TITLE Voltage-gated potassium channel from Kv4 subunits

COMMENT
Gabriela Cirtala, May 15, 2024
Our modelling approach of Kv4 follows the experimental data in (Sacco et al, 2002, Journal of Physiology)
and (Gunay et al, 2008, The Journal of Neuroscience). Both these works show a fast and slow component of Kv4,
which in these mod files we refer to as Kv4f and Kv4s.
Kv4 total = Kv4f + Kv4s

NEURON implementation of a potassium channel from Kv4 subunits
Kv4 activation from Sacco inactivation from SD
Yunliang Zang April 16th 2015
activation from
Channel Density Distributions Explain Spiking Variability in the Globus Pallidus: A Combined Physiology and Computer Simulation Database Approach

ENDCOMMENT

NEURON {
	SUFFIX Kv4
	USEION k READ ek WRITE ik
	RANGE gk, gbar, ik,vshift
:   GLOBAL ninf, taun, hinf, tauh
:    THREADSAFE
}

UNITS {
	(mV) = (millivolt)
	(mA) = (milliamp)
	(nA) = (nanoamp)
	(pA) = (picoamp)
	(S)  = (siemens)
	(nS) = (nanosiemens)
	(pS) = (picosiemens)
	(um) = (micron)
	(molar) = (1/liter)
	(mM) = (millimolar)
}

CONSTANT {
	q10 = 3
	F = 9.6485e4 (coulombs)
	R = 8.3145 (joule/kelvin)
	can = 0.15743 (1/ms)
	cvan = 57 (mV)
	ckan = -32.19976 (mV)
	cbn = 0.15743 (1/ms)
	cvbn = 57 (mV)
	ckbn = 37.51346 (mV)


	cah = 0.01342 (1/ms)
	cvah = 60 (mV)
	ckah = -7.86476 (mV)
	cbh = 0.04477 (1/ms)
	cvbh = 54 (mV)
	ckbh = 11.3615 (mV)

	vh = -75.30348 (mV)
	kh = -6.06329 (mV)
	ki = 150 (mM)			:from Stephane
	ko = 2.5 (mM)
}

PARAMETER {
	v (mV)
	celsius (degC)
	vshift = 0
	gbar = 0.0039 (mho/cm2)   <0,1e9>
}

ASSIGNED {
	ik (mA/cm2)
	ek (mV)
	gk (mho/cm2)
	g (coulombs/cm3)

	T (kelvin)
	qt
	E (volt)
	zeta

	ninf
	taun (ms)
	alphan (1/ms)
	betan (1/ms)
	alphah (1/ms)
	betah (1/ms)

	hinf
:	h1inf
:	h2inf
	tauh (ms)
:	tauh2 (ms)
}

STATE { n h }

INITIAL {
	T = kelvinfkt (celsius)
	qt = q10^((celsius-23 (degC))/10 (degC))
	rates(v)
	n = ninf
	h = hinf
}

BREAKPOINT {
	SOLVE states METHOD cnexp
    gk = gbar * n*n*n*n*h
	ik = gk * (v - ek)
}

DERIVATIVE states {
	rates(v)
	n' = (ninf-n)/taun
	h' = (hinf-h)/tauh

}

PROCEDURE rates(v (mV)) {
	alphan = alphanfkt(v)
	betan = betanfkt(v)

: activation from Jager
	ninf = 1.0 / (1.0 + exp((-49 - v)/12.5))

	taun = 1/((alphan+betan)*qt)
	alphah = alphahfkt(v)
	betah = betahfkt(v)

	hinf = 1/(1+exp((v-(vh-vshift))/-kh))
	tauh =20/qt
	g = ghk(v, ki, ko, 1)
}

FUNCTION ghk( v (mV), ki (mM), ko (mM), z )  (coulombs/cm3) {
    E = (1e-3) * v
      zeta = (z*F*E)/(R*T)


    if ( fabs(1-exp(-zeta)) < 1e-6 ) {
        ghk = (1e-6) * (z*F) * (ki - ko*exp(-zeta)) * (1 + zeta/2)
    } else {
        ghk = (1e-6) * (z*zeta*F) * (ki - ko*exp(-zeta)) / (1-exp(-zeta))
    }
}


FUNCTION alphanfkt(v (mV)) (1/ms) {
	alphanfkt = can * exp(-(v+cvan)/ckan)
}

FUNCTION betanfkt(v (mV)) (1/ms) {
	betanfkt = cbn * exp(-(v+cvbn)/ckbn)
}

FUNCTION kelvinfkt( t (degC) )  (kelvin) {
    kelvinfkt = 273.19 + t
}
FUNCTION alphahfkt(v (mV))  (1/ms) {
	alphahfkt = cah / (1+exp(-(v+cvah)/ckah))
}

FUNCTION betahfkt(v (mV))  (1/ms)  {
	betahfkt = cbh / (1+exp(-(v+cvbh)/ckbh))
}