TITLE Slow Ca-dependent cation current
                             :
                             :   Ca++ dependent nonspecific cation current ICAN
                             :   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)
                             :   ---------------------------------------------
                             :
                             :   Kinetics based on: Partridge & Swandulla, TINS 11: 69-72, 1988.
                             :
                             :   This current has the following properties:
                             :      - inward current (non specific for cations Na, K, Ca, ...)
                             :      - 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
                             :

                             INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}

                             NEURON {
                                     SUFFIX ican
                                     USEION n READ en WRITE in VALENCE 1
                                     USEION ca READ cai
                                     RANGE gbar, m_inf, tau_m, in
                                     GLOBAL beta, cac, taumin
                             }


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


                             PARAMETER {
                                     v               (mV)
                                     celsius = 36    (degC)
                                     en      = -20   (mV)            : reversal potential
                                     cai     	     (mM)           : initial [Ca]i
                                     gbar    = 0.00025 (mho/cm2)
                                     beta    = 0.001 :0.002 (1/ms)          : backward rate constant
                                     cac     = 0.01  (mM)            : middle point of activation fct
                                     taumin  = 0.1   (ms)            : minimal value of time constant
                             }


                             STATE {
                                     m
                             }

                             ASSIGNED {
                                     in      (mA/cm2)
                                     m_inf
                                     tau_m   (ms)
                                     tadj
                             }

                             BREAKPOINT { 
                                     SOLVE states METHOD euler
                                     in = gbar * m*m * (v - en)
                             }

                             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 = 3.0 ^ ((celsius-22.0)/10)

                                     evaluate_fct(v,cai)
                                     m = m_inf
                             }


                             PROCEDURE evaluate_fct(v(mV),cai(mM)) {  LOCAL alpha2

                                     alpha2 = beta * (cai/cac)^2

                                     tau_m = 1 / (alpha2 + beta) / tadj
                                     m_inf = alpha2 / (alpha2 + beta)

                                     if(tau_m < taumin) { tau_m = taumin }   : min value of time cst
                             }
                             UNITSON