XPP model

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

#
# This is the one-cell model with dynamic ion concentrations used in
#
# E. Barreto and J.R. Cressman, "Ion Concentration Dynamics as a Mechanism for Neuronal Bursting",
# Journal of Biological Physics 37, 361-373 (2011).
#
# Link to the paper: http://www.springerlink.com/content/v52215p195159211/
# Author-generated version available at: http://arxiv.org/abs/1012.3124
#
# The variables are:
#	V=y[1]=V, the membrane voltage
#	n=y[2]=n, gating variable
#	h=y[3]=h, gating variable
#	Ko=y[4]=[K]_o, the extracellular potassium concentration
#	Nai=y[5]=[Na]_i, the intracellular sodium concentration
#
# The parameters of interest are
#	rho = strength of pumps
#	epsilon = diffusion constant for potassium diffusion from the extracellular space to the bath
# 	kbath = bath potassium concentration
#	glia = strength of glia
#	beta = ratio of intra- to extra-cellular volume
#
# The remaining parameter is
#	gamma = unit conversion factor

par rho=1.25, epsilon=1.333333333, kbath=4.0, glia=66.666666666, beta=7.0
par gamma=0.044494542, tau=1000
par E_cl=-81.93864549, E_ca=120.0
par Cm=1.0, g_na=100.0, g_naL=0.0175, g_k=40.0, g_kL=0.05
par g_clL=0.05, g_ca=0.1, phi=3.0, I=0.0

########

alpha_n=0.01*(V+34.0)/(1.0-exp(-0.1*(V+34.0)))
beta_n=0.125*exp(-(V+44.0)/80.0)
alpha_m=0.1*(V+30.0)/(1.0-exp(-0.1*(V+30.0)))
beta_m=4.0*exp(-(V+55.0)/18.0)
alpha_h=0.07*exp(-(V+44.0)/20.0)
beta_h=1.0/(1.0+exp(-0.1*(V+14.0)))

m_inf=alpha_m/(alpha_m+beta_m)
Kin=158.0-Nai
Naout=144.0-beta*(Nai-18.0)
E_k=26.64*log((Ko/Kin))
E_na=26.64*log((Naout/Nai))
Ina=g_na*(m_inf*m_inf*m_inf)*h*(V-E_na)+g_naL*(V-E_na)
Ik=g_k*n*n*n*n*(V-E_k)+g_kL*(V-E_k)
Icl=g_clL*(V-E_cl)
Itildepump=(rho/(1.0+exp((25.0-Nai)/3.0)))*(1/(1+exp(5.5-Ko)))
Itildeglia=(glia/(1.0+exp((18.0-Ko)/2.5)))
Itildediff=epsilon*(Ko-kbath)

# differential equations

V'=(1.0/Cm)*(-Ina-Ik-Icl+I)
n'=phi*(alpha_n*(1-n)-beta_n*n)
h'=phi*(alpha_h*(1-h)-beta_h*h)
Ko'=(1/tau)*(gamma*beta*Ik-2.0*beta*Itildepump-Itildeglia-Itildediff)
Nai'=(1/tau)*(-gamma*Ina-3.0*Itildepump)

####

init V=-50,n=0.08553,h=0.96859,Ko=7.8,Nai=15.5
@ TOTAL=10000,BOUND=10000
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.


Model :

id
name
time
substance
extent
volume
area
length
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 0
mod modulo x y x y x y x 0 y 0 x y x y

Parameters [41] name constant value unit derived unit sbo cvterm
rho rho = 1.25 1.25 None
epsilon epsilon = 1.333333333 1.333333333 None
kbath kbath = 4.0 4.0 None
glia glia = 66.666666666 66.666666666 None
beta beta = 7.0 7.0 None
gamma gamma = 0.044494542 0.044494542 None
tau tau = 1000 1000.0 None
e_cl e_cl = -81.93864549 -81.93864549 None
e_ca e_ca = 120.0 120.0 None
cm cm = 1.0 1.0 None
g_na g_na = 100.0 100.0 None
g_nal g_nal = 0.0175 0.0175 None
g_k g_k = 40.0 40.0 None
g_kl g_kl = 0.05 0.05 None
g_cll g_cll = 0.05 0.05 None
g_ca g_ca = 0.1 0.1 None
phi phi = 3.0 3.0 None
i i = 0.0 0.0 None
v v = -50 -50.0 None
n n = 0.08553 0.08553 None
h h = 0.96859 0.96859 None
ko ko = 7.8 7.8 None
nai nai = 15.5 15.5 None
alpha_n 0.0 dimensionless None
beta_n 0.0 dimensionless None
alpha_m 0.0 dimensionless None
beta_m 0.0 dimensionless None
alpha_h 0.0 dimensionless None
beta_h 0.0 dimensionless None
m_inf 0.0 dimensionless None
kin 0.0 dimensionless None
naout 0.0 dimensionless None
e_k 0.0 dimensionless None
e_na 0.0 dimensionless None
ina 0.0 dimensionless None
ik 0.0 dimensionless None
icl 0.0 dimensionless None
itildepump 0.0 dimensionless None
itildeglia 0.0 dimensionless None
itildediff 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [23]   assignment name derived units sbo cvterm
d v/dt = 1 cm ina ik icl i None
d n/dt = phi alpha_n 1 n beta_n n None
d h/dt = phi alpha_h 1 h beta_h h None
d ko/dt = 1 tau gamma beta ik 2 beta itildepump itildeglia itildediff None
d nai/dt = 1 tau gamma ina 3 itildepump None
alpha_n = 0.01 v 34 1 0.1 v 34 None
beta_n = 0.125 v 44 80 None
alpha_m = 0.1 v 30 1 0.1 v 30 None
beta_m = 4 v 55 18 None
alpha_h = 0.07 v 44 20 None
beta_h = 1 1 0.1 v 14 None
m_inf = alpha_m alpha_m beta_m None
kin = 158 nai None
naout = 144 beta nai 18 None
e_k = 26.64 10 ko kin None
e_na = 26.64 10 naout nai None
ina = g_na m_inf m_inf m_inf h v e_na g_nal v e_na None
ik = g_k n n n n v e_k g_kl v e_k None
icl = g_cll v e_cl None
itildepump = rho 1 25 nai 3 1 1 5.5 ko None
itildeglia = glia 1 18 ko 2.5 None
itildediff = epsilon ko kbath None
t = time None