XPP model
This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6
.
###################################################################################################################################
# Rate equations for AD model used in "Large Extracellular Space Leads to [...] Ischemic Injury [...]" by Hubel, Ullah and Andrew #
###################################################################################################################################
# membrane potential 'V' in [mV] #
# gating variables 'n/h' in [1] #
# intracellular ion concentrations 'ki,cli' in [mM=mMol/l] #
# amount of potassium exchanged with external reservoir 'dnk' in [fmol] #
# rates of change 'X_DOT' in [.../msec] #
# (factor 1000. converts to seconds) #
####################################################################################
V' = 1000. * V_DOT
n' = 1000. * N_DOT
h' = 1000. * H_DOT
ki' = 1000. * KI_DOT
cli' = 1000. * CLI_DOT
dnk' = 1000. * DNK_DOT
####################################
# Physiological initial conditions #
####################################
init v=-67.056664
init n=0.070174225
init h=0.97820824
init ki=128.56937
init cli=10.061391
init dnk=0
########################################
# Extracellular volume 'vle' in [um^3] #
########################################
#par vle=720
par vle=3700
###############################################################################################################
# Interruption of pumping and diffusive vascular potassium regulation after 50sec and for 'delta_pmp/dif' sec #
###############################################################################################################
par delta_pmp=200
par delta_dif=200
max_p = (heav(50-t) + heav(t-50-delta_pmp)) * 6.8
lambda = (heav(50-t) + heav(t-50-delta_dif)) * 3.0e-5
###################################
# Hodgkin-Huxley gating functions #
###################################
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)
#####################################
# ion concentrations in [mM=mMol/l] #
#####################################################################
# intracellular sodium 'NAI' from electroneutrality #
# extracellular concentrations 'NAE,KE,CLE' from mass conservation #
# normal resting values 'ki0,ke0 ...' given #
#####################################################################
vli = 2160
ki0 = 128.56935
ke0 = 3.9962559
nai0 = 25.279156
nae0 = 126.84917
cli0 = 10.055541
cle0 = 124.71021
NAI = nai0 + ki0 - ki - cli0 + cli
NAE = nae0 + (nai0 - nai) * vli/vle
KE = ke0 + (ki0 - ki ) * vli/vle + dnk/vle * 1e3
CLE = cle0 + (cli0 - cli) * vli/vle
#############################
# Nernst potentials in [mV] #
#############################
EK = 26.64 * log(ke / ki)
ENA = 26.64 * log(nae / nai)
ECL =-26.64 * log(cle / cli)
############################################################################
# different types of 'l'eak and 'g'ated currents 'I(ION)_l/g' in [uA/cm^2] #
# different channel conductances 'g(ion)_l/g' in [mS/cm^2] #
# Na/K-exchange pump current 'IP' in [uA/cm^2] #
############################################################################
gna_l = 0.0175
gna_g = 100.
gk_l = 0.05
gk_g = 40.
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))
INA = INA_l + INA_g + 3. * IP
IK = IK_l + IK_g - 2. * IP
#######################################################################################
# Vascular potassium regulation as diffusive coupling to extracellular bath reservoir #
#######################################################################################
# baseline potassium concentration 'k_bth' in [mM] #
# coupling strength 'lambda' in [mM/msec] #
# factor 1e-3 to convert diffusive flux 'J_diff' to [fMol/msec] #
###################################################################
k_bth = 4
J_diff = lambda * vle * (k_bth - ke) * 1e-3
#############################
# Full list of change rates #
##########################################################
# membrane capacitance 'C' in [uF/cm^2] #
# conversion factor 'conv' in [XXX] #
# conventional time scale parameter 'phi' in [1/msec] #
##########################################################
c = 1
conv = 9.55589e-2
phi = 3
V_DOT = -1. / c * (INA + IK + ICL_l)
N_DOT = phi * (AN * (1 - n) - BN * n)
H_DOT = phi * (AH * (1 - h) - BH * h)
KI_DOT = -CONV/vli * IK
CLI_DOT = CONV/vli * ICL_l
DNK_DOT = J_diff
####################################################
# auxiliary variables for data output and 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 _MAX_P = max_p
########################
# Numerical parameters #
########################
@ meth=stiff
@ dt=5e-4
@ maxstor=10000000, bounds=10000000
@ total=1000
@ bell=0
#################
# Plot settings #
###########################################################
# '_MAX_P' as a guide to the eye to see pump interruption #
###########################################################
@ xhi=1000
@ nplot=4, yp1=v, yp2=_EK, yp3=_ENA, yp4=_MAX_P, ylo=-150, yhi=160
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 [67]
name
constant
value
unit
derived unit
sbo
cvterm
Parameter
v
v = -67.056664
F
-67.056664
None
Parameter
n
n = 0.070174225
F
0.070174225
None
Parameter
h
h = 0.97820824
F
0.97820824
None
Parameter
ki
ki = 128.56937
F
128.56937
None
Parameter
cli
cli = 10.061391
F
10.061391
None
Parameter
dnk
dnk = 0
F
0.0
None
Parameter
vle
vle = 3700
F
3700.0
None
Parameter
delta_pmp
delta_pmp = 200
F
200.0
None
Parameter
delta_dif
delta_dif = 200
F
200.0
None
Parameter
max_p
F
0.0
dimensionless
None
Parameter
lambda
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
vli
F
0.0
dimensionless
None
Parameter
ki0
F
0.0
dimensionless
None
Parameter
ke0
F
0.0
dimensionless
None
Parameter
nai0
F
0.0
dimensionless
None
Parameter
nae0
F
0.0
dimensionless
None
Parameter
cli0
F
0.0
dimensionless
None
Parameter
cle0
F
0.0
dimensionless
None
Parameter
nai
F
0.0
dimensionless
None
Parameter
nae
F
0.0
dimensionless
None
Parameter
ke
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
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
gcl_l
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
k_bth
F
0.0
dimensionless
None
Parameter
j_diff
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
v_dot
F
0.0
dimensionless
None
Parameter
n_dot
F
0.0
dimensionless
None
Parameter
h_dot
F
0.0
dimensionless
None
Parameter
ki_dot
F
0.0
dimensionless
None
Parameter
cli_dot
F
0.0
dimensionless
None
Parameter
dnk_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
_max_p
F
0.0
dimensionless
None
Parameter
t
model time
F
0.0
dimensionless
None
type
Rules [64]
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 ki/dt
=
1000
ki_dot
None
Rule
d cli/dt
=
1000
cli_dot
None
Rule
d dnk/dt
=
1000
dnk_dot
None
Rule
max_p
=
heav
50
t
heav
t
50
delta_pmp
6.8
None
Rule
lambda
=
heav
50
t
heav
t
50
delta_dif
3 -5
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
vli
=
2160
None
Rule
ki0
=
128.56935
None
Rule
ke0
=
3.9962559
None
Rule
nai0
=
25.279156
None
Rule
nae0
=
126.84917
None
Rule
cli0
=
10.055541
None
Rule
cle0
=
124.71021
None
Rule
nai
=
nai0
ki0
ki
cli0
cli
None
Rule
nae
=
nae0
nai0
nai
vli
vle
None
Rule
ke
=
ke0
ki0
ki
vli
vle
dnk
vle
1 3
None
Rule
cle
=
cle0
cli0
cli
vli
vle
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
gcl_l
=
0.05
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
k_bth
=
4
None
Rule
j_diff
=
lambda
vle
k_bth
ke
1 -3
None
Rule
c
=
1
None
Rule
conv
=
9.55589 -2
None
Rule
phi
=
3
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
ki_dot
=
conv
vli
ik
None
Rule
cli_dot
=
conv
vli
icl_l
None
Rule
dnk_dot
=
j_diff
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
_max_p
=
max_p
None
Rule
t
=
time
None