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
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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:

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  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 [39] name constant value unit derived unit sbo cvterm
gna gna = 0.0231 0.0231 None
gnav gnav = 0.11 0.11 None
gb gb = 0.1372 0.1372 None
gca gca = 1.5 1.5 None
gcaca gcaca = 0.02 0.02 None
iapp iapp = -0.5 -0.5 None
cm cm = 0.02 0.02 None
r r = 0.1 0.1 None
f f = 96485 96485.0 None
gk gk = 0.25 0.25 None
gnattx gnattx = 400.0 400.0 None
gktea gktea = 10.0 10.0 None
vna vna = 40.0 40.0 None
vk vk = -70.0 -70.0 None
vb vb = -58.0 -58.0 None
vca vca = 150.0 150.0 None
ks ks = 50.0 50.0 None
rho rho = 0.002 0.002 None
kbeta kbeta = 15000 15000.0 None
beta beta = 0.00004 4e-05 None
v v = -42 -42.0 None
ca ca = 6e-05 6e-05 None
mb mb = 0.95 0.95 None
hb hb = 0.77 0.77 None
m m = 0.14 0.14 None
n n = 0.048 0.048 None
mca mca = 0.0002 0.0002 None
h 0.0 dimensionless None
vol 0.0 dimensionless None
iappx 0.0 dimensionless None
inav 0.0 dimensionless None
ik 0.0 dimensionless None
ina 0.0 dimensionless None
ib 0.0 dimensionless None
inattx 0.0 dimensionless None
iktea 0.0 dimensionless None
ica 0.0 dimensionless None
icaca 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [19]   assignment name derived units sbo cvterm
d v/dt = inattx iktea ik ina inav ib ica icaca iappx cm None
d ca/dt = rho ica 2 f vol ks ca None
d mb/dt = 1 1 0.4 v 34 mb 0.05 None
d hb/dt = 1 1 0.55 v 43 hb 1.5 None
d m/dt = 1 1 0.4 v 31 m 0.0005 None
d h/dt = 1 1 0.25 v 45 h 0.01 None
d n/dt = 1 1 0.18 v 25 n 0.015 None
d mca/dt = 1 1 0.2 v mca 0.01 None
vol = 4 3 r r r None
iappx = None None
inav = gnav 1 1 0.2 v 45 v vna None
ik = gk v vk None
ina = gna v vna None
ib = gb mb hb v vb None
inattx = gnattx m m m h v vna None
iktea = gktea n n n n v vk None
ica = gca mca mca v vca None
icaca = gcaca 1 1 0.06 v 45 1 1 kbeta ca beta v vca None
t = time None