TITLE Voltagegated potassium channel from Kv4 subunits
COMMENT
NEURON implementation of a potassium channel from Kv4
Kinetical Scheme: HodgkinHuxley m^4*h
DATA TAKEN FROM:
Atype potassium currents active at subthreshold potentials in mouse cerebellar Purkinje cells
Sacco et Tempia, J Physiol 543: 505520, 2002
ACTIVATION:
The rate constants of activation and deactivation were approximated by the following formulas
alphan = can * exp((v+cvan)/ckan)
betan = cbn * exp((v+cvbn)/ckbn)
Parameters can, cvan, ckan, cbn, cvbn, ckbn
were determined from least squarefits to experimental data of G/Gmax(v) and taun(v).
Values are given in the CONSTANT block.
INACTIVATION:
The model includes only the fast component of inactivation
The voltage dependency of the rate constants was approximated by the following formulas
alphah = cah / (1+exp((v+cvah)/ckah))
betah = cbh / (1+exp((v+cvbh)/ckbh))
Parameters cah, cvah, ckah, cbh, cvbh, ckbh
were determined from least squarefits to experimental data of G/Gmax(v) and tauh(v).:
Values are given in the CONSTANT block.
Model includes calculation of gating current
Reference: Akemann et al., Biophys. J. (2009) 96: 39593976
Laboratory for Neuronal Circuit Dynamics
RIKEN Brain Science Institute, Wako City, Japan
http://www.neurodynamics.brain.riken.jp
Date of Implementation: April 2007
Contact: akemann@brain.riken.jp
ENDCOMMENT
NEURON {
SUFFIX Kv4
USEION k READ ek WRITE ik
NONSPECIFIC_CURRENT i
RANGE gbar, g, ik, i, igate, nc
GLOBAL ninf, taun, hinf, tauh
GLOBAL gateCurrent, gunit
}
UNITS {
(mV) = (millivolt)
(mA) = (milliamp)
(nA) = (nanoamp)
(pA) = (picoamp)
(S) = (siemens)
(nS) = (nanosiemens)
(pS) = (picosiemens)
(um) = (micron)
(molar) = (1/liter)
(mM) = (millimolar)
}
CONSTANT {
e0 = 1.60217646e19 (coulombs)
q10 = 2.7
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)
zn = 1.4736 (1) : valence of ngate
zh = 5.4726 (1) : valence of hgate
}
PARAMETER {
gateCurrent = 0 (1) : gating currents ON = 1 OFF = 0
gbar = 0.004 (S/cm2) <0,1e9>
gunit = 16 (pS) : unitary conductance
}
ASSIGNED {
celsius (degC)
v (mV)
ik (mA/cm2)
i (mA/cm2)
igate (mA/cm2)
ek (mV)
g (S/cm2)
nc (1/cm2) : membrane density of channel
qt (1)
ninf (1)
taun (ms)
alphan (1/ms)
betan (1/ms)
hinf (1)
tauh (ms)
alphah (1/ms)
betah (1/ms)
}
STATE { n h }
INITIAL {
nc = (1e12) * gbar / gunit
qt = q10^((celsius22 (degC))/10 (degC))
rates(v)
n = ninf
h = hinf
}
BREAKPOINT {
SOLVE states METHOD cnexp
g = gbar * n^4 * h
ik = g * (v  ek)
igate = nc * (1e6) * e0 * ( 4 * zn * ngateFlip() + zh * hgateFlip() )
if (gateCurrent != 0) {
i = igate
}
}
DERIVATIVE states {
rates(v)
n' = (ninfn)/taun
h' = (hinfh)/tauh
}
PROCEDURE rates(v (mV)) {
alphan = alphanfkt(v)
betan = betanfkt(v)
ninf = alphan / (alphan + betan)
taun = 1 / (qt*(alphan + betan))
alphah = alphahfkt(v)
betah = betahfkt(v)
hinf = alphah / (alphah + betah)
tauh = 1 / (qt*(alphah + betah))
}
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 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))
}
FUNCTION ngateFlip() (1/ms) {
ngateFlip = (ninfn)/taun
}
FUNCTION hgateFlip() (1/ms) {
hgateFlip = (hinfh)/tauh
}
