 20.0 None
gCaPQ 0.17 None
VmCaPQ -10.0 None
nmCaPQ -6.0 None
gCaT 0.05 None
VmCaT -40.0 None
nmCaT -4.0 None
VhCaT -64.0 None
nhCaT 8.0 None
tauhCaT 7.0 None
gkatp 0.01 None
ggabar 0.0 None
gSK 0.1 None
kSK 0.57 None
nSK 5.2 None
Cm 10.0 None
f 0.01 None
B 0.1 None
Volc 1.15e-12 None
Volm 1e-13 None
alpha 5.18e-15 None
Jsercamax 0.06 None
Kserca 0.27 None
Jpmcamax 0.021 None
Kpmca 0.5 None
Jleak 0.00094 None
Jncx0 0.01867 None
Ileak 0.0 dimensionless None
mkvinf 0.0 dimensionless None
taumkv 0.0 dimensionless None
IKv 0.0 dimensionless None
mBKinf 0.0 dimensionless None
IBK 0.0 dimensionless None
ibk 0.0 dimensionless None
mHERGinf 0.0 dimensionless None
hHERGinf 0.0 dimensionless None
IHERG 0.0 dimensionless None
hNainf 0.0 dimensionless None
mNainf 0.0 dimensionless None
INa 0.0 dimensionless None
mCaLinf 0.0 dimensionless None
hCaLinf 0.0 dimensionless None
ICaL 0.0 dimensionless None
mCaPQinf 0.0 dimensionless None
ICaPQ 0.0 dimensionless None
mCaTinf 0.0 dimensionless None
hCaTinf 0.0 dimensionless None
ICaT 0.0 dimensionless None
ICa 0.0 dimensionless None
IKatp 0.0 dimensionless None
Igabar 0.0 dimensionless None
ISK 0.0 dimensionless None
JCaL 0.0 dimensionless None
JCaPQ 0.0 dimensionless None
JCaT 0.0 dimensionless None
Jserca 0.0 dimensionless None
Jpmca 0.0 dimensionless None
Jncx 0.0 dimensionless None
L 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [43]   assignment name derived units sbo cvterm
d V/dt = ISK IBK IKv IHERG INa ICaL ICaPQ ICaT IKatp 1 sigma q Ileak Igabar None
d mkv/dt = mkvinf mkv taumkv None
d mBK/dt = mBKinf mBK taumBK None
d hNa/dt = hNainf hNa tauhNa None
d hCaL/dt = hCaLinf hCaL tauhCaL None
d hCaT/dt = hCaTinf hCaT tauhCaT None
d mHERG/dt = mHERGinf mHERG taumHERG None
d hHERG/dt = hHERGinf hHERG tauhHERG None
d Cam/dt = f JCaL JCaPQ JCaT B Cam Cac Volm Volc L Volm Volc None
d Cac/dt = f B Cam Cac Jserca Jleak None
Ileak = gleak V vleak None
mkvinf = 1 1 V Vmkv nmkv None
taumkv = taumkv0 10 min 10 3 20 V 6 None
IKv = gkv mkv V VK None
mBKinf = 1 1 V VmBK nmBK None
IBK = gBK ICa BBK mBK V VK None
ibk = IBK None
mHERGinf = 1 1 V VmHERG nmHERG None
hHERGinf = 1 1 V VhHERG nhHERG None
IHERG = gHERG mHERG hHERG V VK None
hNainf = 1 1 V VhNa nhNa None
mNainf = 1 1 V VmNa nmNa None
INa = gNa mNainf hNa V VNa None
mCaLinf = 1 1 V VmCaL nmCaL None
hCaLinf = max 0 min 1 1 mCaLinf V VCa 57 None
ICaL = gCaL mCaLinf hCaL V VCa None
mCaPQinf = 1 1 V VmCaPQ nmCaPQ None
ICaPQ = gCaPQ mCaPQinf V VCa None
mCaTinf = 1 1 V VmCaT nmCaT None
hCaTinf = 1 1 V VhCaT nhCaT None
ICaT = gCaT mCaTinf hCaT V VCa None
ICa = ICaL ICaPQ ICaT None
IKatp = gkatp V VK None
Igabar = ggabar V VCl None
ISK = gSK Cam nSK kSK nSK Cam nSK V VK None
JCaL = alpha ICaL Cm Volm None
JCaPQ = alpha ICaPQ Cm Volm None
JCaT = alpha ICaT Cm Volm None
Jserca = Jsercamax Cac 2 Kserca 2 Cac 2 None
Jpmca = Jpmcamax Cam Kpmca Cam None
Jncx = Jncx0 Cam None
L = Jpmca Jncx None
t = time None