Anoxic depolarization, recovery: effect of brain regions and extracellular space (Hubel et al. 2016)

 Download zip file 
Help downloading and running models
Accession:187213
The extent of anoxic depolarization (AD), the initial electrophysiological event during ischemia, determines the degree of brain region-specific neuronal damage. Neurons in higher brain regions have stronger ADs and are more easily injured than neurons in lower brain region. The mechanism leading to such differences is not clear. We use a computational model based on a Hodgkin-Huxley framework which includes neural spiking dynamics, processes of ion accumulation, and homeostatic mechanisms like vascular coupling and Na/K-exchange pumps. We show that a large extracellular space (ECS) explains the recovery failure in high brain regions. A phase-space analysis shows that with a large ECS recovery from AD through potassium regulation is impossible. The code 'time_series.ode' can be used to simulate AD for a large and a small ECS and show the different behaviors. The code ‘continuations.ode’ can be used to show the fixed point structure. Depending on our choice of large or small ECS the fixed point curve implies the presence/absence of a recovery threshold that defines the potassium clearance demand.
Reference:
1 . Hübel N, Andrew RD, Ullah G (2016) Large extracellular space leads to neuronal susceptibility to ischemic injury in a Na+/K+ pumps-dependent manner. J Comput Neurosci 40:177-92 [PubMed]
Citations  Citation Browser
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell;
Brain Region(s)/Organism:
Cell Type(s): Abstract single compartment conductance based cell;
Channel(s): I Chloride; I Na,t; I K; I K,leak; I h; I Sodium; I Potassium; I_K,Na; Na/K pump; I Cl, leak; I Na, leak;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: XPP;
Model Concept(s): Action Potentials; Pathophysiology; Sodium pump; Depolarization block; Homeostasis; Potassium buffering;
Implementer(s):
Search NeuronDB for information about:  I Chloride; I Na,t; I K; I K,leak; I h; I Sodium; I Potassium; I_K,Na; Na/K pump; I Cl, leak; I Na, leak;
/
Huebel_Andrew_Ullah_2015
readme.txt
continuations.ode
time_series.ode
                            
###################################################################################################################################
# Rate equations for AD model used in "Large Extracellular Space Leads to [...] Ischemic Injury [...]" by Hubel, Ullah and Andrew #
###################################################################################################################################
# membrane potential                                    'V'       in  [mV]	   #
# gating variables                                      'n/h'     in  [1]	   #
# intracellular ion concentrations                      'ki,cli'  in  [mM=mMol/l]  #
# amount of potassium exchanged with external reservoir 'dnk'     in  [fmol]	   #
# 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
dnk'   = 1000. * DNK_DOT

####################################
# Physiological initial conditions #
####################################
init v=-67.056664
init n=0.070174225
init h=0.97820824

init ki=128.56937
init cli=10.061391
init dnk=0

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

###############################################################################################################
# Interruption of pumping and diffusive vascular potassium regulation after 50sec and for 'delta_pmp/dif' sec #
###############################################################################################################
par delta_pmp=200
par delta_dif=200
max_p  = (heav(50-t) + heav(t-50-delta_pmp)) * 6.8
lambda = (heav(50-t) + heav(t-50-delta_dif)) * 3.0e-5

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

#######################################################################################
# Vascular potassium regulation as diffusive coupling to extracellular bath reservoir #
#######################################################################################
# baseline potassium concentration       'k_bth'  in [mM]	  #
# coupling strength                      'lambda' in [mM/msec]	  #
# factor 1e-3 to convert diffusive flux  'J_diff' to [fMol/msec]  #
###################################################################
k_bth  = 4
J_diff = lambda * vle * (k_bth - ke) * 1e-3

#############################
# 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
DNK_DOT =  J_diff

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

aux _MAX_P = max_p

########################
# Numerical parameters #
########################
@ meth=stiff
@ dt=5e-4
@ maxstor=10000000, bounds=10000000
@ total=1000
@ bell=0

#################
# Plot settings #
###########################################################
# '_MAX_P' as a guide to the eye to see pump interruption #
###########################################################
@ xhi=1000
@ nplot=4, yp1=v, yp2=_EK, yp3=_ENA, yp4=_MAX_P, ylo=-150, yhi=160

done