XPP model

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

#############################
# SYSTEM DEFINING EQUATIONS #
#############################
v'    = 1000. * V_DOT(v,n,k_so,k_ex,h)
n'    = 1000. * N_DOT(v,n,k_so,k_ex)
k_so' = 1000. * K_SO_DOT(v,n,k_so,k_ex)
k_ex' = 1000. * K_EX_DOT(v,n,k_so,k_ex)
h'    = 1000. * H_DOT(v,h)

######################
# INITIAL CONDITIONS #
######################

# PHYSIOLOGICAL
###############
# par KBATH=4
# init v=-68.019025 
# init n=0.064944565
# init k_so=130.99026  
# init k_ex=3.9992148  

# TONIC FIRING
##############
# par KBATH=7
# init v=-56.844971
# init n=0.14995722
# init k_so=136.81308
# init k_ex=6.9882756

# SEIZURE-LIKE
##############

# kbath:
#KBATH=4+20*heav(t-10)*heav(50-t)
#par IAPP=0
#par MAX_PUMP=5.2471672

# iapp:
#IAPP=50*heav(t-10)*heav(17-t)
#par KBATH=4.01
#par MAX_PUMP=5.2471672

# pump:
par t1=10
par t2=23.60
par t3=28.60
stim(arg)=heav(t1-arg)*(1-((1-0.2)/t1)*arg)+ 0.2*heav(arg-(t1+0.000001))*heav(t2-arg) + heav(arg-(t2+0.000001))*heav(t3-arg)*(0.2+(1-0.2)/(t3-t2)*(arg-t2))+heav(arg-(t3+0.000001))
MAX_PUMP(t)=5.2471672*stim(t)
par KBATH=4.0
par IAPP=0

init v=-67.971672
init n=0.065193631
init k_so=131.07088
init k_ex=4.0102115
init h=0.69483376

# TONIC FIRING
##############
# par KBATH=12
# init v=-5.8720033538E+01
# init n=1.3065201430E-01
# init k_so=1.3504571762E+02
# init k_ex=1.1993252621E+01

# PERIODIC SD
#############
# par KBATH=17
# init v=-93.984886
# init n=0.0063529861
# init k_so=117.70079
# init k_ex=5.4777171


par F_DIFF=0.05

##########
# GATING #
##########
ALPHA_N(v) = 0.01 * (v + 34.0) / (1.0 - exp(-0.1 * (v + 34.0))) 
BETA_N(v)  = 0.125 * exp(-(v + 44.0) / 80.0)
ALPHA_M(v) = 0.1 * (v + 30.0) / (1.0 - exp(-0.1 * (v + 30.0))) 
BETA_M(v)  = 4.0 * exp(-(v + 55.0) / 18.0) 
ALPHA_H(v) = 0.07* exp( -0.05* (v+44))
BETA_H(v)  = 1.0 / (1 + exp(-0.1 * (v + 14)))
M(v)       = ALPHA_M(v) / (ALPHA_M(v) + BETA_M(v))
#H(n)       = 1 - 1. / (1 + exp(-6.5*(n-0.35)))

######################
# ION CONCENTRATIONS #
######################
par VOL_SO=2.16
par VOL_EX=0.72
par NA_SO_INI=27.
par K_SO_INI=130.98993
par NA_EX_INI=120.
#par V_INI=-68.

NA_SO(k_so) =  NA_SO_INI + K_SO_INI - k_so
NA_EX(k_so) = (NA_SO_INI * VOL_SO + NA_EX_INI * VOL_EX - NA_SO(k_so) * VOL_SO) / VOL_EX

#####################
# NERNST POTENTIALS #
#####################
EK(k_so,k_ex) = 26.64 * log(k_ex/k_so)	      
ENA(k_so)     = 26.64 * log(NA_EX(k_so)/NA_SO(k_so))

############
# CURRENTS #
############
par G_NA_L=0.0175
par G_NA_G=100.
par G_K_L=0.05
par G_K_G=40.

par NA_PUMP=25
par K_PUMP=5.5

I_NA_L(v,k_so)       = G_NA_L * (v - ENA(k_so))
I_NA_G(v,n,k_so,h)     = G_NA_G * M(v) * M(v) * M(v) * h * (v - ENA(k_so))
I_K_L(v,k_so,k_ex)   = G_K_L * (v - EK(k_so,k_ex))
I_K_G(v,n,k_so,k_ex) = G_K_G * n * n * n * n * (v - EK(k_so,k_ex))
IPUMP(k_so,k_ex)     = MAX_PUMP(t) / (1.0 + exp((NA_PUMP - NA_SO(k_so))/3.)) / (1. + exp(K_PUMP - k_ex))

I_NA(v,n,k_so,k_ex,h) = I_NA_L(v,k_so) + I_NA_G(v,n,k_so,h) + 3. * IPUMP(k_so,k_ex)
I_K(v,n,k_so,k_ex)  = I_K_L(v,k_so,k_ex)  + I_K_G(v,n,k_so,k_ex)  - 2. * IPUMP(k_so,k_ex)
#I_NA_gl(v,n,k_so,k_ex,h) = I_NA_L(v,k_so) + I_NA_G(v,n,k_so,h) 
#I_K_gl(v,n,k_so,k_ex)  = I_K_L(v,k_so,k_ex)  + I_K_G(v,n,k_so,k_ex)
JDIFF(k_ex)         = F_DIFF * 4. / 3. * (KBATH - k_ex) / 1000.

##################
# RATE FUNCTIONS #
##################
par PHI=3
par C=1
par CONV=9.55589e-05

V_DOT(v,n,k_so,k_ex,h)  = -1. / C * (I_NA(v,n,k_so,k_ex,h) + I_K(v,n,k_so,k_ex)-IAPP)
N_DOT(v,n,k_so,k_ex)    =  PHI * (ALPHA_N(v) * (1 - n) - BETA_N(v) * n)
K_SO_DOT(v,n,k_so,k_ex) = -1. / VOL_SO * CONV * I_K(v,n,k_so,k_ex)
K_EX_DOT(v,n,k_so,k_ex) =  1. / VOL_EX * CONV * I_K(v,n,k_so,k_ex) + JDIFF(k_ex)
H_DOT(v,h)	        = PHI * (ALPHA_H(v)*(1-h) - BETA_H(v)*h)

###############
# AUXILIARIES #
###############
#aux _Ina_gl = I_NA_L(v,k_so) + I_NA_G(v,n,k_so,h)
#aux _Ik_gl  = I_K_L(v,k_so,k_ex)  + I_K_G(v,n,k_so,k_ex)
aux _ENA    = ENA(k_so)
aux _EK	    = EK(k_so,k_ex)
aux _stim   = stim(t)
aux _Ip     = IPUMP(k_so,k_ex)

############
# NUMERICS #
############
#@ meth=runge-kutta
@ meth=cvode
@ dt=1e-4,tol=1e-10,atol=1e-10
@ maxstor=1000000000, bounds=10000000
@ total=100
@ bell=0

############
# GRAPHICS #
############
@ xhi=100
@ nplot=5, yp1=v, yp2=_EK, yp3=_ENA, yp4=_stim, yp5=k_ex, ylo=-150, yhi=160
#@ nplot=4, yp1=k_so, yp2=k_ex, yp3=_NA_SO, yp4=_NA_EX, ylo=0, yhi=150

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 [30] 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
stim arg t1 t2 t3 heav t1 arg 1 1 0.2 t1 arg 0.2 heav arg t1 1 -6 heav t2 arg heav arg t2 1 -6 heav t3 arg 0.2 1 0.2 t3 t2 arg t2 heav arg t3 1 -6
max_pump t t1 t2 t3 5.2471672 stim t t3 t2 t1
alpha_n v 0.01 v 34 1 0.1 v 34
beta_n v 0.125 v 44 80
alpha_m v 0.1 v 30 1 0.1 v 30
beta_m v 4 v 55 18
alpha_h v 0.07 0.05 v 44
beta_h v 1 1 0.1 v 14
m v alpha_m v alpha_m v beta_m v
na_so k_so k_so_ini na_so_ini na_so_ini k_so_ini k_so
na_ex k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so na_so_ini vol_so na_ex_ini vol_ex na_so k_so na_so_ini k_so_ini vol_so vol_ex
ek k_so k_ex 26.64 10 k_ex k_so
ena k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so 26.64 10 na_ex k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so na_so k_so na_so_ini k_so_ini
i_na_l v k_so g_na_l k_so_ini na_ex_ini na_so_ini vol_ex vol_so g_na_l v ena k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so
i_na_g v n k_so h g_na_g k_so_ini na_ex_ini na_so_ini vol_ex vol_so g_na_g m v m v m v h v ena k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so
i_k_l v k_so k_ex g_k_l g_k_l v ek k_so k_ex
i_k_g v n k_so k_ex g_k_g g_k_g n n n n v ek k_so k_ex
ipump k_so k_ex k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 max_pump t t1 t2 t3 1 na_pump na_so k_so na_so_ini k_so_ini 3 1 k_pump k_ex
i_na v n k_so k_ex h g_na_g g_na_l k_pump k_so_ini na_ex_ini na_pump na_so_ini t t1 t2 t3 vol_ex vol_so i_na_l v k_so g_na_l k_so_ini na_ex_ini na_so_ini vol_ex vol_so i_na_g v n k_so h g_na_g k_so_ini na_ex_ini na_so_ini vol_ex vol_so 3 ipump k_so k_ex k_pump k_so_ini na_pump na_so_ini t t1 t2 t3
i_k v n k_so k_ex g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 i_k_l v k_so k_ex g_k_l i_k_g v n k_so k_ex g_k_g 2 ipump k_so k_ex k_pump k_so_ini na_pump na_so_ini t t1 t2 t3
jdiff k_ex f_diff kbath f_diff 4 3 kbath k_ex 1000
v_dot v n k_so k_ex h c g_k_g g_k_l g_na_g g_na_l iapp k_pump k_so_ini na_ex_ini na_pump na_so_ini t t1 t2 t3 vol_ex vol_so 1 c i_na v n k_so k_ex h g_na_g g_na_l k_pump k_so_ini na_ex_ini na_pump na_so_ini t t1 t2 t3 vol_ex vol_so i_k v n k_so k_ex g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 iapp
n_dot v n k_so k_ex phi phi alpha_n v 1 n beta_n v n
k_so_dot v n k_so k_ex conv g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 vol_so 1 vol_so conv i_k v n k_so k_ex g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3
k_ex_dot v n k_so k_ex conv f_diff g_k_g g_k_l k_pump k_so_ini kbath na_pump na_so_ini t t1 t2 t3 vol_ex 1 vol_ex conv i_k v n k_so k_ex g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 jdiff k_ex f_diff kbath
h_dot v h phi phi alpha_h v 1 h beta_h v h

Parameters [30] name constant value unit derived unit sbo cvterm
t1 t1 = 10 10.0 None
t2 t2 = 23.60 23.6 None
t3 t3 = 28.60 28.6 None
kbath kbath = 4.0 4.0 None
iapp iapp = 0 0.0 None
v v = -67.971672 -67.971672 None
n n = 0.065193631 0.065193631 None
k_so k_so = 131.07088 131.07088 None
k_ex k_ex = 4.0102115 4.0102115 None
h h = 0.69483376 0.69483376 None
f_diff f_diff = 0.05 0.05 None
vol_so vol_so = 2.16 2.16 None
vol_ex vol_ex = 0.72 0.72 None
na_so_ini na_so_ini = 27. 27.0 None
k_so_ini k_so_ini = 130.98993 130.98993 None
na_ex_ini na_ex_ini = 120. 120.0 None
g_na_l g_na_l = 0.0175 0.0175 None
g_na_g g_na_g = 100. 100.0 None
g_k_l g_k_l = 0.05 0.05 None
g_k_g g_k_g = 40. 40.0 None
na_pump na_pump = 25 25.0 None
k_pump k_pump = 5.5 5.5 None
phi phi = 3 3.0 None
c c = 1 1.0 None
conv conv = 9.55589e-05 9.55589e-05 None
_ena 0.0 dimensionless None
_ek 0.0 dimensionless None
_stim 0.0 dimensionless None
_ip 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [10]   assignment name derived units sbo cvterm
d v/dt = 1000 v_dot v n k_so k_ex h c g_k_g g_k_l g_na_g g_na_l iapp k_pump k_so_ini na_ex_ini na_pump na_so_ini t t1 t2 t3 vol_ex vol_so None
d n/dt = 1000 n_dot v n k_so k_ex phi None
d k_so/dt = 1000 k_so_dot v n k_so k_ex conv g_k_g g_k_l k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 vol_so None
d k_ex/dt = 1000 k_ex_dot v n k_so k_ex conv f_diff g_k_g g_k_l k_pump k_so_ini kbath na_pump na_so_ini t t1 t2 t3 vol_ex None
d h/dt = 1000 h_dot v h phi None
_ena = ena k_so k_so_ini na_ex_ini na_so_ini vol_ex vol_so None
_ek = ek k_so k_ex None
_stim = stim t t1 t2 t3 None
_ip = ipump k_so k_ex k_pump k_so_ini na_pump na_so_ini t t1 t2 t3 None
t = time None