Dentate granule cell: mAHP & sAHP; SK & Kv7/M channels (Mateos-Aparicio et al., 2014)

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Accession:169240
The model is based on that of Aradi & Holmes (1999; Journal of Computational Neuroscience 6, 215-235). It was used to help understand the contribution of M and SK channels to the medium afterhyperpolarization (mAHP) following one or seven spikes, as well as the contribution of M channels to the slow afterhyperpolarization (sAHP). We found that SK channels are the main determinants of the mAHP, in contrast to CA1 pyramidal cells where the mAHP is primarily caused by the opening of M channels. The model reproduced these experimental results, but we were unable to reproduce the effects of the M-channel blocker XE991 on the sAHP. It is suggested that either the XE991-sensitive component of the sAHP is not due to M channels, or that when contributing to the sAHP, these channels operate in a mode different from that associated with the mAHP.
Reference:
1 . Mateos-Aparicio P, Murphy R, Storm JF (2014) Complementary functions of SK and Kv7-M potassium channels in excitability control and synaptic integration in rat hippocampal dentate granule cells. J Physiol 592:669-93 [PubMed]
Model Information (Click on a link to find other models with that property)
Model Type: Neuron or other electrically excitable cell; Axon; Channel/Receptor; Dendrite;
Brain Region(s)/Organism:
Cell Type(s): Dentate gyrus granule cell;
Channel(s): I Na,t; I L high threshold; I N; I T low threshold; I A; I K; I M; I K,Ca; I Sodium; I Calcium; I Potassium;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Ion Channel Kinetics; Detailed Neuronal Models; Action Potentials; Calcium dynamics; Spike Frequency Adaptation; Conductance distributions;
Implementer(s): Murphy, Ricardo [ricardo.murphy at medisin.uio.no];
Search NeuronDB for information about:  Dentate gyrus granule cell; I Na,t; I L high threshold; I N; I T low threshold; I A; I K; I M; I K,Ca; I Sodium; I Calcium; I Potassium;
: Ca channels (T,N,L-type)


NEURON {
	SUFFIX Ca
	USEION ca WRITE ica
	RANGE gtcabar, gncabar, glcabar, gtca, gnca, glca
	RANGE ainf, taua, binf, taub, e_ca, gbar, i
	GLOBAL ca0, cao, taucadiv, B, tauctdiv, Vshift
}

UNITS {
	(molar) = (1/liter)
	(mM) = (millimolar)
	(mV) = (millivolt)
	(mA) = (milliamp)
	(S) = (siemens)
	F = (faraday) (coulomb)
	R = (k-mole) (joule/degC)
}

PARAMETER {
	ca0 = .00007	(mM)		: initial calcium concentration inside
	cao = 1.6		  (mM)	  : calcium concentration outside
	tau = 9		    (ms)
	taucadiv = 1
	tauctdiv = 1
	gtcabar = .01	(S/cm2)
	gncabar = .01	(S/cm2)
	glcabar = .01	(S/cm2)
	B = .26 (mM-cm2/mA-ms)
	Vshift = 0    (mV)
}

ASSIGNED {
	v		(mV)
	e_ca		(mV)
	ica			(mA/cm2)
	i 			(mA/cm2)
	gtca		(S/cm2)
	gnca		(S/cm2)
	glca		(S/cm2)
	gbar		(S/cm2)
	celsius	(degC)
	taua    (ms)
	ainf
	taub    (ms)
	binf
}

STATE { 
	ca_i (mM)  <1e-5>
	a 
	b 
	c 
	d 
	e
}

BREAKPOINT {
	SOLVE state METHOD cnexp
	e_ca = (1000)*(celsius+273.15)*R/(2*F)*log(cao/ca_i)
	gtca = gtcabar*a*a*b
	gnca = gncabar*c*c*d
	glca = glcabar*e*e
	ica = (gtca+gnca+glca)*(v - e_ca)
	i = ica
}

DERIVATIVE state {	: exact when v held constant; integrates over dt step
	ca_i' = -B*ica - taucadiv*(ca_i-ca0)/tau
	ainf = alphaa(v)/(alphaa(v) + betaa(v))
	taua = 1/(alphaa(v) + betaa(v))
	a' = (ainf - a)/taua
	binf = alphab(v)/(alphab(v) + betab(v))
	taub = 1/(alphab(v+Vshift) + betab(v+Vshift))
	b' = (binf - b)/taub
	c' = alphac(v)*(1-c)-betac(v)*c
	d' = alphad(v)*(1-d)-betad(v)*d
	e' = alphae(v)*(1-e)-betae(v)*e
}

INITIAL {
	ca_i = ca0
	a = alphaa(v)/(alphaa(v)+betaa(v))
	b = alphab(v)/(alphab(v)+betab(v))
	c = alphac(v)/(alphac(v)+betac(v))
	d = alphad(v)/(alphad(v)+betad(v))
	e = alphae(v)/(alphae(v)+betae(v))
	gbar = gtcabar + gncabar + glcabar 
}

FUNCTION alphaa(v (mV)) (/ms) {
	alphaa = f(2,0.1,v,19.26)
}

FUNCTION betaa(v (mV)) (/ms) {
	betaa = exponential(0.009,-0.045393,v,0)
}

FUNCTION alphab(v (mV)) (/ms) {
	alphab = exponential(1e-6,-0.061501,v,0)
}

FUNCTION betab(v (mV)) (/ms) {
	betab = logistic(1,-0.1,v,29.79)
}

FUNCTION alphac(v (mV)) (/ms) {
	alphac = f(1.9,0.1,v,19.88)
}

FUNCTION betac(v (mV)) (/ms) {
	betac = exponential(0.046,-0.048239,v,0)
}

FUNCTION alphad(v (mV)) (/ms) {
	alphad = exponential(1.6e-4,-0.020661,v,0)
}

FUNCTION betad(v (mV)) (/ms) {
	betad = logistic(1,-0.1,v,39)
}

FUNCTION alphae(v (mV)) (/ms) {
	alphae = f(156.9,0.1,v,81.5)
}

FUNCTION betae(v (mV)) (/ms) {
	betae = exponential(0.29,-0.092081,v,0)
}

FUNCTION f(A, k, v (mV), D) (/ms) {
	LOCAL x
	UNITSOFF
	x = k*(v-D)
	if (fabs(x) > 1e-6) {
		f = A*x/(1-exp(-x))
	}else{
		f = A/(1-0.5*x)
	}
	UNITSON
}

FUNCTION logistic(A, k, v (mV), D) (/ms) {
	UNITSOFF
	logistic = A/(1+exp(k*(v-D)))
	UNITSON
}

FUNCTION exponential(A, k, v (mV), D) (/ms) {
	UNITSOFF
	exponential = A*exp(k*(v-D))
	UNITSON
}

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