TITLE anomalous rectifier channel
COMMENT
:
: Anomalous Rectifier Ih - cation (Na/K) channel in thalamocortical neurons
:
: Kinetic model of calcium-induced shift in the activation of Ih channels.
: Model of Destexhe et al., Biophys J. 65: 1538-1552, 1993, based on the
: voltage-clamp data on the calcium dependence of If in heart cells
: (Harigawa & Irisawa, J. Physiol. 409: 121, 1989)
:
: The voltage-dependence is derived from Huguenard & McCormick,
: J Neurophysiol. 68: 1373-1383, 1992, based on voltage-clamp data of
: McCormick & Pape, J. Physiol. 431: 291, 1990.
:
: Modified model of the binding of calcium through a calcium-binding (CB)
: protein, which in turn acts on Ih channels. This model was described in
: detail in the following reference:
: Destexhe, A., Bal, T., McCormick, D.A. and Sejnowski, T.J. Ionic
: mechanisms underlying synchronized oscillations and propagating waves
: in a model of ferret thalamic slices. Journal of Neurophysiology 76:
: 2049-2070, 1996.
: See also http://www.cnl.salk.edu/~alain , http://cns.fmed.ulaval.ca
:
: KINETIC MODEL:
:
: Normal voltage-dependent opening of Ih channels:
:
: c1 (closed) <-> o1 (open) ; rate cst alpha(V),beta(V)
:
: Ca++ binding on CB protein
:
: p0 (inactive) + nca Ca <-> p1 (active) ; rate cst k1,k2
:
: Binding of active CB protein on the open form (nexp binding sites) :
:
: o1 (open) + nexp p1 <-> o2 (open) ; rate cst k3,k4
:
:
: PARAMETERS:
: It is more useful to reformulate the parameters k1,k2 into
: k2 and cac = (k2/k1)^(1/nca) = half activation calcium dependence,
: and idem for k3,k4 into k4 and Pc = (k4/k3)^(1/nexp) = half activation
: of Ih binding (this is like dealing with tau_m and m_inf instead of
: alpha and beta in Hodgkin-Huxley equations)
: - k2: this rate constant is the inverse of the real time constant of
: the binding of Ca to the CB protein
: - cac: the half activation (affinity) of the CB protein;
: around 1 to 10 microM.
: - k4: this rate constant is the inverse of the real time constant of
: the binding of the CB protein to Ih channels
: very low: it basically governs the interspindle period
: - Pc: the half activation (affinity) of the Ih channels for the
: CB protein;
: - nca: number of binding sites of calcium on CB protein; usually 4
: - nexp: number of binding sites on Ih channels
: - ginc: augmentation of conductance associated with the Ca bound state
: (about 2-3; see Harigawa & Hirisawa, 1989)
:
:
: IMPORTANT REMARKS:
: - This simple model for the binding of Ca++ on the open channel
: suffies to account for the shift in the voltage-dependence of Ih
: activation with calcium (see details in Destexhe et al, 1993).
: - It may be that calcium just binds to the Ih channel, preventing the
: conformational change between open and closed; in this case one
: should take into account binding on the closed state, which is
: neglected here.
:
: MODIFICATIONS
: - this file also contains a procedure ("activation") to estimate
: the steady-state activation of the current; callable from outside
: - the time constant now contains a changeable minimal value (taum)
: - shift: new local variable to displace the voltage-dependence
: (shift>0 -> depolarizing shift)
:
:
: Alain Destexhe, Salk Institute and Laval University, 1995
:
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
SUFFIX iar
USEION h READ eh WRITE ih VALENCE 1
USEION ca READ cai
RANGE ghbar, h_inf, tau_s, m, shift
GLOBAL k2, cac, k4, Pc, nca, nexp, ginc, taum
}
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(mA) = (milliamp)
(mV) = (millivolt)
(msM) = (ms mM)
}
PARAMETER {
eh = -40 (mV)
celsius = 36 (degC)
ghbar = 2e-5 (mho/cm2)
cac = 0.002 (mM) : half-activation of calcium dependence
k2 = 0.0004 (1/ms) : inverse of time constant
Pc = 0.01 : half-activation of CB protein dependence
k4 = 0.001 (1/ms) : backward binding on Ih
nca = 4 : number of binding sites of ca++
nexp = 1 : number of binding sites on Ih channels
ginc = 2 : augmentation of conductance with Ca++
taum = 20 (ms) : min value of tau
shift = 0 (mV) : shift of Ih voltage-dependence
}
STATE {
c1 : closed state of channel
o1 : open state
o2 : CB-bound open state
p0 : resting CB
p1 : Ca++-bound CB
}
ASSIGNED {
v (mV)
cai (mM)
ih (mA/cm2)
gh (mho/cm2)
h_inf
tau_s (ms)
alpha (1/ms)
beta (1/ms)
k1ca (1/ms)
k3p (1/ms)
m
tadj
}
BREAKPOINT {
SOLVE ihkin METHOD sparse
m = o1 + ginc * o2
ih = ghbar * m * (v - eh)
}
KINETIC ihkin {
:
: Here k1ca and k3p are recalculated at each call to evaluate_fct
: because Ca or p1 have to be taken at some power and this does
: not work with the KINETIC block.
: So the kinetics is actually equivalent to
: c1 <-> o1
: p0 + nca Cai <-> p1
: o1 + nexp p1 <-> o2
evaluate_fct(v,cai)
~ c1 <-> o1 (alpha,beta)
~ p0 <-> p1 (k1ca,k2)
~ o1 <-> o2 (k3p,k4)
CONSERVE p0 + p1 = 1
CONSERVE c1 + o1 + o2 = 1
}
INITIAL {
:
: Experiments of McCormick & Pape were at 36 deg.C
: Q10 is assumed equal to 3
:
tadj = 3.0 ^ ((celsius-36 (degC) )/10 (degC) )
evaluate_fct(v,cai)
c1 = 1
o1 = 0
o2 = 0
p0 = 1
p1 = 0
}
UNITSOFF
PROCEDURE evaluate_fct(v (mV), cai (mM)) {
h_inf = 1 / ( 1 + exp((v+75-shift)/5.5) )
tau_s = (taum + 1000 / ( exp((v+71.5-shift)/14.2) + exp(-(v+89-shift)/11.6) ) ) / tadj
alpha = h_inf / tau_s
beta = ( 1 - h_inf ) / tau_s
k1ca = k2 * (cai/cac)^nca
k3p = k4 * (p1/Pc)^nexp
}
:
: procedure for evaluating the activation curve of Ih
:
PROCEDURE activation(v (mV), cai (mM)) { LOCAL cc
evaluate_fct(v,cai)
cc = 1 / (1 + (cac/cai)^nca ) : equil conc of CB-protein
m = 1 / ( 1 + beta/alpha + (cc/Pc)^nexp )
m = ( 1 + ginc * (cc/Pc)^nexp ) * m
}
UNITSON