model of DCN pyramidal neuron
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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
:
: <closed> + n cai <-> <open> (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.
:
: Modifications by Arthur Houweling for use in MyFirstNEURON
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
THREADSAFE
SUFFIX kpksk
USEION k READ ek WRITE ik
USEION ca READ cai
RANGE m_inf, tau_m, gbar, gk
GLOBAL beta, cac
RANGE ik
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(molar) = (1/liter)
(mM) = (millimolar)
}
PARAMETER {
v (mV)
celsius (degC)
dt (ms)
ek (mV)
cai (mM)
gbar = .01 (mho/cm2)
beta = 0.002 (1/ms) : backward rate constant
cac = 0.010 (mM) : middle point of activation fct
taumin = 0.1 (ms) : minimal value of the time cst
}
STATE {
m
}
ASSIGNED {
ik (mA/cm2)
gk (mho/cm2)
m_inf
tau_m (ms)
tadj ()
}
BREAKPOINT {
SOLVE states :METHOD euler
gk = gbar * m*m
ik = gk * (v - ek)
}
:DERIVATIVE states {
: evaluate_fct(v,cai)
:
: m'= (m_inf-m) / tau_m
:}
PROCEDURE states() {
evaluate_fct(v,cai)
m= m + (1-exp(-dt/tau_m))*(m_inf-m)
}
INITIAL {
:
: activation kinetics are assumed to be at 22 deg. C
: Q10 is assumed to be 3
:
tadj = 3 ^ ((celsius-22.0)/10 (degC))
evaluate_fct(v,cai)
m = m_inf
}
PROCEDURE evaluate_fct(v(mV),cai(mM)) { LOCAL car
car = (cai/cac)^2
m_inf = car / ( 1 + car )
tau_m = 1 / beta / (1 + car) / tadj
if(tau_m < taumin) { tau_m = taumin } : min value of time cst
}