TITLE Cortical M current
: FORREST MD (2014) Two Compartment Model of the Cerebellar Purkinje Neuron
:
:   M-current, responsible for the adaptation of firing rate and the 
:   afterhyperpolarization (AHP) of cortical pyramidal cells
:
:   First-order model described by hodgkin-Hyxley like equations.
:   K+ current, activated by depolarization, noninactivating.
:
:   Model taken from Yamada, W.M., Koch, C. and Adams, P.R.  Multiple 
:   channels and calcium dynamics.  In: Methods in Neuronal Modeling, 
:   edited by C. Koch and I. Segev, MIT press, 1989, p 97-134.
:
:   See also: McCormick, D.A., Wang, Z. and Huguenard, J. Neurotransmitter 
:   control of neocortical neuronal activity and excitability. 
:   Cerebral Cortex 3: 387-398, 1993.
:
:   Written by Alain Destexhe, Laval University, 1995
:

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

NEURON {
	SUFFIX km
	USEION k READ ek WRITE ik
        RANGE gkbar, m_inf, tau_m, ik, taumax

}

UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
}


PARAMETER {
	v		(mV)
	celsius = 36    (degC)
	ek		(mV)
	gkbar	= 1e-6	(mho/cm2)
	taumax	= 1000	(ms)		: peak value of tau
}



STATE {
	m
}

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

BREAKPOINT {
	SOLVE states METHOD euler
	ik = gkbar * m * (v - ek)
}

DERIVATIVE states { 
	evaluate_fct(v)

	m' = (m_inf - m) / tau_m
}

UNITSOFF
INITIAL {
	evaluate_fct(v)
	m = 0
:
:  The Q10 value is assumed to be 2.3
:
        tadj = 2.3 ^ ((celsius-36)/10)
	tau_peak = taumax / tadj
}

PROCEDURE evaluate_fct(v(mV)) {

	m_inf = 1 / ( 1 + exptable(-(v+35)/10) )
	tau_m = tau_peak / ( 3.3 * exptable((v+35)/20) + exptable(-(v+35)/20) )
}
UNITSON


FUNCTION exptable(x) { 
	TABLE  FROM -25 TO 25 WITH 10000

	if ((x > -25) && (x < 25)) {
		exptable = exp(x)
	} else {
		exptable = 0.
	}
}