Ion concentration dynamics as a mechanism for neuronal bursting (Barreto & Cressman 2011)

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Accession:142630
"We describe a simple conductance-based model neuron that includes intra and extracellular ion concentration dynamics and show that this model exhibits periodic bursting. The bursting arises as the fast-spiking behavior of the neuron is modulated by the slow oscillatory behavior in the ion concentration variables and vice versa. By separating these time scales and studying the bifurcation structure of the neuron, we catalog several qualitatively different bursting profiles that are strikingly similar to those seen in experimental preparations. Our work suggests that ion concentration dynamics may play an important role in modulating neuronal excitability in real biological systems."
Reference:
1 . Barreto E, Cressman JR (2011) Ion concentration dynamics as a mechanism for neuronal bursting. J Biol Phys 37:361-73 [PubMed]
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: Generic;
Cell Type(s): Hodgkin-Huxley neuron;
Channel(s):
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: C or C++ program; XPP;
Model Concept(s): Bursting; Oscillations; Simplified Models; Depolarization block;
Implementer(s): Barreto, Ernest ;
#
# This is the one-cell model with dynamic ion concentrations used in
#
# E. Barreto and J.R. Cressman, "Ion Concentration Dynamics as a Mechanism for Neuronal Bursting",
# Journal of Biological Physics 37, 361-373 (2011).
#
# Link to the paper: http://www.springerlink.com/content/v52215p195159211/
# Author-generated version available at: http://arxiv.org/abs/1012.3124
#
# The variables are:
#	V=y[1]=V, the membrane voltage
#	n=y[2]=n, gating variable
#	h=y[3]=h, gating variable
#	Ko=y[4]=[K]_o, the extracellular potassium concentration
#	Nai=y[5]=[Na]_i, the intracellular sodium concentration
#
# The parameters of interest are
#	rho = strength of pumps
#	epsilon = diffusion constant for potassium diffusion from the extracellular space to the bath
# 	kbath = bath potassium concentration
#	glia = strength of glia
#	beta = ratio of intra- to extra-cellular volume
#
# The remaining parameter is
#	gamma = unit conversion factor

par rho=1.25, epsilon=1.333333333, kbath=4.0, glia=66.666666666, beta=7.0
par gamma=0.044494542, tau=1000
par E_cl=-81.93864549, E_ca=120.0
par Cm=1.0, g_na=100.0, g_naL=0.0175, g_k=40.0, g_kL=0.05
par g_clL=0.05, g_ca=0.1, phi=3.0, I=0.0

########

alpha_n=0.01*(V+34.0)/(1.0-exp(-0.1*(V+34.0)))
beta_n=0.125*exp(-(V+44.0)/80.0)
alpha_m=0.1*(V+30.0)/(1.0-exp(-0.1*(V+30.0)))
beta_m=4.0*exp(-(V+55.0)/18.0)
alpha_h=0.07*exp(-(V+44.0)/20.0)
beta_h=1.0/(1.0+exp(-0.1*(V+14.0)))

m_inf=alpha_m/(alpha_m+beta_m)
Kin=158.0-Nai
Naout=144.0-beta*(Nai-18.0)
E_k=26.64*log((Ko/Kin))
E_na=26.64*log((Naout/Nai))
Ina=g_na*(m_inf*m_inf*m_inf)*h*(V-E_na)+g_naL*(V-E_na)
Ik=g_k*n*n*n*n*(V-E_k)+g_kL*(V-E_k)
Icl=g_clL*(V-E_cl)
Itildepump=(rho/(1.0+exp((25.0-Nai)/3.0)))*(1/(1+exp(5.5-Ko)))
Itildeglia=(glia/(1.0+exp((18.0-Ko)/2.5)))
Itildediff=epsilon*(Ko-kbath)

# differential equations

V'=(1.0/Cm)*(-Ina-Ik-Icl+I)
n'=phi*(alpha_n*(1-n)-beta_n*n)
h'=phi*(alpha_h*(1-h)-beta_h*h)
Ko'=(1/tau)*(gamma*beta*Ik-2.0*beta*Itildepump-Itildeglia-Itildediff)
Nai'=(1/tau)*(-gamma*Ina-3.0*Itildepump)

####

init V=-50,n=0.08553,h=0.96859,Ko=7.8,Nai=15.5
@ TOTAL=10000,BOUND=10000
done


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