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ITGHK.mod
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ITGHK.mod
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TITLE Low threshold calcium current
:
: Ca++ current responsible for low threshold spikes (LTS)
: Differential equations
:
: Model of Huguenard & McCormick, J Neurophysiol 68: 1373-1383, 1992.
: The kinetics is described by Goldman-Hodgkin-Katz equations,
: using a m2h format, according to the voltage-clamp data
: (whole cell patch clamp) of Huguenard & Prince, J. Neurosci.
: 12: 3804-3817, 1992.
:
: This model is described in detail in:
: Destexhe A, Neubig M, Ulrich D and Huguenard JR.
: Dendritic low-threshold calcium currents in thalamic relay cells.
: Journal of Neuroscience 18: 3574-3588, 1998.
: (a postscript version of this paper, including figures, is available on
: the Internet at http://cns.fmed.ulaval.ca)
:
: - shift parameter for screening charge
: - empirical correction for contamination by inactivation (Huguenard)
: - GHK equations
:
:
: Written by Alain Destexhe, Laval University, 1995
:
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX itGHK
USEION ca READ cai,cao WRITE ica
RANGE pcabar, m_inf, tau_m, h_inf, tau_h, shift, actshift
GLOBAL qm, qh
}
UNITS {
(molar) = (1/liter)
(mV) = (millivolt)
(mA) = (milliamp)
(mM) = (millimolar)
FARADAY = (faraday) (coulomb)
R = (k-mole) (joule/degC)
}
PARAMETER {
v (mV)
celsius = 36 (degC)
pcabar =.2e-3 (cm/s) : Maximum Permeability
shift = 2 (mV) : corresponds to 2mM ext Ca++
actshift = 0 (mV) : shift of activation curve (towards hyperpol)
cai = 2.4e-4 (mM) : adjusted for eca=120 mV
cao = 2 (mM)
qm = 5 : q10's for activation and inactivation
qh = 3 : from Coulter et al., J Physiol 414: 587, 1989
}
STATE {
m h
}
ASSIGNED {
ica (mA/cm2)
m_inf
tau_m (ms)
h_inf
tau_h (ms)
phi_m
phi_h
}
BREAKPOINT {
SOLVE castate METHOD cnexp
ica = pcabar * m*m*h * ghk(v, cai, cao)
}
DERIVATIVE castate {
evaluate_fct(v)
m' = (m_inf - m) / tau_m
h' = (h_inf - h) / tau_h
}
UNITSOFF
INITIAL {
phi_m = qm ^ ((celsius-24)/10)
phi_h = qh ^ ((celsius-24)/10)
evaluate_fct(v)
m = m_inf
h = h_inf
}
PROCEDURE evaluate_fct(v(mV)) {
:
: The kinetic functions are taken as described in the model of
: Huguenard & McCormick, and corresponds to a temperature of 23-25 deg.
: Transformation to 36 deg assuming Q10 of 5 and 3 for m and h
: (as in Coulter et al., J Physiol 414: 587, 1989).
:
: The activation functions were estimated by John Huguenard.
: The V_1/2 were of -57 and -81 in the vclamp simulations,
: and -60 and -84 in the current clamp simulations.
:
: The activation function were empirically corrected in order to account
: for the contamination of inactivation. Therefore the simulations
: using these values reproduce more closely the voltage clamp experiments.
: (cfr. Huguenard & McCormick, J Neurophysiol, 1992).
:
m_inf = 1.0 / ( 1 + exp(-(v+shift+actshift+57)/6.2) )
h_inf = 1.0 / ( 1 + exp((v+shift+81)/4.0) )
tau_m = ( 0.612 + 1.0 / ( exp(-(v+shift+actshift+132)/16.7) + exp((v+shift+actshift+16.8)/18.2) ) ) / phi_m
if( (v+shift) < -80) {
tau_h = exp((v+shift+467)/66.6) / phi_h
} else {
tau_h = ( 28 + exp(-(v+shift+22)/10.5) ) / phi_h
}
}
FUNCTION ghk(v(mV), ci(mM), co(mM)) (.001 coul/cm3) {
LOCAL z, eci, eco
z = (1e-3)*2*FARADAY*v/(R*(celsius+273.15))
eco = co*efun(z)
eci = ci*efun(-z)
:high cao charge moves inward
:negative potential charge moves inward
ghk = (.001)*2*FARADAY*(eci - eco)
}
FUNCTION efun(z) {
if (fabs(z) < 1e-4) {
efun = 1 - z/2
}else{
efun = z/(exp(z) - 1)
}
}
FUNCTION nongat(v,cai,cao) { : non gated current
nongat = pcabar * ghk(v, cai, cao)
}
UNITSON