XPP model

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

# Traveling waves equations for model CA1 pyramidal cell apical dendrite
# For simulation in XPPAUT (Bard Ermentrout)
# Download: http://www.pitt.edu/~phase/
# Get the book too: Ermentrout B. Simulating, analyzing, and animating dynamical systems: SIAM, 2002.

# Corey Acker
# Boston University
# July 16, 2004

# Membrane equations from Migliore et al. (1999) J Comput Neurosci 7: 5-15

# Model parameters, including shooting parameter K
param Cm=2.0,Ra=150
param VNa=55.0,VK=-90,VL=-65
param GNa=32,GKDR=10,GL=0.2,b=0.5
param d_tau=0.1
param d_inf=0.1
param GKA=48
param diam=1.8
param Iapp=0.925
param K=4  # bad initial guess
# param K=5.010975  # actual value to be found by shooting method

# Wave Speed
aux c = sqrt((K*diam*10)/(4*Ra*Cm))

# Initial conditions
init V=-68.1,Vdot=0,m=0.016,h=0.99,i=0.95,nKDR=0.0002,n=0.0005,l=0.8

# Dynamic equations
V'=Vdot
Vdot'=K*(Vdot+(fion(V)-Iapp)/Cm)
m'=1/taum(V)*(minf(V)-m)
h'=1/tauh(V)*(hinf(V)-h)
i'=1/taui(V)*(iinf(V)-i)
nKDR'=1/taunKDR(V)*(nKDRinf(V)-nKDR)
n'=1/taun(V)*(ninf(V)-n)
l'=1/taul(V)*(linf(V)-l)

# All other equations
fion(V)=INa(V)+IKDR(V)+IKA(V)+IL(V)
INa(V)=GNa*m^3*h*i*(V-VNa)
IKDR(V)=GKDR*nKDR*(V-VK)
IKA(V)=GKA*n*l*(V-VK)
IL(V)=GL*(V-VL)

# Rate equations
# Sodium activation, m
minf(V)=alm(V)/(alm(V)+bem(V))
taum1(V)=0.5/(alm(V)+bem(V))
taum(V)=if(taum1(V)<0.02)then(0.02)else(taum1(V))
alm(V)=0.4*(V+30)/(1-exp(-(V+30)/7.2))
bem(V)=0.124*(V+30)/(exp((V+30)/7.2)-1)

# Sodium inactivation, h
hinf(V)=1/(1+exp((V+50)/4))
tauh1(V)=0.5/(alh(V)+beh(V))
tauh(V)=if(tauh1(V)<0.5)then(0.5)else(tauh1(V))
alh(V)=0.03*(V+45)/(1-exp(-(V+45)/1.5))
beh(V)=0.01*(V+45)/(exp((V+45)/1.5)-1)

# Slow Inactivation of INa, i
iinf(V)=(1+b*exp((V+58)/2))/(1+exp((V+58)/2))
taui1(V)=3e4*bei(V)/(1+ali(V))
taui(V)=if(taui1(V)<10)then(10)else(taui1(V))
ali(V)=exp(0.45*(V+60))
bei(V)=exp(0.09*(V+60))

# Activation of IKDR
nKDRinf(V)=1/(1+alnKDR(V))
taunKDR1(V)=50*benKDR(V)/(1+alnKDR(V))
taunKDR(V)=if(taunKDR1(V)<2)then(2)else(taunKDR1(V))
alnKDR(V)=exp(-0.11*(V-13))
benKDR(V)=exp(-0.08*(V-13))

# Equations for proximal version of IA activation
ninfprox(V)=1/(1+alnprox(V))
taunprox1(V)=4*benprox(V)/(1+alnprox(V))
taunprox(V)=if(taunprox1(V)<0.1)then(0.1)else(taunprox1(V))
alnprox(V)=exp(-0.038*(1.5+1/(1+exp(V+40)/5))*(V-11))
benprox(V)=exp(-0.038*(0.825+1/(1+exp(V+40)/5))*(V-11))

# Equations for distal version of IA activation
ninfdist(V)=1/(1+alndist(V))
taundist1(V)=2*bendist(V)/(1+alndist(V))
taundist(V)=if(taundist1(V)<0.1)then(0.1)else(taundist1(V))
alndist(V)=exp(-0.038*(1.8+1/(1+exp(V+40)/5))*(V+1))
bendist(V)=exp(-0.038*(0.7+1/(1+exp(V+40)/5))*(V+1))

# Weighted averaging of IA equations
taun(V)=d_tau*taunprox(V)+(1-d_tau)*taundist(V)
ninf(V)=d_inf*ninfprox(V)+(1-d_inf)*ninfdist(V)

# IA inactivation, l
linf(V)=1/(1+all(V))
taul1(V)=0.26*(V+50)
taul(V)=if(taul1(V)<2)then(2)else(taul1(V))
all(V)=exp(0.11*(V+56))

# Setup XPP's numerics, and plotting
@ xp=V,yp=vdot,xlo=-90,xhi=30,ylo=-1000,yhi=300
@ dt=0.01,total=20
@ method=cvode,tol=1e-6,atoler=1e-5,bounds=1e4
@ jac_eps=1e-5,newt_tol=1e-5,newt_iter=10000
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.


Model :

id
name
time
substance
extent
volume
area
length
Access SBML model  L3V1

FunctionDefinitions [45] 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
fion v gka gkdr gl gna h i l m n nkdr vk vl vna ina v i h vna m gna ikdr v nkdr vk gkdr ika v n vk gka l il v gl vl
ina v gna h i m vna gna m 3 h i v vna
ikdr v gkdr nkdr vk gkdr nkdr v vk
ika v gka l n vk gka n l v vk
il v gl vl gl v vl
minf v alm v alm v bem v
taum1 v 0.5 alm v bem v
taum v 0.02 taum1 v 0.02 taum1 v
alm v 0.4 v 30 1 v 30 7.2
bem v 0.124 v 30 v 30 7.2 1
hinf v 1 1 v 50 4
tauh1 v 0.5 alh v beh v
tauh v 0.5 tauh1 v 0.5 tauh1 v
alh v 0.03 v 45 1 v 45 1.5
beh v 0.01 v 45 v 45 1.5 1
iinf v b 1 b v 58 2 1 v 58 2
taui1 v 3 4 bei v 1 ali v
taui v 10 taui1 v 10 taui1 v
ali v 0.45 v 60
bei v 0.09 v 60
nkdrinf v 1 1 alnkdr v
taunkdr1 v 50 benkdr v 1 alnkdr v
taunkdr v 2 taunkdr1 v 2 taunkdr1 v
alnkdr v 0.11 v 13
benkdr v 0.08 v 13
ninfprox v 1 1 alnprox v
taunprox1 v 4 benprox v 1 alnprox v
taunprox v 0.1 taunprox1 v 0.1 taunprox1 v
alnprox v 0.038 1.5 1 1 v 40 5 v 11
benprox v 0.038 0.825 1 1 v 40 5 v 11
ninfdist v 1 1 alndist v
taundist1 v 2 bendist v 1 alndist v
taundist v 0.1 taundist1 v 0.1 taundist1 v
alndist v 0.038 1.8 1 1 v 40 5 v 1
bendist v 0.038 0.7 1 1 v 40 5 v 1
taun v d_tau d_tau taunprox v 1 d_tau taundist v
ninf v d_inf d_inf ninfprox v 1 d_inf ninfdist v
linf v 1 1 all v
taul1 v 0.26 v 50
taul v 2 taul1 v 2 taul1 v
all v 0.11 v 56

Parameters [25] name constant value unit derived unit sbo cvterm
cm cm = 2.0 2.0 None
ra ra = 150 150.0 None
vna vna = 55.0 55.0 None
vk vk = -90 -90.0 None
vl vl = -65 -65.0 None
gna gna = 32 32.0 None
gkdr gkdr = 10 10.0 None
gl gl = 0.2 0.2 None
b b = 0.5 0.5 None
d_tau d_tau = 0.1 0.1 None
d_inf d_inf = 0.1 0.1 None
gka gka = 48 48.0 None
diam diam = 1.8 1.8 None
iapp iapp = 0.925 0.925 None
k k 0.0 None
v v = -68.1 -68.1 None
vdot vdot = 0 0.0 None
m m = 0.016 0.016 None
h h = 0.99 0.99 None
i i = 0.95 0.95 None
nkdr nkdr = 0.0002 0.0002 None
n n = 0.0005 0.0005 None
l l = 0.8 0.8 None
c 0.0 dimensionless None
t model time 0.0 dimensionless None

InitialAssignments [1] name assignment derived units sbo cvterm
k = None None

Rules [10]   assignment name derived units sbo cvterm
d v/dt = vdot None
d vdot/dt = k vdot fion v gka gkdr gl gna h i l m n nkdr vk vl vna iapp cm None
d m/dt = 1 taum v minf v m None
d h/dt = 1 tauh v hinf v h None
d i/dt = 1 taui v iinf v b i None
d nkdr/dt = 1 taunkdr v nkdrinf v nkdr None
d n/dt = 1 taun v d_tau ninf v d_inf n None
d l/dt = 1 taul v linf v l None
c = 2 k diam 10 4 ra cm None
t = time None