Model :

id
name
time
substance
extent
volume
area
length
L3V1

XPP model

This model was converted from XPP ode format to SBML using sbmlutils-0.4.10.

# 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
This file has been produced by sbmlutils.

Terms of use

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:

  1. Redistributions of this SBML file must retain the above copyright notice, this list of conditions and the following disclaimer.
  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.


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 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 uncertainties
q 0.0 None
sigma sigma = 0 0.0 None
V V = -63 -63.0 None
mkv mkv = 0.02 0.02 None
mBK mBK = 0.002 0.002 None
hNa hNa = 0.97 0.97 None
hCaL hCaL = 0.98 0.98 None
hCaT hCaT = 0.52 0.52 None
mHERG mHERG = 0.1 0.1 None
hHERG hHERG = 0.7 0.7 None
Cam Cam = 0.30 0.3 None
Cac Cac = 0.17 0.17 None
VNa VNa = 70 70.0 None
VCa VCa = 65 65.0 None
VK VK = -75 -75.0 None
VCl VCl = -40 -40.0 None
gleak gleak = 0.015 0.015 None
vleak vleak = -30 -30.0 None
taumkv0 taumkv0 = 2 2.0 None
Vmkv Vmkv = 0 0.0 None
nmkv nmkv = -10 -10.0 None
gkv gkv = 1 1.0 None
taumBK taumBK = 2 2.0 None
VmBK VmBK = 0 0.0 None
nmBK nmBK = -10 -10.0 None
BBK BBK = 20 20.0 None
gBK gBK = 0.02 0.02 None
VmHERG VmHERG = -30 -30.0 None
nmHERG nmHERG = -10 -10.0 None
taumHERG taumHERG = 100 100.0 None
VhHERG VhHERG = -42 -42.0 None
nhHERG nhHERG = 17.5 17.5 None
tauhHERG tauhHERG = 50 50.0 None
gHERG gHERG = 0 0.0 None
gNa gNa = 0.4 0.4 None
VmNa VmNa = -18 -18.0 None
nmNa nmNa = -5 -5.0 None
VhNa VhNa = -42 -42.0 None
nhNa nhNa = 6 6.0 None
tauhNa tauhNa = 2 2.0 None
gCaL gCaL = 0.14 0.14 None
VmCaL VmCaL = -25 -25.0 None
nmCaL nmCaL = -6 -6.0 None
tauhCaL tauhCaL = 20 20.0 None
gCaPQ gCaPQ = 0.17 0.17 None
VmCaPQ VmCaPQ = -10 -10.0 None
nmCaPQ nmCaPQ = -6 -6.0 None
gCaT gCaT = 0.05 0.05 None
VmCaT VmCaT = -40 -40.0 None
nmCaT nmCaT = -4 -4.0 None
VhCaT VhCaT = -64 -64.0 None
nhCaT nhCaT = 8 8.0 None
tauhCaT tauhCaT = 7 7.0 None
gkatp gkatp = 0.01 0.01 None
ggabar ggabar = 0 0.0 None
gSK gSK = 0.1 0.1 None
kSK kSK = 0.57 0.57 None
nSK nSK = 5.2 5.2 None
Cm Cm = 10 10.0 None
f f = 0.01 0.01 None
B B = 0.1 0.1 None
Volc Volc = 1.15e-12 1.15e-12 None
Volm Volm = 1e-13 1e-13 None
alpha alpha = 5.18e-15 5.18e-15 None
Jsercamax Jsercamax = 0.06 0.06 None
Kserca Kserca = 0.27 0.27 None
Jpmcamax Jpmcamax = 0.021 0.021 None
Kpmca Kpmca = 0.5 0.5 None
Jleak Jleak = 0.94e-3 0.00094 None
Jncx0 Jncx0 = 0.01867 0.01867 None
Ileak nan dimensionless None
mkvinf nan dimensionless None
taumkv nan dimensionless None
IKv nan dimensionless None
mBKinf nan dimensionless None
IBK nan dimensionless None
ibk nan dimensionless None
mHERGinf nan dimensionless None
hHERGinf nan dimensionless None
IHERG nan dimensionless None
hNainf nan dimensionless None
mNainf nan dimensionless None
INa nan dimensionless None
mCaLinf nan dimensionless None
hCaLinf nan dimensionless None
ICaL nan dimensionless None
mCaPQinf nan dimensionless None
ICaPQ nan dimensionless None
mCaTinf nan dimensionless None
hCaTinf nan dimensionless None
ICaT nan dimensionless None
ICa nan dimensionless None
IKatp nan dimensionless None
Igabar nan dimensionless None
ISK nan dimensionless None
JCaL nan dimensionless None
JCaPQ nan dimensionless None
JCaT nan dimensionless None
Jserca nan dimensionless None
Jpmca nan dimensionless None
Jncx nan dimensionless None
L nan dimensionless None
t model time nan dimensionless None

Rules [43]   assignment name derived units sbo cvterm uncertainties
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