XPP model
This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6
.
###########################################################
# simulation code for Fig. 3; #
# with "g_cl=0" (in line 135) also Fig. 4 can be produced #
###########################################################
# t: time in [msec] #
# v: membrane potential in [mV] #
# n,h: gating variables in [1] #
# n_ki: amount of potassium in the ICS in [fmol] #
# n_cli: amount of chloride in the ICS in [fmol] #
# vli: ICS volume in [um^3] #
######################################################
##################################################
# rate equations used by solver #
# factor 1000. converts from [x/msec] to [x/sec] #
##################################################
v' = 1000. * V_DOT
n' = 1000. * N_DOT
h' = 1000. * H_DOT
n_ki' = 1000. * N_KI_DOT
n_cli' = 1000. * N_CLI_DOT
vli' = 1000. * VLI_DOT
############################################
# initial conditions: normal resting state #
############################################
init v=-67.
init n=0.070
init h=0.978
init n_ki=277.7
init n_cli=21.7
init vli=2160.
######################################################
# maximal pump rate drops from 6.8 to 0 after 50 sec #
# unit: [umA/cm^2] #
######################################################
max_p = 6.8 * heav(50.-t)
#######################################
# parameter to between volume models: #
# s=0 -> derived volume model #
# s=1 -> exponential volume model #
#######################################
par s=0
########################################
# Hodgkin-Huxley like gating functions #
# adiabatic value for "M" #
########################################
AN = 0.01 * (v + 34.0) / (1.0 - exp(-0.1 * (v + 34.0)))
BN = 0.125 * exp(-(v + 44.0) / 80.0)
AM = 0.1 * (v + 30.0) / (1.0 - exp(-0.1 * (v + 30.0)))
BM = 4.0 * exp(-(v + 55.0) / 18.0)
AH = 0.07 * exp(-(v + 44.0) / 20)
BH = 1.0 / (1.0 + exp(-0.1 * (v + 14.0)))
M = AM / (AM + BM)
#####################################################################
# - resting state ion and impermeant particle amounts in [fmol] #
# in the ICS (...i0) and the ECS (...e0) #
# - "k,na,cl,imp" means potassium, sodium, chloride and impermeant #
#####################################################################
n_ki0 = 277.7
n_ke0 = 2.8
n_nai0 = 54.6
n_nae0 = 91.3
n_cli0 = 21.7
n_cle0 = 89.8
n_impi = 318.0
n_impe = 40
############################################################################
# electroneutrality (first line) and mass conservation (second to fourth) #
# conditions to compute ion amounts other than intracellular potassium and #
# chloride #
############################################################################
n_nai = n_nai0 + n_ki0 - n_ki - n_cli0 + n_cli
n_nae = n_nae0 + n_nai0 - n_nai
n_ke = n_ke0 + n_ki0 - n_ki
n_cle = n_cle0 + n_cli0 - n_cli
########################################################################
# ECS volume "vle" follows from conservation of total volume "vl_tot" #
# units: [um^3] #
########################################################################
vl_tot = 2880.
vle = vl_tot - vli
########################################
# ion concentrations in [mM]=[mMol/l] #
########################################
nai = n_nai / vli * 1000.
nae = n_nae / vle * 1000.
ki = n_ki / vli * 1000.
ke = n_ke / vle * 1000.
cli = n_cli / vli * 1000.
cle = n_cle / vle * 1000.
##################################################
# choice between two volume models: #
# vli_inf0: equil. volume in derived model #
# vli_inf1: equil. volume in exponential model #
######################################################
# n_i/e: total amount of particles in ICS/ECS #
# p_i/e: total concentration of particles in ICS/ECS #
######################################################
n_i = n_nai + n_ki + n_cli + n_impi
n_e = n_nae + n_ke + n_cle + n_impe
vli_inf0 = vl_tot * n_i / (n_i + n_e)
vli0 = 2160.
p_i = n_i / vli * 1000.
p_e = n_e / vle * 1000.
vli_inf1 = vli0 * (1.35 - 0.35*exp((p_e-p_i)/20.))
vli_inf = (1-s) * vli_inf0 + s * vli_inf1
#####################
# Nernst potentials #
#####################
EK = 26.64 * log(ke / ki)
ENA = 26.64 * log(nae / nai)
ECL =-26.64 * log(cle / cli)
##############################################################################
# - different leak and gated currents "IION_l/g" in [umA/cm^2] #
# - leak and gated conductances for each channel "gion_l/g" in [mS/cm^2] #
# - Na/K-exchange pump current "IP" with maximal turnover rate "max_p" #
##############################################################################
gna_l = 0.0175
gna_g = 100.
gk_l = 0.05
gk_g = 40.
par gcl_l=0.05
INA_l = gna_l * (v - ENA)
INA_g = gna_g * M**3 * h * (v - ENA)
IK_l = gk_l * (v - EK)
IK_g = gk_g * n**4 * (v - EK)
ICL_l = gcl_l * (v - ECL)
IP = max_p / (1.0 + exp((25 - nai)/3.)) / (1. + exp(5.5 - ke))
#####################################
# full sodium and potassium current #
#####################################
INA = INA_l + INA_g + 3. * IP
IK = IK_l + IK_g - 2. * IP
#############################
# list of all changes rates #
#####################################################################
# c: membrane capacitance in [uF/cm^2] #
# conv: conversion from currents to fluxes in [fmol/msec*cm^2/uA] #
# phi: gating timescale parameter in [1/msec] #
# t_vl: timescale of volume dynamics in [msec] #
#####################################################################
c = 1
conv = 9.55589e-5
phi = 3
t_vl = 250
V_DOT = -1. / c * (INA + IK + ICL_l)
N_DOT = phi * (AN * (1 - n) - BN * n)
H_DOT = phi * (AH * (1 - h) - BH * h)
N_KI_DOT = -conv * IK
N_CLI_DOT = conv * ICL_l
VLI_DOT = 1. / t_vl * (vli_inf - vli)
####################################
# auxiliary variables for plotting #
####################################
aux _ki = ki
aux _ke = ke
aux _nai = nai
aux _nae = nae
aux _cli = cli
aux _cle = cle
aux _EK = EK
aux _ENA = ENA
aux _ECL = ECL
aux _vli = vli
aux _vle = vle
############
# numerics #
############
@ meth=cvode
@ dt=5e-4
@ maxstor=10000000, bounds=10000000
@ total=1000
@ bell=0
#############################################
# plot options corresponding to Fig. 3a/b/c #
#############################################
@ xhi=1000
@ nplot=4, yp1=v, yp2=_EK, yp3=_ENA, yp4=_ECL, ylo=-150, yhi=160
#@ nplot=2, yp1=_vli, yp2=_vle, ylo=0, yhi=2900
#@ nplot=6, yp1=_ki, yp2=_ke, yp3=_cli, yp4=_cle, yp5=_nai, yp6=_nae, ylo=0, yhi=150
done
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:
Redistributions of this SBML file must retain the above copyright notice, this list of conditions
and the following disclaimer.
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
L3V1
type
FunctionDefinitions [4]
name
math
sbo
cvterm
FunctionDefinition
max
minimum
x
y
x
x
y
y
FunctionDefinition
min
maximum
x
y
x
x
y
y
FunctionDefinition
heav
heavyside
x
0
x
0
0.5
x
0
1
x
0
0
FunctionDefinition
mod
modulo
x
y
x
y
x
y
x
0
y
0
x
y
x
y
type
Parameters [81]
name
constant
value
unit
derived unit
sbo
cvterm
Parameter
v
v = -67.
F
-67.0
None
Parameter
n
n = 0.070
F
0.07
None
Parameter
h
h = 0.978
F
0.978
None
Parameter
n_ki
n_ki = 277.7
F
277.7
None
Parameter
n_cli
n_cli = 21.7
F
21.7
None
Parameter
vli
vli = 2160.
F
2160.0
None
Parameter
s
s = 0
F
0.0
None
Parameter
gcl_l
gcl_l = 0.05
F
0.05
None
Parameter
max_p
F
0.0
dimensionless
None
Parameter
an
F
0.0
dimensionless
None
Parameter
bn
F
0.0
dimensionless
None
Parameter
am
F
0.0
dimensionless
None
Parameter
bm
F
0.0
dimensionless
None
Parameter
ah
F
0.0
dimensionless
None
Parameter
bh
F
0.0
dimensionless
None
Parameter
m
F
0.0
dimensionless
None
Parameter
n_ki0
F
0.0
dimensionless
None
Parameter
n_ke0
F
0.0
dimensionless
None
Parameter
n_nai0
F
0.0
dimensionless
None
Parameter
n_nae0
F
0.0
dimensionless
None
Parameter
n_cli0
F
0.0
dimensionless
None
Parameter
n_cle0
F
0.0
dimensionless
None
Parameter
n_impi
F
0.0
dimensionless
None
Parameter
n_impe
F
0.0
dimensionless
None
Parameter
n_nai
F
0.0
dimensionless
None
Parameter
n_nae
F
0.0
dimensionless
None
Parameter
n_ke
F
0.0
dimensionless
None
Parameter
n_cle
F
0.0
dimensionless
None
Parameter
vl_tot
F
0.0
dimensionless
None
Parameter
vle
F
0.0
dimensionless
None
Parameter
nai
F
0.0
dimensionless
None
Parameter
nae
F
0.0
dimensionless
None
Parameter
ki
F
0.0
dimensionless
None
Parameter
ke
F
0.0
dimensionless
None
Parameter
cli
F
0.0
dimensionless
None
Parameter
cle
F
0.0
dimensionless
None
Parameter
n_i
F
0.0
dimensionless
None
Parameter
n_e
F
0.0
dimensionless
None
Parameter
vli_inf0
F
0.0
dimensionless
None
Parameter
vli0
F
0.0
dimensionless
None
Parameter
p_i
F
0.0
dimensionless
None
Parameter
p_e
F
0.0
dimensionless
None
Parameter
vli_inf1
F
0.0
dimensionless
None
Parameter
vli_inf
F
0.0
dimensionless
None
Parameter
ek
F
0.0
dimensionless
None
Parameter
ena
F
0.0
dimensionless
None
Parameter
ecl
F
0.0
dimensionless
None
Parameter
gna_l
F
0.0
dimensionless
None
Parameter
gna_g
F
0.0
dimensionless
None
Parameter
gk_l
F
0.0
dimensionless
None
Parameter
gk_g
F
0.0
dimensionless
None
Parameter
ina_l
F
0.0
dimensionless
None
Parameter
ina_g
F
0.0
dimensionless
None
Parameter
ik_l
F
0.0
dimensionless
None
Parameter
ik_g
F
0.0
dimensionless
None
Parameter
icl_l
F
0.0
dimensionless
None
Parameter
ip
F
0.0
dimensionless
None
Parameter
ina
F
0.0
dimensionless
None
Parameter
ik
F
0.0
dimensionless
None
Parameter
c
F
0.0
dimensionless
None
Parameter
conv
F
0.0
dimensionless
None
Parameter
phi
F
0.0
dimensionless
None
Parameter
t_vl
F
0.0
dimensionless
None
Parameter
v_dot
F
0.0
dimensionless
None
Parameter
n_dot
F
0.0
dimensionless
None
Parameter
h_dot
F
0.0
dimensionless
None
Parameter
n_ki_dot
F
0.0
dimensionless
None
Parameter
n_cli_dot
F
0.0
dimensionless
None
Parameter
vli_dot
F
0.0
dimensionless
None
Parameter
_ki
F
0.0
dimensionless
None
Parameter
_ke
F
0.0
dimensionless
None
Parameter
_nai
F
0.0
dimensionless
None
Parameter
_nae
F
0.0
dimensionless
None
Parameter
_cli
F
0.0
dimensionless
None
Parameter
_cle
F
0.0
dimensionless
None
Parameter
_ek
F
0.0
dimensionless
None
Parameter
_ena
F
0.0
dimensionless
None
Parameter
_ecl
F
0.0
dimensionless
None
Parameter
_vli
F
0.0
dimensionless
None
Parameter
_vle
F
0.0
dimensionless
None
Parameter
t
model time
F
0.0
dimensionless
None
type
Rules [79]
assignment
name
derived units
sbo
cvterm
Rule
d v/dt
=
1000
v_dot
None
Rule
d n/dt
=
1000
n_dot
None
Rule
d h/dt
=
1000
h_dot
None
Rule
d n_ki/dt
=
1000
n_ki_dot
None
Rule
d n_cli/dt
=
1000
n_cli_dot
None
Rule
d vli/dt
=
1000
vli_dot
None
Rule
max_p
=
6.8
heav
50
t
None
Rule
an
=
0.01
v
34
1
0.1
v
34
None
Rule
bn
=
0.125
v
44
80
None
Rule
am
=
0.1
v
30
1
0.1
v
30
None
Rule
bm
=
4
v
55
18
None
Rule
ah
=
0.07
v
44
20
None
Rule
bh
=
1
1
0.1
v
14
None
Rule
m
=
am
am
bm
None
Rule
n_ki0
=
277.7
None
Rule
n_ke0
=
2.8
None
Rule
n_nai0
=
54.6
None
Rule
n_nae0
=
91.3
None
Rule
n_cli0
=
21.7
None
Rule
n_cle0
=
89.8
None
Rule
n_impi
=
318
None
Rule
n_impe
=
40
None
Rule
n_nai
=
n_nai0
n_ki0
n_ki
n_cli0
n_cli
None
Rule
n_nae
=
n_nae0
n_nai0
n_nai
None
Rule
n_ke
=
n_ke0
n_ki0
n_ki
None
Rule
n_cle
=
n_cle0
n_cli0
n_cli
None
Rule
vl_tot
=
2880
None
Rule
vle
=
vl_tot
vli
None
Rule
nai
=
n_nai
vli
1000
None
Rule
nae
=
n_nae
vle
1000
None
Rule
ki
=
n_ki
vli
1000
None
Rule
ke
=
n_ke
vle
1000
None
Rule
cli
=
n_cli
vli
1000
None
Rule
cle
=
n_cle
vle
1000
None
Rule
n_i
=
n_nai
n_ki
n_cli
n_impi
None
Rule
n_e
=
n_nae
n_ke
n_cle
n_impe
None
Rule
vli_inf0
=
vl_tot
n_i
n_i
n_e
None
Rule
vli0
=
2160
None
Rule
p_i
=
n_i
vli
1000
None
Rule
p_e
=
n_e
vle
1000
None
Rule
vli_inf1
=
vli0
1.35
0.35
p_e
p_i
20
None
Rule
vli_inf
=
1
s
vli_inf0
s
vli_inf1
None
Rule
ek
=
26.64
10
ke
ki
None
Rule
ena
=
26.64
10
nae
nai
None
Rule
ecl
=
26.64
10
cle
cli
None
Rule
gna_l
=
0.0175
None
Rule
gna_g
=
100
None
Rule
gk_l
=
0.05
None
Rule
gk_g
=
40
None
Rule
ina_l
=
gna_l
v
ena
None
Rule
ina_g
=
gna_g
m
3
h
v
ena
None
Rule
ik_l
=
gk_l
v
ek
None
Rule
ik_g
=
gk_g
n
4
v
ek
None
Rule
icl_l
=
gcl_l
v
ecl
None
Rule
ip
=
max_p
1
25
nai
3
1
5.5
ke
None
Rule
ina
=
ina_l
ina_g
3
ip
None
Rule
ik
=
ik_l
ik_g
2
ip
None
Rule
c
=
1
None
Rule
conv
=
9.55589 -5
None
Rule
phi
=
3
None
Rule
t_vl
=
250
None
Rule
v_dot
=
1
c
ina
ik
icl_l
None
Rule
n_dot
=
phi
an
1
n
bn
n
None
Rule
h_dot
=
phi
ah
1
h
bh
h
None
Rule
n_ki_dot
=
conv
ik
None
Rule
n_cli_dot
=
conv
icl_l
None
Rule
vli_dot
=
1
t_vl
vli_inf
vli
None
Rule
_ki
=
ki
None
Rule
_ke
=
ke
None
Rule
_nai
=
nai
None
Rule
_nae
=
nae
None
Rule
_cli
=
cli
None
Rule
_cle
=
cle
None
Rule
_ek
=
ek
None
Rule
_ena
=
ena
None
Rule
_ecl
=
ecl
None
Rule
_vli
=
vli
None
Rule
_vle
=
vle
None
Rule
t
=
time
None