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(2):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
fig10
readme.html
AmpaCOD.mod *
GRC_CA.mod *
GRC_CALC.mod *
GRC_GABA.mod *
GRC_KA.mod *
GRC_KCA.mod *
GRC_KIR.mod *
GRC_KM.mod *
GRC_KV.mod *
GRC_LKG1.mod *
GRC_LKG2.mod *
GRC_NA.mod *
NmdaS.mod *
Pregen.mod *
ComPanel.hoc
Grc_Cell.hoc
mosinit.hoc
Parametri.hoc
screenshot.jpg
simple.ses
Start.hoc
                            
TITLE Cerebellum Granule Cell Model

COMMENT
        KA channel
   
	Author: E.D'Angelo, T.Nieus, A. Fontana
	Last revised: Egidio 3.12.2003
ENDCOMMENT

NEURON { 
	SUFFIX GRC_KA
	USEION k READ ek WRITE ik 
	RANGE gkbar, ik, g, alpha_a, beta_a, alpha_b, beta_b
	RANGE Aalpha_a, Kalpha_a, V0alpha_a
	RANGE Abeta_a, Kbeta_a, V0beta_a
	RANGE Aalpha_b, Kalpha_b, V0alpha_b
	RANGE Abeta_b, Kbeta_b, V0beta_b
	RANGE V0_ainf, K_ainf, V0_binf, K_binf
	RANGE a_inf, tau_a, b_inf, tau_b 
} 
 
UNITS { 
	(mA) = (milliamp) 
	(mV) = (millivolt) 
} 
 
PARAMETER { 
	Aalpha_a = 0.8147 (/ms) :4.88826
	Kalpha_a = -23.32708 (mV)
	V0alpha_a = -9.17203 (mV)
	Abeta_a = 0.1655 (/ms)   : 0.99285	
	Kbeta_a = 19.47175 (mV)
	V0beta_a = -18.27914 (mV)

	Aalpha_b = 0.0368 (/ms)  : 0.11042 
	Kalpha_b = 12.8433 (mV)
	V0alpha_b = -111.33209 (mV)   
	Abeta_b = 0.0345(/ms)   : 0.10353 
	Kbeta_b = -8.90123 (mV)
	V0beta_b = -49.9537 (mV)

	V0_ainf = -38(mV)
	K_ainf = -17(mV)

	V0_binf = -78.8 (mV)
	K_binf = 8.4 (mV)
	v (mV) 
	gkbar= 0.0032 (mho/cm2) :0.003 
	ek = -84.69 (mV) 
	celsius = 30 (degC) 
} 

STATE { 
	a
	b 
} 

ASSIGNED { 
	ik (mA/cm2) 
	a_inf 
	b_inf 
	tau_a (ms) 
	tau_b (ms) 
	g (mho/cm2) 
	alpha_a (/ms)
	beta_a (/ms)
	alpha_b (/ms)
	beta_b (/ms)
} 
 
INITIAL { 
	rate(v) 
	a = a_inf 
	b = b_inf 
} 
 
BREAKPOINT { 
	SOLVE states METHOD derivimplicit 
	g = gkbar*a*a*a*b 
	ik = g*(v - ek)
	alpha_a = alp_a(v)
	beta_a = bet_a(v) 
	alpha_b = alp_b(v)
	beta_b = bet_b(v) 
} 
 
DERIVATIVE states { 
	rate(v) 
	a' =(a_inf - a)/tau_a 
	b' =(b_inf - b)/tau_b 
} 
 
FUNCTION alp_a(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-25.5(degC))/10(degC))
:	alp_a = Q10*Aalpha_a*exp(Kalpha_a*(v-V0alpha_a)) 
:	alp_a = -0.04148(/mV-ms)*linoid(v+67.697(mV),-3.857(mV))
	alp_a = Q10*Aalpha_a*sigm(v-V0alpha_a,Kalpha_a)
} 
 
FUNCTION bet_a(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-25.5(degC))/10(degC))
:	bet_a = Q10*Abeta_a*exp(Kbeta_a*(v-V0beta_a)) 
:	bet_a = 0.0359(/mV-ms)*linoid(v+45.878(mV),23.654(mV))
	bet_a = Q10*Abeta_a/(exp((v-V0beta_a)/Kbeta_a))
} 
 
FUNCTION alp_b(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-25.5(degC))/10(degC))
:	alp_b = Q10*Aalpha_b*exp(Kalpha_b*(v-V0alpha_b)) 
:	alp_b = 0.356(/mV-ms)*linoid(v+231.03(mV),17.8(mV))
	alp_b = Q10*Aalpha_b*sigm(v-V0alpha_b,Kalpha_b)
} 
 
FUNCTION bet_b(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-25.5(degC))/10(degC))
:	bet_b = Q10*Abeta_b*exp(Kbeta_b*(v-V0beta_b)) 
:	bet_b = -0.00825(/mV-ms)*linoid(v+43.284(mV),-8.927(mV))
	bet_b = Q10*Abeta_b*sigm(v-V0beta_b,Kbeta_b)
} 
 
PROCEDURE rate(v (mV)) {LOCAL a_a, b_a, a_b, b_b 
	TABLE a_inf, tau_a, b_inf, tau_b 
	DEPEND Aalpha_a, Kalpha_a, V0alpha_a, 
	       Abeta_a, Kbeta_a, V0beta_a,
               Aalpha_b, Kalpha_b, V0alpha_b,
               Abeta_b, Kbeta_b, V0beta_b, celsius FROM -100 TO 30 WITH 13000 
	a_a = alp_a(v)  
	b_a = bet_a(v) 
	a_b = alp_b(v)  
	b_b = bet_b(v) 
	a_inf = 1/(1+exp((v-V0_ainf)/K_ainf)) 
	tau_a = 1/(a_a + b_a) 
	b_inf = 1/(1+exp((v-V0_binf)/K_binf))
	tau_b = 1/(a_b + b_b) 
: Bardoni Belluzzi data
:	a_inf = 1/(1+exp(-(v+46.7)/19.8))
:	tau_a = 0.41*exp(-(v+43.5)/42.8)+0.167
:	b_inf = 1/(1+exp((v+78.8)/8.4))
:	tau_b = 10.8 + 0.03*v + 1/(57.9*exp(0.127*v)+0.000134*exp(-0.059*v))
}

FUNCTION linoid(x (mV),y (mV)) (mV) {
        if (fabs(x/y) < 1e-6) {
                linoid = y*(1 - x/y/2)
        }else{
                linoid = x/(exp(x/y) - 1)
        }
} 

FUNCTION sigm(x (mV),y (mV)) {
                sigm = 1/(exp(x/y) + 1)
}

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