XPP model

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

###############################################################################################
# Code for fixed point continuations/bifurcation diagrams used in                             #
# "Large Extracellular Space Leads to [...] Ischemic Injury [...]" by Hubel, Ullah and Andrew #
###############################################################################################


##############################################################################################################
##############################################################################################################
###													   ###
###     The fixed point curves from Figs. 4 and 5 can be obtained as follows:				   ###
###     												   ###
###     1.) open file with XPPAUT									   ###
###     2.) run simulation twice to make sure the system is in its fixed point:				   ###
###         click "Initialconds" + "(G)o"; "Initialconds" + "(L)ast"					   ###
###         (keyboard shortcuts: "I" + "G", "I" + "L")							   ###
###     3.) open AUTO interface:									   ###
###         click "File" + "Auto"									   ###
###         (keyboard shortcut: "F" + "A")								   ###
###     4.) run 'forward' fixed point continuation:							   ###
###         click "Run" + "Steady state"								   ###
###         (keyboard shortcut: "R" + "S")								   ###
###     5.) grab point to start 'backward' continuation if desired:					   ###
###         click "Grab", then navigate along the curve with "tab" key, press "enter" to choose point 	   ###
###     6.) set continuation step size to negative:							   ###
###         click "Numerics" and change 'Ds:0.002' to 'Ds:-0.002', click "Ok"				   ###
###     7.) run backward coninuation by clicking "Run"							   ###
###     8.) save the fixed point curves and bifurcation information:					   ###
###         click "File" + "All info", choose a filename and click "Ok"					   ###
###     												   ###
###     Remark for Fig. 4:										   ###
###     Start from the 'physiological' (i.e. upper set of) initial conditions and 'par vle=720'.	   ###
###     Change 'PARMIN=-250' to 'PARMIN=-50' and accordingly 'XAUTOMIN=-250' to 'XAUTOMIN=-50'.		   ###
###     For more negative parameter values the continuation produces convergence errors "MX" at		   ###
###     extreme negative values of 'V'									   ###
###     												   ###
###     Remark for Fig. 5a:										   ###
###     Start from the 'FES' (i.e. lower set of) initial conditions and 'par vle=3700' to obntain	   ###
###     the upper branch of the continuation. Use 'physiological' initial conditions and 'par vle=3700'	   ###
###     to obtain the lower loop of the bifurcation diagram						   ###
###													   ###
##############################################################################################################
##############################################################################################################


####################################################################################
# membrane potential                                    'V'       in  [mV]	   #
# gating variables                                      'n/h'     in  [1]	   #
# intracellular ion concentrations                      'ki,cli'  in  [mM=mMol/l]  #
# 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

######################
# Initial conditions #
######################
# physiological #
#################
# init v=-67.056664
# init n=0.070174225
# init h=0.97820824
# init ki=128.56937
# init cli=10.061391
######################
# FES for 'vle=3700' #
######################
init v=-20.288656
init n=0.66411209
init h=0.057942949
init ki=77.408791
init cli=47.911449

#########################################################################
# MAIN BIFURCATION PARAMETER:                                           #
# amount of potassium exchanged with external reservoir 'dnk' in [fmol]	#
#########################################################################
par dnk=0

########################################
# Extracellular volume 'vle' in [um^3] #
########################################
# par vle=720
par vle=3700

##################################
# Pump strength 'max_p' constant #
##################################
max_p = 6.8

###################################
# 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

#############################
# 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

####################################################
# 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


####################################
# Numerical parameters: simulation #
####################################
@ meth=stiff
@ dt=5e-3
@ maxstor=10000000, bounds=10000000
@ total=200
@ bell=0

#############################################################
# Parameters for fixed point continuation in AUTO interface #
#############################################################
@ NTST=50, NMAX=115000, NPR=115000
@ DS=0.002, DSMIN=0.001, DSMAX=0.005
@ PARMIN=-250, PARMAX=50
@ AUTOXMIN=-250, AUTOXMAX=50, AUTOYMIN=-150, AUTOYMAX=50
@ EPSL=0.001, EPSU=0.001, EPSS=0.001


#################
# Plot settings #
###########################################################
# '_MAX_P' as a guide to the eye to see pump interruption #
###########################################################
@ xhi=200
@ nplot=3, yp1=v, yp2=_EK, yp3=_ENA, ylo=-150, yhi=160

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 [60] name constant value unit derived unit sbo cvterm
v v = -20.288656 -20.288656 None
n n = 0.66411209 0.66411209 None
h h = 0.057942949 0.057942949 None
ki ki = 77.408791 77.408791 None
cli cli = 47.911449 47.911449 None
dnk dnk = 0 0.0 None
vle vle = 3700 3700.0 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
vli 0.0 dimensionless None
ki0 0.0 dimensionless None
ke0 0.0 dimensionless None
nai0 0.0 dimensionless None
nae0 0.0 dimensionless None
cli0 0.0 dimensionless None
cle0 0.0 dimensionless None
nai 0.0 dimensionless None
nae 0.0 dimensionless None
ke 0.0 dimensionless None
cle 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
gcl_l 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
v_dot 0.0 dimensionless None
n_dot 0.0 dimensionless None
h_dot 0.0 dimensionless None
ki_dot 0.0 dimensionless None
cli_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
t model time 0.0 dimensionless None

Rules [58]   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 ki/dt = 1000 ki_dot None
d cli/dt = 1000 cli_dot None
max_p = 6.8 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
vli = 2160 None
ki0 = 128.56935 None
ke0 = 3.9962559 None
nai0 = 25.279156 None
nae0 = 126.84917 None
cli0 = 10.055541 None
cle0 = 124.71021 None
nai = nai0 ki0 ki cli0 cli None
nae = nae0 nai0 nai vli vle None
ke = ke0 ki0 ki vli vle dnk vle 1 3 None
cle = cle0 cli0 cli vli vle 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
gcl_l = 0.05 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 -2 None
phi = 3 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
ki_dot = conv vli ik None
cli_dot = conv vli icl_l 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
t = time None