Computer simulations of neuron-glia interactions mediated by ion flux (Somjen et al. 2008)

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Accession:113446
"... To examine the effect of glial K+ uptake, we used a model neuron equipped with Na+, K+, Ca2+ and Cl− conductances, ion pumps and ion exchangers, surrounded by interstitial space and glia. The glial membrane was either “passive”, incorporating only leak channels and an ion exchange pump, or it had rectifying K+ channels. We computed ion fluxes, concentration changes and osmotic volume changes. ... We conclude that voltage gated K+ currents can boost the effectiveness of the glial “potassium buffer” and that this buffer function is important even at moderate or low levels of excitation, but especially so in pathological states."
Reference:
1 . Somjen GG, Kager H, Wadman WJ (2008) Computer simulations of neuron-glia interactions mediated by ion flux. J Comput Neurosci 25:349-65 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Electrogenic pump; Glia;
Brain Region(s)/Organism:
Cell Type(s): Astrocyte;
Channel(s): I Na,p; I Na,t; I T low threshold; I A; I K; I K,Ca; Na/Ca exchanger; Na/K pump;
Gap Junctions:
Receptor(s): NMDA;
Gene(s):
Transmitter(s): Ions;
Simulation Environment: NEURON;
Model Concept(s): Epilepsy; Calcium dynamics; Sodium pump;
Implementer(s):
Search NeuronDB for information about:  NMDA; I Na,p; I Na,t; I T low threshold; I A; I K; I K,Ca; Na/Ca exchanger; Na/K pump; Ions;
TITLE nap
: Persistent Na-current nu v en ko afhankelijk
: boltzman met halfmaximale concentratie = 7mM
: en activatie bij 3.5mM (1%)
: simple, with no inactivation-gate
: tau_activation = constant, 6ms
: tau_inactivation = very slow; 50000 keer trager dan tau_inact_m^3*h
:
: Activation from -60mV, peak at -10 mV
:
: Tweede poging door toevoeging inactivation gate met
: zelfde voltage gevoeligheid als Traub's m^3*h kanaal
: maar dan 100 keer langzamer.
:
: door aanpassing van het model CaChan.
: A Molecular Model of Low-Voltage-Activated Calcium Conductance
: van Wang?

UNITS {
	(molar) = (1/liter)
	(mV) =	(millivolt)
	(mA) =	(milliamp)
	(mM) =	(millimolar)
}

INDEPENDENT {t FROM 0 TO 1 WITH 100 (ms)}

NEURON {
	SUFFIX nap
	USEION k READ ko
	USEION na READ nai, nao, ena WRITE ina
	GLOBAL ina_p_h, tau_act, conc_half, helling
	RANGE gnabar, ina
}

UNITS {
	:FARADAY	= (faraday) (coulomb)
	FARADAY		= 96485.309 (coul)
	R = (k-mole) (joule/degC)
}

PARAMETER {
	celsius		(degC)
	gnabar=1e-6	(mho/cm2)	: Maximum Permeability .2e-3*5 hans
	helling=-.765	(mM)		: K-slope of boltzman
	conc_half=7 	(mM)		: conc. for halfmax. activation
	ina_p_h = 25000	(ms)		:taufactor tov snelle na-stroom
	tau_act = 6	(ms)
}

ASSIGNED { 
	ina	(mA/cm2)
	ena	(mV)
	v	(mV)	
	nai	(mM)		: <-vanwege deze 
	nao	(mM)		: <-en deze regel.
	ko	(mM)
}

STATE { ma mb ha hb }		: fraction of states, m=fraction in open state.

BREAKPOINT {
	SOLVE nastate METHOD sparse
	:boltzman()
	ina = gnabar*ma*ma*ha*kdep(ko)*(v-ena) :*ghk(v,nai,nao)
	:ma = 1 - mb
	:ha = 1 - hb
}

INITIAL {
	:SOLVE nastate STEADYSTATE sparse
	ma=m_inf(v)
	mb=1-ma
	ha=h_inf(v)
	hb=1-ha
	ina = gnabar*ma*ma*ha*kdep(ko)*(v-ena) :*ghk(v,nai,nao)
}

LOCAL a1,a2,b1,b2

KINETIC nastate {
	a1 = m_a(v)
	a2 = m_b(v)
	b1 = h_a(v)
	b2 = h_b(v)

	~ mb <-> ma (a1, a2)
	~ hb <-> ha (b1, b2)
	CONSERVE ma + mb = 1
	CONSERVE ha + hb = 1
}

FUNCTION kdep(ko (mM)) {
	TABLE DEPEND conc_half, helling FROM 0 TO 150 WITH 150
	kdep=1+ 2/(1+exp((ko-conc_half)/helling))
}

FUNCTION m_a(v(mV)) {
	:LOCAL m_inf
	TABLE FROM -150 TO 150 WITH 200
	:if (v<=-70) {
	:	m_inf=0
	:}else{
	:	m_inf=1/(1+(exp(-(v+39.7)/7.0)))
	:}
	m_a = m_inf(v)/tau_act
}

FUNCTION m_inf(v) {
	TABLE FROM -150 TO 150 WITH 200
	m_inf=1/(1+(exp(-(v+39.7)/7.0)))
}

FUNCTION m_b(v(mV)) {
	:LOCAL m_inf
	TABLE FROM -150 TO 150 WITH 200
	:m_inf=1/(1+(exp(-(v+39.7)/7.0)))
	m_b = (1-m_inf(v))/tau_act
}

FUNCTION h_a(v(mV)) {
	TABLE FROM -150 TO 150 WITH 200
	h_a = (1/ina_p_h)*(0.128*exp((7-v-70)/18))
}
: 37 was 17
FUNCTION h_b(v(mV)) {
	TABLE FROM -150 TO 150 WITH 200
	h_b = (1/ina_p_h)*4/(1+exp((30-v-70)/5))
}
: 60 was 40

FUNCTION h_inf(v) {
	TABLE FROM -150 TO 150 WITH 200
	h_inf=h_a(v)/(h_a(v)+h_b(v))
}

FUNCTION ghk(v(mV), ci(mM), co(mM)) (.001 coul/cm3) {
	LOCAL z, eci, eco
	z = (1e-3)*1*FARADAY*v/(R*(celsius+273.11247574)) : *1* -> valentie kalium
	eco = co*efun(z)
	eci = ci*efun(-z)
	:high nao charge moves inward, mogelijke fouten vanwege oorsprong Ca(2+)!
	:negative potential charge moves inward
	ghk = (.001)*1*FARADAY*(eci - eco)
}

FUNCTION efun(z) {
	if (fabs(z) < 1e-4) {
		efun = 1 - z/2
	}else{
		efun = z/(exp(z) - 1)
	}
}

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