Multicompartmental cerebellar granule cell model (Diwakar et al. 2009)

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Accession:116835
A detailed multicompartmental model was used to study neuronal electroresponsiveness of cerebellar granule cells in rats. Here we show that, in cerebellar granule cells, Na+ channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing EPSPs to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock, whose activation promoted spike back-propagation with marginal delay (<200 micros) and attenuation (<20 mV) into the somato-dendritic compartment. For details check the cited article.
Reference:
1 . Diwakar S, Magistretti J, Goldfarb M, Naldi G, D'Angelo E (2009) Axonal Na+ channels ensure fast spike activation and back-propagation in cerebellar granule cells. J Neurophysiol 101:519-32 [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: Cerebellum;
Cell Type(s): Cerebellum interneuron granule cell;
Channel(s): I A; I M; I h; I K,Ca; I Sodium; I Calcium; I Potassium; I A, slow;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Action Potential Initiation; Active Dendrites; Detailed Neuronal Models; Axonal Action Potentials; Action Potentials; Intrinsic plasticity;
Implementer(s): Diwakar, Shyam [shyam at amrita.edu];
Search NeuronDB for information about:  Cerebellum interneuron granule cell; I A; I M; I h; I K,Ca; I Sodium; I Calcium; I Potassium; I A, slow;
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GrC
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ComPanel.hoc
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simple.ses
Start.hoc
                            
TITLE Cerebellum Granule Cell Model

COMMENT
Based on Raman 13 state model. Adapted from Magistretti et al, 2006.
ENDCOMMENT

NEURON {
	SUFFIX GRC_NA
	USEION na READ ena WRITE ina
	RANGE gnabar, ina, g
	RANGE alfa, beta, gamma, delta, epsilon, teta, Con, Coff, Oon, Ooff
	RANGE Aalfa, Valfa, Abeta, Vbeta, Ateta, Vteta, Agamma, Adelta, Aepsilon, ACon, ACoff, AOon, AOoff
	RANGE n1,n2,n3,n4
}

UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
}

PARAMETER {
	v (mV)
	celsius = 20  	(degC)
	ena = 87.39		(mV)
	gnabar = 0.013	(mho/cm2)
	Aalfa = 353.91 ( /ms)
	Valfa = 13.99 ( /mV) 
	Abeta = 1.272  ( /ms)
	Vbeta = 13.99 ( /mV)
	Agamma = 150 ( /ms)
	Adelta = 40  ( /ms)
	Aepsilon = 1.75 ( /ms)
	Ateta = 0.0201 ( /ms)
	Vteta = 25
	ACon = 0.005    ( /ms)
	ACoff = 0.5     ( /ms)
	AOon = 0.75     ( /ms)
	AOoff = 0.005   ( /ms)
	n1 = 5.422
	n2 = 3.279
	n3 = 1.83
	n4 = 0.738
}

ASSIGNED {
	ina  (mA/cm2)
	g   (mho/cm2)
	
	gamma
	delta
	epsilon
	Con
	Coff
	Oon
	Ooff
	a
	b
	Q10
	
}

STATE {
	C1
	C2
	C3
	C4
	C5
	O
	OB
	I1
	I2
	I3
	I4
	I5
	I6
}


INITIAL {
	C1=1
	C2=0
	C3=0
	C4=0
	C5=0
	O=0
	OB=0
	I1=0
	I2=0
	I3=0
	I4=0
	I5=0
	I6=0
	Q10 =3^((celsius-20(degC))/10 (degC))
	gamma = Q10 * Agamma
	delta = Q10 * Adelta
	epsilon = Q10 * Aepsilon
	Con = Q10 * ACon
	Coff = Q10 * ACoff
	Oon = Q10 * AOon
	Ooff = Q10 * AOoff
	a = (Oon/Con)^0.25
	b = (Ooff/Coff)^0.25

}

BREAKPOINT {
	SOLVE kstates METHOD sparse
	g = gnabar * O	      	: (mho/cm2)
	ina = g * (v - ena)  	: (mA/cm2)
}


FUNCTION alfa(v(mV))(/ms){ 
	alfa = Q10*Aalfa*exp(v/Valfa) 
}

FUNCTION beta(v(mV))(/ms){ 
	beta = Q10*Abeta*exp(-v/Vbeta) 
}

FUNCTION teta(v(mV))(/ms){ 
	teta = Q10*Ateta*exp(-v/Vteta) 
}
 

KINETIC kstates {
	: 1 riga
	~ C1 <-> C2 (n1*alfa(v),n4*beta(v))
	~ C2 <-> C3 (n2*alfa(v),n3*beta(v))
	~ C3 <-> C4 (n3*alfa(v),n2*beta(v))
	~ C4 <-> C5 (n4*alfa(v),n1*beta(v))
	~ C5 <-> O  (gamma,delta)
	~  O <-> OB (epsilon,teta(v))
	
	: 2 riga
	~ I1 <-> I2	(n1*alfa(v)*a,n4*beta(v)*b)
	~ I2 <-> I3	(n2*alfa(v)*a,n3*beta(v)*b)
	~ I3 <-> I4	(n3*alfa(v)*a,n2*beta(v)*b)
	~ I4 <-> I5 (n4*alfa(v)*a,n1*beta(v)*b)
	~ I5 <-> I6 (gamma,delta)
	
	: connette 1 riga con 2 riga
	~ C1 <-> I1 (Con,Coff)
	~ C2 <-> I2 (Con*a,Coff*b)
	~ C3 <-> I3 (Con*a^2,Coff*b^2)
	~ C4 <-> I4 (Con*a^3,Coff*b^3)
	~ C5 <-> I5 (Con*a^4,Coff*b^4)
	~  O <-> I6 (Oon,Ooff)
	
	CONSERVE C1+C2+C3+C4+C5+O+OB+I1+I2+I3+I4+I5+I6=1
}


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