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
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Model :
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type | FunctionDefinitions [4] | name | math | sbo | cvterm |
---|---|---|---|---|---|
FunctionDefinition | max
|
minimum | |||
FunctionDefinition | min
|
maximum | |||
FunctionDefinition | heav
|
heavyside | |||
FunctionDefinition | mod
|
modulo |
type | Parameters [103] | name | constant | value | unit | derived unit | sbo | cvterm |
---|---|---|---|---|---|---|---|---|
Parameter | q
|
T | 0.0 | None | ||||
Parameter | sigma
|
F | 0.0 | None | ||||
Parameter | V
|
F | -63.0 | None | ||||
Parameter | mkv
|
F | 0.02 | None | ||||
Parameter | mBK
|
F | 0.002 | None | ||||
Parameter | hNa
|
F | 0.97 | None | ||||
Parameter | hCaL
|
F | 0.98 | None | ||||
Parameter | hCaT
|
F | 0.52 | None | ||||
Parameter | mHERG
|
F | 0.1 | None | ||||
Parameter | hHERG
|
F | 0.7 | None | ||||
Parameter | Cam
|
F | 0.3 | None | ||||
Parameter | Cac
|
F | 0.17 | None | ||||
Parameter | VNa
|
F | 70.0 | None | ||||
Parameter | VCa
|
F | 65.0 | None | ||||
Parameter | VK
|
F | -75.0 | None | ||||
Parameter | VCl
|
F | -40.0 | None | ||||
Parameter | gleak
|
F | 0.015 | None | ||||
Parameter | vleak
|
F | -30.0 | None | ||||
Parameter | taumkv0
|
F | 2.0 | None | ||||
Parameter | Vmkv
|
F | 0.0 | None | ||||
Parameter | nmkv
|
F | -10.0 | None | ||||
Parameter | gkv
|
F | 1.0 | None | ||||
Parameter | taumBK
|
F | 2.0 | None | ||||
Parameter | VmBK
|
F | 0.0 | None | ||||
Parameter | nmBK
|
F | -10.0 | None | ||||
Parameter | BBK
|
F | 20.0 | None | ||||
Parameter | gBK
|
F | 0.02 | None | ||||
Parameter | VmHERG
|
F | -30.0 | None | ||||
Parameter | nmHERG
|
F | -10.0 | None | ||||
Parameter | taumHERG
|
F | 100.0 | None | ||||
Parameter | VhHERG
|
F | -42.0 | None | ||||
Parameter | nhHERG
|
F | 17.5 | None | ||||
Parameter | tauhHERG
|
F | 50.0 | None | ||||
Parameter | gHERG
|
F | 0.0 | None | ||||
Parameter | gNa
|
F | 0.4 | None | ||||
Parameter | VmNa
|
F | -18.0 | None | ||||
Parameter | nmNa
|
F | -5.0 | None | ||||
Parameter | VhNa
|
F | -42.0 | None | ||||
Parameter | nhNa
|
F | 6.0 | None | ||||
Parameter | tauhNa
|
F | 2.0 | None | ||||
Parameter | gCaL
|
F | 0.14 | None | ||||
Parameter | VmCaL
|
F | -25.0 | None | ||||
Parameter | nmCaL
|
F | -6.0 | None | ||||
Parameter | tauhCaL
|
F | 20.0 | None | ||||
Parameter | gCaPQ
|
F | 0.17 | None | ||||
Parameter | VmCaPQ
|
F | -10.0 | None | ||||
Parameter | nmCaPQ
|
F | -6.0 | None | ||||
Parameter | gCaT
|
F | 0.05 | None | ||||
Parameter | VmCaT
|
F | -40.0 | None | ||||
Parameter | nmCaT
|
F | -4.0 | None | ||||
Parameter | VhCaT
|
F | -64.0 | None | ||||
Parameter | nhCaT
|
F | 8.0 | None | ||||
Parameter | tauhCaT
|
F | 7.0 | None | ||||
Parameter | gkatp
|
F | 0.01 | None | ||||
Parameter | ggabar
|
F | 0.0 | None | ||||
Parameter | gSK
|
F | 0.1 | None | ||||
Parameter | kSK
|
F | 0.57 | None | ||||
Parameter | nSK
|
F | 5.2 | None | ||||
Parameter | Cm
|
F | 10.0 | None | ||||
Parameter | f
|
F | 0.01 | None | ||||
Parameter | B
|
F | 0.1 | None | ||||
Parameter | Volc
|
F | 1.15e-12 | None | ||||
Parameter | Volm
|
F | 1e-13 | None | ||||
Parameter | alpha
|
F | 5.18e-15 | None | ||||
Parameter | Jsercamax
|
F | 0.06 | None | ||||
Parameter | Kserca
|
F | 0.27 | None | ||||
Parameter | Jpmcamax
|
F | 0.021 | None | ||||
Parameter | Kpmca
|
F | 0.5 | None | ||||
Parameter | Jleak
|
F | 0.00094 | None | ||||
Parameter | Jncx0
|
F | 0.01867 | None | ||||
Parameter | Ileak
|
F | 0.0 | dimensionless | None | |||
Parameter | mkvinf
|
F | 0.0 | dimensionless | None | |||
Parameter | taumkv
|
F | 0.0 | dimensionless | None | |||
Parameter | IKv
|
F | 0.0 | dimensionless | None | |||
Parameter | mBKinf
|
F | 0.0 | dimensionless | None | |||
Parameter | IBK
|
F | 0.0 | dimensionless | None | |||
Parameter | ibk
|
F | 0.0 | dimensionless | None | |||
Parameter | mHERGinf
|
F | 0.0 | dimensionless | None | |||
Parameter | hHERGinf
|
F | 0.0 | dimensionless | None | |||
Parameter | IHERG
|
F | 0.0 | dimensionless | None | |||
Parameter | hNainf
|
F | 0.0 | dimensionless | None | |||
Parameter | mNainf
|
F | 0.0 | dimensionless | None | |||
Parameter | INa
|
F | 0.0 | dimensionless | None | |||
Parameter | mCaLinf
|
F | 0.0 | dimensionless | None | |||
Parameter | hCaLinf
|
F | 0.0 | dimensionless | None | |||
Parameter | ICaL
|
F | 0.0 | dimensionless | None | |||
Parameter | mCaPQinf
|
F | 0.0 | dimensionless | None | |||
Parameter | ICaPQ
|
F | 0.0 | dimensionless | None | |||
Parameter | mCaTinf
|
F | 0.0 | dimensionless | None | |||
Parameter | hCaTinf
|
F | 0.0 | dimensionless | None | |||
Parameter | ICaT
|
F | 0.0 | dimensionless | None | |||
Parameter | ICa
|
F | 0.0 | dimensionless | None | |||
Parameter | IKatp
|
F | 0.0 | dimensionless | None | |||
Parameter | Igabar
|
F | 0.0 | dimensionless | None | |||
Parameter | ISK
|
F | 0.0 | dimensionless | None | |||
Parameter | JCaL
|
F | 0.0 | dimensionless | None | |||
Parameter | JCaPQ
|
F | 0.0 | dimensionless | None | |||
Parameter | JCaT
|
F | 0.0 | dimensionless | None | |||
Parameter | Jserca
|
F | 0.0 | dimensionless | None | |||
Parameter | Jpmca
|
F | 0.0 | dimensionless | None | |||
Parameter | Jncx
|
F | 0.0 | dimensionless | None | |||
Parameter | L
|
F | 0.0 | dimensionless | None | |||
Parameter | t
|
model time | F | 0.0 | dimensionless | None |
type | Rules [43] | assignment | name | derived units | sbo | cvterm | |
---|---|---|---|---|---|---|---|
Rule | d V/dt
|
= | None | ||||
Rule | d mkv/dt
|
= | None | ||||
Rule | d mBK/dt
|
= | None | ||||
Rule | d hNa/dt
|
= | None | ||||
Rule | d hCaL/dt
|
= | None | ||||
Rule | d hCaT/dt
|
= | None | ||||
Rule | d mHERG/dt
|
= | None | ||||
Rule | d hHERG/dt
|
= | None | ||||
Rule | d Cam/dt
|
= | None | ||||
Rule | d Cac/dt
|
= | None | ||||
Rule | Ileak
|
= | None | ||||
Rule | mkvinf
|
= | None | ||||
Rule | taumkv
|
= | None | ||||
Rule | IKv
|
= | None | ||||
Rule | mBKinf
|
= | None | ||||
Rule | IBK
|
= | None | ||||
Rule | ibk
|
= | None | ||||
Rule | mHERGinf
|
= | None | ||||
Rule | hHERGinf
|
= | None | ||||
Rule | IHERG
|
= | None | ||||
Rule | hNainf
|
= | None | ||||
Rule | mNainf
|
= | None | ||||
Rule | INa
|
= | None | ||||
Rule | mCaLinf
|
= | None | ||||
Rule | hCaLinf
|
= | None | ||||
Rule | ICaL
|
= | None | ||||
Rule | mCaPQinf
|
= | None | ||||
Rule | ICaPQ
|
= | None | ||||
Rule | mCaTinf
|
= | None | ||||
Rule | hCaTinf
|
= | None | ||||
Rule | ICaT
|
= | None | ||||
Rule | ICa
|
= | None | ||||
Rule | IKatp
|
= | None | ||||
Rule | Igabar
|
= | None | ||||
Rule | ISK
|
= | None | ||||
Rule | JCaL
|
= | None | ||||
Rule | JCaPQ
|
= | None | ||||
Rule | JCaT
|
= | None | ||||
Rule | Jserca
|
= | None | ||||
Rule | Jpmca
|
= | None | ||||
Rule | Jncx
|
= | None | ||||
Rule | L
|
= | None | ||||
Rule | t
|
= | None |