Bursting and resonance in cerebellar granule cells (D'Angelo et al. 2001)

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Accession:46839
In this study we report theta-frequency (3-12 Hz) bursting and resonance in rat cerebellar granule cells and show that these neurons express a previously unidentified slow repolarizing K1 current (IK-slow ). Our experimental and modeling results indicate that IK-slow was necessary for both bursting and resonance. See paper for more.
Reference:
1 . D'Angelo E, Nieus T, Maffei A, Armano S, Rossi P, Taglietti V, Fontana A, Naldi G (2001) Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow k+-dependent mechanism. J Neurosci 21:759-70 [PubMed]
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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:
Cell Type(s): Cerebellum interneuron granule GLU cell;
Channel(s): I A; I K; I h; I Calcium; I A, slow;
Gap Junctions:
Receptor(s):
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Bursting; Ion Channel Kinetics; Oscillations;
Implementer(s): D'Angelo, Egidio [dangelo at unipv.it];
Search NeuronDB for information about:  Cerebellum interneuron granule GLU cell; I A; I K; I h; I Calcium; I A, slow;
TITLE Cerebellum Granule Cell Model

COMMENT
	Reference: Theta-Frequency Bursting and Resonance in Cerebellar Granule Cells:Experimental
	Evidence and Modeling of a Slow K+-Dependent Mechanism
	Egidio D'Angelo,Thierry Nieus,Arianna Maffei,Simona Armano,Paola Rossi,Vanni Taglietti,
	Andrea Fontana and Giovanni Naldi
ENDCOMMENT
 
NEURON { 
	SUFFIX GrG_Nar
	USEION na READ ena WRITE ina 
	RANGE gnabar, ina, g
	RANGE Aalpha_s,Abeta_s,V0alpha_s,V0beta_s,Kalpha_s,Kbeta_s 
        RANGE Shiftalpha_s,Shiftbeta_s,tau_s,s_inf
	RANGE Aalpha_f,Abeta_f,V0alpha_f,V0beta_f,Kalpha_f, Kbeta_f
	RANGE tau_f,f_inf
} 
 
UNITS {    
	(mA) = (milliamp) 
	(mV) = (millivolt) 
} 
 
PARAMETER { 
	
	: s-ALFA
	Aalpha_s = -0.00493 (/ms)
	V0alpha_s = -4.48754 (mV)
	Kalpha_s = -6.81881 (mV)
	Shiftalpha_s = 0.00008 (/ms)

	: s-BETA
	Abeta_s = 0.01558 (/ms)
	V0beta_s = 43.97494 (mV)
	Kbeta_s =  0.10818 (mV)
	Shiftbeta_s = 0.04752 (/ms)

	: f-ALFA
	Aalpha_f = 0.31836 (/ms)
	V0alpha_f = -80 (mV)
	Kalpha_f = -62.52621 (mV)

	: f-BETA
	Abeta_f = 0.01014 (/ms)
	V0beta_f = -83.3332 (mV)
	Kbeta_f = 16.05379 (mV)

	v (mV) 
	gnabar= 0.0005 (mho/cm2)
	ena = 87.39 (mV) 
	celsius = 30 (degC) 
} 

STATE { 
	s 
	f
} 

ASSIGNED { 
	ina (mA/cm2) 
	g (mho/cm2) 

	alpha_s (/ms)
	beta_s (/ms)
	s_inf
	tau_s (ms)
	
	alpha_f (/ms)
	beta_f (/ms)
	f_inf
	tau_f (ms) 
} 
 
INITIAL { 
	rate(v) 

	s = s_inf
	f = f_inf
} 
 
BREAKPOINT { 
	SOLVE states METHOD derivimplicit 
	g = gnabar*s*f
	ina = g*(v - ena)

	alpha_s = alp_s(v)
	beta_s = bet_s(v) 

	alpha_f = alp_f(v)
	beta_f = bet_f(v) 
} 
 
DERIVATIVE states { 
	rate(v) 
	s' = ( s_inf - s ) / tau_s 
	f' = ( f_inf - f ) / tau_f 
} 
 
PROCEDURE rate(v (mV)) { LOCAL a_s,b_s,a_f,b_f

	a_s = alp_s(v)  
	b_s = bet_s(v) 
	s_inf = a_s / ( a_s + b_s ) 
	tau_s = 1 / ( a_s + b_s ) 

	a_f = alp_f(v)  
	b_f = bet_f(v) 
	f_inf = a_f / ( a_f + b_f ) 
	tau_f = 1 / ( a_f + b_f ) 
} 



FUNCTION alp_s(v (mV)) (/ms){ LOCAL Q10
	Q10 = 3^( ( celsius - 20 (degC) ) / 10 (degC) )
	alp_s = Q10*(Shiftalpha_s+Aalpha_s*((v+V0alpha_s)/ 1 (mV) )/(exp((v+V0alpha_s)/Kalpha_s)-1))
}

FUNCTION bet_s(v (mV)) (/ms){ LOCAL Q10
	Q10 = 3^((celsius-20(degC))/10(degC))	
	bet_s =	Q10*(Shiftbeta_s+Abeta_s*((v+V0beta_s)/1 (mV) )/(exp((v+V0beta_s)/Kbeta_s)-1))
}

FUNCTION alp_f(v (mV)) (/ms){ LOCAL Q10
	Q10 = 3^( ( celsius - 20 (degC) ) / 10 (degC) )
	alp_f =	Q10 * Aalpha_f * exp( ( v - V0alpha_f ) / Kalpha_f)
}

FUNCTION bet_f(v (mV)) (/ms){ LOCAL Q10
	Q10 = 3^( ( celsius - 20 (degC) ) / 10 (degC) )
	bet_f =	Q10 * Abeta_f * exp( ( v - V0beta_f ) / Kbeta_f )	
}