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

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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 [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 [81] name constant value unit derived unit sbo cvterm
v v = -67. -67.0 None
n n = 0.070 0.07 None
h h = 0.978 0.978 None
n_ki n_ki = 277.7 277.7 None
n_cli n_cli = 21.7 21.7 None
vli vli = 2160. 2160.0 None
s s = 0 0.0 None
gcl_l gcl_l = 0.05 0.05 None
max_p 0.0 dimensionless None
an 0.0 dimensionless None
bn 0.0 dimensionless None
am 0.0 dimensionless None
bm 0.0 dimensionless None
ah 0.0 dimensionless None
bh 0.0 dimensionless None
m 0.0 dimensionless None
n_ki0 0.0 dimensionless None
n_ke0 0.0 dimensionless None
n_nai0 0.0 dimensionless None
n_nae0 0.0 dimensionless None
n_cli0 0.0 dimensionless None
n_cle0 0.0 dimensionless None
n_impi 0.0 dimensionless None
n_impe 0.0 dimensionless None
n_nai 0.0 dimensionless None
n_nae 0.0 dimensionless None
n_ke 0.0 dimensionless None
n_cle 0.0 dimensionless None
vl_tot 0.0 dimensionless None
vle 0.0 dimensionless None
nai 0.0 dimensionless None
nae 0.0 dimensionless None
ki 0.0 dimensionless None
ke 0.0 dimensionless None
cli 0.0 dimensionless None
cle 0.0 dimensionless None
n_i 0.0 dimensionless None
n_e 0.0 dimensionless None
vli_inf0 0.0 dimensionless None
vli0 0.0 dimensionless None
p_i 0.0 dimensionless None
p_e 0.0 dimensionless None
vli_inf1 0.0 dimensionless None
vli_inf 0.0 dimensionless None
ek 0.0 dimensionless None
ena 0.0 dimensionless None
ecl 0.0 dimensionless None
gna_l 0.0 dimensionless None
gna_g 0.0 dimensionless None
gk_l 0.0 dimensionless None
gk_g 0.0 dimensionless None
ina_l 0.0 dimensionless None
ina_g 0.0 dimensionless None
ik_l 0.0 dimensionless None
ik_g 0.0 dimensionless None
icl_l 0.0 dimensionless None
ip 0.0 dimensionless None
ina 0.0 dimensionless None
ik 0.0 dimensionless None
c 0.0 dimensionless None
conv 0.0 dimensionless None
phi 0.0 dimensionless None
t_vl 0.0 dimensionless None
v_dot 0.0 dimensionless None
n_dot 0.0 dimensionless None
h_dot 0.0 dimensionless None
n_ki_dot 0.0 dimensionless None
n_cli_dot 0.0 dimensionless None
vli_dot 0.0 dimensionless None
_ki 0.0 dimensionless None
_ke 0.0 dimensionless None
_nai 0.0 dimensionless None
_nae 0.0 dimensionless None
_cli 0.0 dimensionless None
_cle 0.0 dimensionless None
_ek 0.0 dimensionless None
_ena 0.0 dimensionless None
_ecl 0.0 dimensionless None
_vli 0.0 dimensionless None
_vle 0.0 dimensionless None
t model time 0.0 dimensionless None

Rules [79]   assignment name derived units sbo cvterm
d v/dt = 1000 v_dot None
d n/dt = 1000 n_dot None
d h/dt = 1000 h_dot None
d n_ki/dt = 1000 n_ki_dot None
d n_cli/dt = 1000 n_cli_dot None
d vli/dt = 1000 vli_dot None
max_p = 6.8 heav 50 t None
an = 0.01 v 34 1 0.1 v 34 None
bn = 0.125 v 44 80 None
am = 0.1 v 30 1 0.1 v 30 None
bm = 4 v 55 18 None
ah = 0.07 v 44 20 None
bh = 1 1 0.1 v 14 None
m = am am bm None
n_ki0 = 277.7 None
n_ke0 = 2.8 None
n_nai0 = 54.6 None
n_nae0 = 91.3 None
n_cli0 = 21.7 None
n_cle0 = 89.8 None
n_impi = 318 None
n_impe = 40 None
n_nai = n_nai0 n_ki0 n_ki n_cli0 n_cli None
n_nae = n_nae0 n_nai0 n_nai None
n_ke = n_ke0 n_ki0 n_ki None
n_cle = n_cle0 n_cli0 n_cli None
vl_tot = 2880 None
vle = vl_tot vli None
nai = n_nai vli 1000 None
nae = n_nae vle 1000 None
ki = n_ki vli 1000 None
ke = n_ke vle 1000 None
cli = n_cli vli 1000 None
cle = n_cle vle 1000 None
n_i = n_nai n_ki n_cli n_impi None
n_e = n_nae n_ke n_cle n_impe None
vli_inf0 = vl_tot n_i n_i n_e None
vli0 = 2160 None
p_i = n_i vli 1000 None
p_e = n_e vle 1000 None
vli_inf1 = vli0 1.35 0.35 p_e p_i 20 None
vli_inf = 1 s vli_inf0 s vli_inf1 None
ek = 26.64 10 ke ki None
ena = 26.64 10 nae nai None
ecl = 26.64 10 cle cli None
gna_l = 0.0175 None
gna_g = 100 None
gk_l = 0.05 None
gk_g = 40 None
ina_l = gna_l v ena None
ina_g = gna_g m 3 h v ena None
ik_l = gk_l v ek None
ik_g = gk_g n 4 v ek None
icl_l = gcl_l v ecl None
ip = max_p 1 25 nai 3 1 5.5 ke None
ina = ina_l ina_g 3 ip None
ik = ik_l ik_g 2 ip None
c = 1 None
conv = 9.55589 -5 None
phi = 3 None
t_vl = 250 None
v_dot = 1 c ina ik icl_l None
n_dot = phi an 1 n bn n None
h_dot = phi ah 1 h bh h None
n_ki_dot = conv ik None
n_cli_dot = conv icl_l None
vli_dot = 1 t_vl vli_inf vli None
_ki = ki None
_ke = ke None
_nai = nai None
_nae = nae None
_cli = cli None
_cle = cle None
_ek = ek None
_ena = ena None
_ecl = ecl None
_vli = vli None
_vle = vle None
t = time None