LTP in cerebellar mossy fiber-granule cell synapses (Saftenku 2002)

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Accession:51196
We simulated synaptic transmission and modified a simple model of long-term potentiation (LTP) and long-term depression (LTD) in order to describe long-term plasticity related changes in cerebellar mossy fiber-granule cell synapses. In our model, protein autophosphorylation, leading to the maintenance of long-term plasticity, is controlled by Ca2+ entry through the NMDA receptor channels. The observed nonlinearity in the development of long-term changes of EPSP in granule cells is explained by the difference in the rate constants of two independent autocatalytic processes.
Reference:
1 . Saftenku EE (2002) A simplified model of long-term plasticity in cerebellar mossy fiber-granule cell synapses. Neurophysiology/Neirofiziologiya 34:216-218
Model Information (Click on a link to find other models with that property)
Model Type: Synapse;
Brain Region(s)/Organism:
Cell Type(s):
Channel(s):
Gap Junctions:
Receptor(s): AMPA; NMDA;
Gene(s):
Transmitter(s):
Simulation Environment: NEURON;
Model Concept(s): Simplified Models; Long-term Synaptic Plasticity; Maintenance;
Implementer(s): Saftenku, Elena [esaft at biph.kiev.ua];
Search NeuronDB for information about:  AMPA; NMDA;
TITLE Cerebellum Granule Cell Model, Na channel

COMMENT
Reference: E.D'Angelo, T.Nieus, A. Maffei, S. Armano, P. Rossi,
V. Taglietti, A. Fontana, G. Naldi "Theta-frequency bursting and 
resonance in cerebellar granule cells: experimental evidence and 
modeling of a slow K+-dependent mechanism", J. neurosci., 2001,
21,P. 759-770.
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)

	gnabar= 0.013 (mho/cm2)
 } 

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)
      ena (mV)
      celsius (degC) 
      v (mV) 
} 
 
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)) 
if((v-V0beta_m)/Kbeta_m >200){
bet_m = Q10*Abeta_m*exp(200)
}else{
	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))
if((v-V0alpha_h)/Kalpha_h>200){
alp_h = Q10*Aalpha_h*exp(200) 
}else{
	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)) 
if((v-V0beta_h)/Kbeta_h >200){
bet_h = Q10*Abeta_h/(1+exp(200))
}else{
	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{
if(x/y>200){
linoid = x/(exp(200) - 1)
}else{
                linoid = x/(exp(x/y) - 1)
}
        }
}


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