TITLE Hyperpolarization-activated current Ih
COMMENT
Model of the Hyperpolarization-activated current Ih, also called
the "Anomalous Rectifier". Cationic (Na/K) channel based on
data from thalamic relay neurons.
Voltage dependence: derived from the data and models given in
Huguenard & McCormick, J Neurophysiol. 68: 1373-1383, 1992, based
on voltage-clamp characterization of the Ih current in thalamic
neurons by McCormick & Pape, J. Physiol. 431: 291, 1990.
Calcium regulation: the model includes one of the features of Ih in
thalamic neurons (and elsewhere), which is the regulation of this
current by intracellular calcium. Voltage-clamp experiments of
Ih in heart cells (Harigawa & Irisawa, J. Physiol. 409: 121, 1989)
showed that intracellular calcium induces a shift in the voltage-
dependent activation of the current. This shift can be reproduced
by assuming that calcium binds only to the open state of the
channel, "locking" Ih in the open configuration (see Destexhe et
al., Biophys J. 65: 1538-1552, 1993). It was later found that
calcium does not bind directly to Ih, but cAMP binds to the open
state of the channel, and cAMP production is stimulated by
calcium (Luthi and McCormick, Nat. Neurosci. 2: 634-641, 1999).
The present model simulates such "indirect" regulation by calcium
and is a modified version from the model given in Destexhe et al.,
J. Neurophysiol. 76: 2049-2070, 1996.
See also http://cns.iaf.cnrs-gif.fr
KINETIC MODEL:
Normal voltage-dependent opening of Ih channels:
c1 (closed) <-> o1 (open) ; rate cst alpha(V),beta(V)
Ca++ binding on second messenger
p0 (inactive) + nca Ca <-> p1 (active) ; rate cst k1,k2
Binding of active messenger 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 2nd messenger
- cac: the half activation (affinity) of the 2nd messenger;
around 1 to 10 microM.
- k4: this rate constant is the inverse of the real time constant of
the binding of the 2nd messenger to Ih channels
very low, of the order of seconds (Luthi and McCormick, 1999)
- Pc: the half activation (affinity) of the Ih channels for the
2nd messenger;
- nca: number of binding sites of calcium on 2nd messenger; 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)
Alain Destexhe, destexhe@iaf.cnrs-gif.fr
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, o1, o2, p0, p1
GLOBAL k2, cac, k4, Pc, nca, nexp, ginc, taum
}
UNITS {
(molar) = (1/liter)
(mM) = (millimolar)
(mA) = (milliamp)
(mV) = (millivolt)
(msM) = (ms mM)
}
PARAMETER {
eh = -20 (mV)
celsius = 36 (degC)
ghbar = 2e-5 (mho/cm2)
cac = 0.006 (mM) : half-activation of calcium dependence
k2 = 0.0001 (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