COMMENT
26 Ago 2002 Modification of original channel to allow variable time step and to correct an initialization error.
    Done by Michael Hines(michael.hines@yale.e) and Ruggero Scorcioni(rscorcio@gmu.edu) at EU Advance Course in Computational Neuroscience. Obidos, Portugal

na.mod

Sodium channel, Hodgkin-Huxley style kinetics.  

Kinetics were fit to data from Huguenard et al. (1988) and Hamill et
al. (1991)

qi is not well constrained by the data, since there are no points
between -80 and -55.  So this was fixed at 5 while the thi1,thi2,Rg,Rd
were optimized using a simplex least square proc

voltage dependencies are shifted approximately from the best
fit to give higher threshold

Author: Zach Mainen, Salk Institute, 1994, zach@salk.edu

May 2006: set the tha -28 mV, vshift 0 and thinf -55 mV to comply with measured 
Somatic Na+ kinetics in neocortex. Kole, ANU, 2006

ENDCOMMENT

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

NEURON {
	SUFFIX nat : renenamed to account for transient behaviour (Armin, Jul 09)
	USEION na READ ena WRITE ina
	RANGE m, h, gna, gbar, vshift, vshift2, timefactor_m, timefactor_h,gbarfactor, ina
	GLOBAL tha, thi1, thi2, qa, qi, qinf, thinf
	RANGE minf, hinf, mtau, htau
	GLOBAL Ra, Rb, Rd, Rg
	GLOBAL q10, temp, tadj, vmin, vmax
}

PARAMETER {
	gbar = 0   	(pS/um2)	: 0.12 mho/cm2
	vshift = 0	(mV)		: voltage shift
	vshift2 = 0	(mV)		: voltage shift 2
	
	tha  = -28	(mV)		: v 1/2 for act		(-42)
	qa   = 9	(mV)			: act slope		
	Ra   = 0.182	(/ms)	: open (v)		
	Rb   = 0.124	(/ms)	: close (v)		

	thi1  = -50	(mV)		: v 1/2 for inact 	
	thi2  = -75	(mV)		: v 1/2 for inact 	
	qi   = 5	(mV)	        	: inact tau slope
	thinf  = -55	(mV)		: inact inf slope	
	qinf  = 6.2	(mV)		: inact inf slope
	Rg   = 0.0091	(/ms)	: inact (v)	
	Rd   = 0.024	(/ms)	: inact recov (v) 

	temp = 23	(degC)		: original temp 
	q10  = 2.3			: temperature sensitivity

	v 		(mV)
	dt		(ms)
	celsius		(degC)
	vmin = -120	(mV)
	vmax = 100	(mV)
	
	gbarfactor = 1
	timefactor_m = 1		: increase, decrease the speed of the the activation of the channels
	timefactor_h = 1		: increase, decrease the speed of the the activation of the channels
}


UNITS {
	(mA) = (milliamp)
	(mV) = (millivolt)
	(pS) = (picosiemens)
	(um) = (micron)
} 

ASSIGNED {
	ina 		(mA/cm2)
	gna		(pS/um2)
	ena		(mV)
	minf 		hinf
	mtau (ms)	htau (ms)
	tadj
}
 

STATE { m h }

INITIAL { 
	trates(v-vshift-vshift2)
	m = minf
	h = hinf
}

BREAKPOINT {

	SOLVE states METHOD cnexp
    gna = gbarfactor*tadj*gbar*m*m*m*h
	ina = (1e-4) * gna * (v - ena)
} 

LOCAL mexp, hexp 

DERIVATIVE states {   :Computes state variables m, h, and n 
        trates(v-vshift-vshift2)      :             at the current v and dt.
        m' =  (minf-m)/(timefactor_m*mtau)
        h' =  (hinf-h)/(timefactor_h*htau)
}

PROCEDURE trates(v) {  
                      
        
    TABLE minf,  hinf, mtau, htau
	DEPEND  celsius, temp, Ra, Rb, Rd, Rg, tha, thi1, thi2, qa, qi, qinf
	
	FROM vmin TO vmax WITH 199

	rates(v): not consistently executed from here if usetable == 1

:        tinc = -dt * tadj

:        mexp = 1 - exp(tinc/mtau)
:        hexp = 1 - exp(tinc/htau)
}


PROCEDURE rates(vm) {  
        LOCAL  a, b

	a = trap0(vm,tha,Ra,qa)
	b = trap0(-vm,-tha,Rb,qa)

        tadj = q10^((celsius - temp)/10)

	mtau = 1/tadj/(a+b)
	minf = a/(a+b)

		:"h" inactivation 

	a = trap0(vm,thi1,Rd,qi)
	b = trap0(-vm,-thi2,Rg,qi)
	htau = 1/tadj/(a+b)
	hinf = 1/(1+exp((vm-thinf)/qinf))
}


FUNCTION trap0(v,th,a,q) {
	if (fabs(v/th) > 1e-6) {
	        trap0 = a * (v - th) / (1 - exp(-(v - th)/q))
	} else {
	        trap0 = a * q
 	}
}