TITLE Slow Ca-dependent potassium current
:
:   Ca++ dependent K+ current IC responsible for slow AHP
:   Differential equations
:
:   Model based on a first order kinetic scheme
:
:       + n cai <->     (alpha,beta)
:
:   Following this model, the activation fct will be half-activated at 
:   a concentration of Cai = (beta/alpha)^(1/n) = cac (parameter)
:
:   The mod file is here written for the case n=2 (2 binding sites)
:   ---------------------------------------------
:
:   This current models the "slow" IK[Ca] (IAHP): 
:      - potassium current
:      - activated by intracellular calcium
:      - NOT voltage dependent
:
:   A minimal value for the time constant has been added
:
:   Ref: Destexhe et al., J. Neurophysiology 72: 803-818, 1994.
:   See also: http://www.cnl.salk.edu/~alain , http://cns.fmed.ulaval.ca
:   modifications by Yiota Poirazi 2001 (poirazi@LNC.usc.edu)
:   taumin = 0.5 ms instead of 0.1 ms	

NEURON {
        SUFFIX kca
        USEION k READ ek WRITE ik
        USEION ca READ cai
        RANGE gk, gbar, m_inf, tau_m,ik
        GLOBAL beta, cac
}


UNITS {
        (mA) = (milliamp)
        (mV) = (millivolt)
        (molar) = (1/liter)
        (mM) = (millimolar)
}


PARAMETER {
        v               (mV)
        celsius = 36    (degC)
        ek      = -80   (mV)
        cai     = 2.4e-5 (mM)           : initial [Ca]i
        gbar    = 0.01   (mho/cm2)
        beta    = 0.03   (1/ms)          : backward rate constant
        cac     = 0.00035  (mM)            : middle point of activation fct
        taumin  = 0.5    (ms)            : minimal value of the time cst
        gk
      }


STATE {m}        : activation variable to be solved in the DEs       

ASSIGNED {       : parameters needed to solve DE 
        ik      (mA/cm2)
        m_inf
        tau_m   (ms)
        tadj
}
BREAKPOINT { 
        SOLVE states METHOD derivimplicit
        gk = gbar*m*m*m     : maximum channel conductance
        ik = gk*(v - ek)    : potassium current induced by this channel
}

DERIVATIVE states { 
        evaluate_fct(v,cai)
        m' = (m_inf - m) / tau_m
}

UNITSOFF
INITIAL {
:
:  activation kinetics are assumed to be at 22 deg. C
:  Q10 is assumed to be 3
:
        tadj = 3 ^ ((celsius-22.0)/10) : temperature-dependent adjastment factor
        evaluate_fct(v,cai)
        m = m_inf
}

PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL car
        car = (cai/cac)^4
        m_inf = car / ( 1 + car )      : activation steady state value
        tau_m =  1 / beta / (1 + car) / tadj
        if(tau_m < taumin) { tau_m = taumin }   : activation min value of time cst
}
UNITSON