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_Na 
	USEION na READ ena WRITE ina 
	RANGE gnabar, ina, g, alpha_m, beta_m, alpha_h, beta_h 
	RANGE Aalpha_m, Kalpha_m, V0alpha_m
	RANGE Abeta_m, Kbeta_m, V0beta_m

	RANGE Aalpha_h, Kalpha_h, V0alpha_h
	RANGE Abeta_h, Kbeta_h, V0beta_h

	RANGE m_inf, tau_m, h_inf, tau_h 
} 
 
UNITS { 
	(mA) = (milliamp) 
	(mV) = (millivolt) 
} 
 
PARAMETER { 



	Aalpha_m = -0.3 (/ms-mV)
	Kalpha_m = -10 (mV)
	V0alpha_m = -19 (mV)
	
	Abeta_m = 12 (/ms)
	Kbeta_m = -18.182 (mV)
	V0beta_m = -44 (mV)

	Aalpha_h = 0.105 (/ms)
	Kalpha_h = -3.333 (mV)
	V0alpha_h = -44 (mV)
 
	Abeta_h = 1.5 (/ms)
	Kbeta_h = -5 (mV)
	V0beta_h = -11 (mV)

	v (mV) 
	gnabar= 0.013 (mho/cm2)
	ena = 87.39 (mV) 
	celsius = 30 (degC) 
} 

STATE { 
	m 
	h 
} 

ASSIGNED { 
	ina (mA/cm2) 
	m_inf 
	h_inf 
	tau_m (ms) 
	tau_h (ms) 
	g (mho/cm2) 
	alpha_m (/ms)
	beta_m (/ms)
	alpha_h (/ms)
	beta_h (/ms)
} 
 
INITIAL { 
	rate(v) 
	m = m_inf 
	h = h_inf 
} 
 
BREAKPOINT { 
	SOLVE states METHOD derivimplicit 
	g = gnabar*m*m*m*h 
	ina = g*(v - ena)
	alpha_m = alp_m(v)
	beta_m = bet_m(v) 
	alpha_h = alp_h(v)
	beta_h = bet_h(v) 
} 
 
DERIVATIVE states { 
	rate(v) 
	m' =(m_inf - m)/tau_m 
	h' =(h_inf - h)/tau_h 
} 
 
FUNCTION alp_m(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-20(degC))/10(degC)) 
	alp_m = Q10*Aalpha_m*linoid(v-V0alpha_m,Kalpha_m) 
} 
 
FUNCTION bet_m(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-20(degC))/10(degC)) 
	bet_m = Q10*Abeta_m*exp((v-V0beta_m)/Kbeta_m) 
} 
 
FUNCTION alp_h(v(mV))(/ms) { LOCAL Q10
	Q10 = 3^((celsius-20(degC))/10(degC)) 
	alp_h = Q10*Aalpha_h*exp((v-V0alpha_h)/Kalpha_h) 
} 
 
FUNCTION bet_h(v(mV))(/ms) { LOCAL Q10 
	Q10 = 3^((celsius-20(degC))/10(degC)) 
	bet_h = Q10*Abeta_h/(1+exp((v-V0beta_h)/Kbeta_h))
} 
 
PROCEDURE rate(v (mV)) {LOCAL a_m, b_m, a_h, b_h 
	TABLE m_inf, tau_m, h_inf, tau_h 
	DEPEND Aalpha_m, Kalpha_m, V0alpha_m, 
	       Abeta_m, Kbeta_m, V0beta_m,
               Aalpha_h, Kalpha_h, V0alpha_h,
               Abeta_h, Kbeta_h, V0beta_h, celsius FROM -100 TO 100 WITH 200 
	a_m = alp_m(v)  
	b_m = bet_m(v) 
	a_h = alp_h(v)  
	b_h = bet_h(v) 
	m_inf = a_m/(a_m + b_m) 
	tau_m = 1/(a_m + b_m) 
	h_inf = a_h/(a_h + b_h) 
	tau_h = 1/(a_h + b_h) 
} 

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)
        }
}