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)
}
}