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 http://www.cnl.salk.edu/~alain)
:
:   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 gbar, 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)
        gbar   = 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 = gbar * 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
}