XPP model
This model was converted from XPP ode format to SBML using sbmlutils-0.1.5a6
.
# Komendantov A.0 and Kononenko N.I.
# Determenistic chaos in mathematical model of pacemaker activity in bursting neuron, Helix pomatia.
# J. theor. Biol: 183, 219-230, 1996
#################################### Control parameters ############################################
# Example 1. Chaotic activity
#p gB=0.1372
#p gNa=0.0231, gNaV=0.11, gCa=1.5, gCaCa=0.02, Iapp=0.0
# Example 2. Spiking (beating) activity
#p gB=0.11
# Example 3. Period-two spiking activity
# gB=0.124
# Example 4. Period-four spiking activity
# gB=0.130
# Example 5. Bursting activity
# p gB=0.1650
###################################################################################################
# Example 6. Mode transition from chaotic activity into bursting one evoked by short depolarization)
p gNa=0.0231,gNaV=0.11,gB=0.1372,gCa=1.5,gCaCa=0.02,Iapp=-0.5
# Example 7. Chaotic bursting mode
#p gNa=0.02, gNaV=0.13, gB=0.18, gCa=1.0, gCaCa=0.01, Iapp=0.0
############################# Fixed parameter #######################################################
number Cm=0.02,R=0.1,F=96485
p gK=0.25,gNaTTX=400.0,gKTEA=10.0
p VNa=40.0,VK=-70.0,VB=-58.0,VCa=150.0
p ks=50.0,rho=0.002,kbeta=15000,beta=0.00004
########################### Equations
vol=4/3*pi*R*R*R
Iappx=if((t>=70.0)&(t<=72.0))then(Iapp)else(0.0)
########################### Currents ####################################
INaV=gNaV*(1/(1+exp(-0.2*(V+45))))*(V-VNa)
IK=gK*(V-Vk)
INa=gNa*(V-VNa)
IB=gB*mB*hB*(V-VB)
INaTTX=gNaTTX*m*m*m*h*(V-VNa)
IKTEA=gKTEA *n*n*n*n*(V-VK)
ICa=gCa*mCa*mCa*(V-VCa)
ICaCa=gCaCa*(1/(1+exp(-0.06*(V+45))))*(1/(1+exp(kbeta*(Ca-beta))))*(V-VCa)
########################## Differential equations ####################
V'=-(INaTTX+IKTEA+IK+INa+INaV+IB+ICa+ICaCa+Iappx)/Cm
Ca'=rho*(-ICa/(2*F*vol)-ks*Ca)
mB'=(1/(1+exp(0.4*(V+34)))-mB)/0.05
hB'=(1/(1+exp(-0.55*(V+43)))-hB)/1.5
m'=(1/(1+exp(-0.4*(V+31)))-m)/0.0005
h'=(1/(1+exp(0.25*(V+45)))-h)/0.01
n'=(1/(1+exp(-0.18*(V+25)))-n)/0.015
mCa'=(1/(1+exp(-0.2*V))-mCa)/0.01
####################### Initial conditions ###########################
# initial conditions: Examples 1-6.
V(0)=-42
Ca(0)=6e-05
mB(0)=0.95
hB(0)=0.77
m(0)=0.14
n(0)=0.048
mCa(0)=0.0002
# initial conditions: Example 7, chaotic bursting
#V(0)=-55.56913
#Ca(0)=3.593358e-05
#mB(0)=0.0
#hB(0)=0.0
#m(0)=0.0
#n(0)=0.0
#mCa(0)=0.0
@ MAXSTOR=10000000
@ TOTAL=150.0
@ DT=0.0001
@ XLO=0.0, XHI=150.0, YLO=-65.0, YHI=55.0
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 [39]
name
constant
value
unit
derived unit
sbo
cvterm
Parameter
gna
gna = 0.0231
F
0.0231
None
Parameter
gnav
gnav = 0.11
F
0.11
None
Parameter
gb
gb = 0.1372
F
0.1372
None
Parameter
gca
gca = 1.5
F
1.5
None
Parameter
gcaca
gcaca = 0.02
F
0.02
None
Parameter
iapp
iapp = -0.5
F
-0.5
None
Parameter
cm
cm = 0.02
F
0.02
None
Parameter
r
r = 0.1
F
0.1
None
Parameter
f
f = 96485
F
96485.0
None
Parameter
gk
gk = 0.25
F
0.25
None
Parameter
gnattx
gnattx = 400.0
F
400.0
None
Parameter
gktea
gktea = 10.0
F
10.0
None
Parameter
vna
vna = 40.0
F
40.0
None
Parameter
vk
vk = -70.0
F
-70.0
None
Parameter
vb
vb = -58.0
F
-58.0
None
Parameter
vca
vca = 150.0
F
150.0
None
Parameter
ks
ks = 50.0
F
50.0
None
Parameter
rho
rho = 0.002
F
0.002
None
Parameter
kbeta
kbeta = 15000
F
15000.0
None
Parameter
beta
beta = 0.00004
F
4e-05
None
Parameter
v
v = -42
F
-42.0
None
Parameter
ca
ca = 6e-05
F
6e-05
None
Parameter
mb
mb = 0.95
F
0.95
None
Parameter
hb
hb = 0.77
F
0.77
None
Parameter
m
m = 0.14
F
0.14
None
Parameter
n
n = 0.048
F
0.048
None
Parameter
mca
mca = 0.0002
F
0.0002
None
Parameter
h
F
0.0
dimensionless
None
Parameter
vol
F
0.0
dimensionless
None
Parameter
iappx
F
0.0
dimensionless
None
Parameter
inav
F
0.0
dimensionless
None
Parameter
ik
F
0.0
dimensionless
None
Parameter
ina
F
0.0
dimensionless
None
Parameter
ib
F
0.0
dimensionless
None
Parameter
inattx
F
0.0
dimensionless
None
Parameter
iktea
F
0.0
dimensionless
None
Parameter
ica
F
0.0
dimensionless
None
Parameter
icaca
F
0.0
dimensionless
None
Parameter
t
model time
F
0.0
dimensionless
None
type
Rules [19]
assignment
name
derived units
sbo
cvterm
Rule
d v/dt
=
inattx
iktea
ik
ina
inav
ib
ica
icaca
iappx
cm
None
Rule
d ca/dt
=
rho
ica
2
f
vol
ks
ca
None
Rule
d mb/dt
=
1
1
0.4
v
34
mb
0.05
None
Rule
d hb/dt
=
1
1
0.55
v
43
hb
1.5
None
Rule
d m/dt
=
1
1
0.4
v
31
m
0.0005
None
Rule
d h/dt
=
1
1
0.25
v
45
h
0.01
None
Rule
d n/dt
=
1
1
0.18
v
25
n
0.015
None
Rule
d mca/dt
=
1
1
0.2
v
mca
0.01
None
Rule
vol
=
4
3
r
r
r
None
Rule
iappx
=
None
None
Rule
inav
=
gnav
1
1
0.2
v
45
v
vna
None
Rule
ik
=
gk
v
vk
None
Rule
ina
=
gna
v
vna
None
Rule
ib
=
gb
mb
hb
v
vb
None
Rule
inattx
=
gnattx
m
m
m
h
v
vna
None
Rule
iktea
=
gktea
n
n
n
n
v
vk
None
Rule
ica
=
gca
mca
mca
v
vca
None
Rule
icaca
=
gcaca
1
1
0.06
v
45
1
1
kbeta
ca
beta
v
vca
None
Rule
t
=
time
None