TITLE Hippocampal/cortical HH channels
COMMENT
Fast Na+ and K+ currents responsible for action potentials
Iterative equations
Equations modified by Traub, for Hippocampal Pyramidal cells, in:
Traub & Miles, Neuronal Networks of the Hippocampus, Cambridge, 1991
range variable vtraub adjust threshold
Written by Alain Destexhe, Salk Institute, Aug 1992
Modified Oct 96 for compatibility with Windows: trap low values of arguments
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX mchh2
USEION na READ ena WRITE ina
USEION k READ ek WRITE ik
RANGE gnabar, gkbar, vtraub
RANGE m_inf, h_inf, n_inf
RANGE tau_m, tau_h, tau_n
RANGE m_exp, h_exp, n_exp
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
}
PARAMETER {
gnabar = .003 (mho/cm2)
gkbar = .005 (mho/cm2)
ena = 50 (mV)
ek = -90 (mV)
celsius = 36 (degC)
dt (ms)
v (mV)
vtraub = -63 (mV)
}
STATE {
m h n
}
ASSIGNED {
ina (mA/cm2)
ik (mA/cm2)
il (mA/cm2)
m_inf
h_inf
n_inf
tau_m
tau_h
tau_n
m_exp
h_exp
n_exp
tadj
}
BREAKPOINT {
SOLVE states
ina = gnabar * m*m*m*h * (v - ena)
ik = gkbar * n*n*n*n * (v - ek)
}
:DERIVATIVE states { : exact Hodgkin-Huxley equations
: evaluate_fct(v)
: m' = (m_inf - m) / tau_m
: h' = (h_inf - h) / tau_h
: n' = (n_inf - n) / tau_n
:}
PROCEDURE states() { : exact when v held constant
evaluate_fct(v)
m = m + m_exp * (m_inf - m)
h = h + h_exp * (h_inf - h)
n = n + n_exp * (n_inf - n)
VERBATIM
return 0;
ENDVERBATIM
}
UNITSOFF
INITIAL {
:
: Q10 was assumed to be 3 for both currents
:
tadj = 3.0 ^ ((celsius-36)/ 10 )
m = 0
h = 0
n = 0
}
PROCEDURE evaluate_fct(v(mV)) { LOCAL a,b,v2
v2 = v - vtraub : convert to traub convention
: a = 0.32 * (13-v2) / ( Exp((13-v2)/4) - 1)
a = 0.32 * vtrap(13-v2, 4)
: b = 0.28 * (v2-40) / ( Exp((v2-40)/5) - 1)
b = 0.28 * vtrap(v2-40, 5)
tau_m = 1 / (a + b) / tadj
m_inf = a / (a + b)
a = 0.128 * Exp((17-v2)/18)
b = 4 / ( 1 + Exp((40-v2)/5) )
tau_h = 1 / (a + b) / tadj
h_inf = a / (a + b)
: a = 0.032 * (15-v2) / ( Exp((15-v2)/5) - 1)
a = 0.032 * vtrap(15-v2, 5)
b = 0.5 * Exp((10-v2)/40)
tau_n = 1 / (a + b) / tadj
n_inf = a / (a + b)
m_exp = 1 - Exp(-dt/tau_m)
h_exp = 1 - Exp(-dt/tau_h)
n_exp = 1 - Exp(-dt/tau_n)
}
FUNCTION vtrap(x,y) {
if (fabs(x/y) < 1e-6) {
vtrap = y*(1 - x/y/2)
}else{
vtrap = x/(Exp(x/y)-1)
}
}
FUNCTION Exp(x) {
if (x < -100) {
Exp = 0
}else{
Exp = exp(x)
}
}