COMMENT
kv.mod
Potassium channel, HodgkinHuxley style kinetics
Kinetic rates based roughly on Sah et al. and Hamill et al. (1991)
Author: Zach Mainen, Salk Institute, 1995, zach@salk.edu
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
20110202 made threadsafe by Ted Carnevale
20120514 fixed singularity in PROCEDURE rates
Special comment:
This mechanism was designed to be run at a single operating
temperature37 deg Cwhich can be specified by the hoc
assignment statement
celsius = 37
This mechanism is not intended to be used at other temperatures,
or to investigate the effects of temperature changes.
Zach Mainen created this particular model by adapting conductances
from lower temperature to run at higher temperature, and found it
necessary to reduce the temperature sensitivity of spike amplitude
and time course. He accomplished this by increasing the net ionic
conductance through the heuristic of changing the standard HH
formula
g = gbar*product_of_gating_variables
to
g = tadj*gbar*product_of_gating_variables
where
tadj = q10^((celsius  temp)/10)
temp is the "reference temperature" (at which the gating variable
time constants were originally determined)
celsius is the "operating temperature"
Users should note that this is equivalent to changing the channel
density from gbar at the "reference temperature" temp (the
temperature at which the at which the gating variable time
constants were originally determined) to tadj*gbar at the
"operating temperature" celsius.
ENDCOMMENT
NEURON {
THREADSAFE
SUFFIX kv
USEION k READ ek WRITE ik
RANGE n, gk, gbar
RANGE ninf, ntau
GLOBAL Ra, Rb
GLOBAL q10, temp, tadj, vmin, vmax
}
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(pS) = (picosiemens)
(um) = (micron)
}
PARAMETER {
gbar = 5 (pS/um2) : 0.03 mho/cm2
tha = 25 (mV) : v 1/2 for inf
qa = 9 (mV) : inf slope
Ra = 0.02 (/ms) : max act rate
Rb = 0.002 (/ms) : max deact rate
: dt (ms)
temp = 23 (degC) : original temp
q10 = 2.3 : temperature sensitivity
vmin = 120 (mV)
vmax = 100 (mV)
}
ASSIGNED {
v (mV)
celsius (degC)
a (/ms)
b (/ms)
ik (mA/cm2)
gk (pS/um2)
ek (mV)
ninf
ntau (ms)
tadj
}
STATE { n }
INITIAL {
tadj = q10^((celsius  temp)/(10 (degC))) : make all threads calculate tadj at initialization
trates(v)
n = ninf
}
BREAKPOINT {
SOLVE states METHOD cnexp
gk = tadj*gbar*n
ik = (1e4) * gk * (v  ek)
}
DERIVATIVE states { :Computes state variable n
trates(v) : at the current v and dt.
n' = (ninfn)/ntau
}
PROCEDURE trates(v (mV)) { :Computes rate and other constants at current v.
:Call once from HOC to initialize inf at resting v.
TABLE ninf, ntau
DEPEND celsius, temp, Ra, Rb, tha, qa
FROM vmin TO vmax WITH 199
rates(v): not consistently executed from here if usetable_hh == 1
: tinc = dt * tadj
: nexp = 1  exp(tinc/ntau)
}
UNITSOFF
PROCEDURE rates(v (mV)) { :Computes rate and other constants at current v.
:Call once from HOC to initialize inf at resting v.
: singular when v = tha
: a = Ra * (v  tha) / (1  exp((v  tha)/qa))
: a = Ra * qa*((v  tha)/qa) / (1  exp((v  tha)/qa))
: a = Ra * qa*((v  tha)/qa) / (exp((v  tha)/qa)  1)
a = Ra * qa * efun((v  tha)/qa)
: singular when v = tha
: b = Rb * (v  tha) / (1  exp((v  tha)/qa))
: b = Rb * qa*((v  tha)/qa) / (1  exp((v  tha)/qa))
: b = Rb * qa*((v  tha)/qa) / (exp((v  tha)/qa)  1)
b = Rb * qa * efun((v  tha)/qa)
tadj = q10^((celsius  temp)/10)
ntau = 1/tadj/(a+b)
ninf = a/(a+b)
}
UNITSON
FUNCTION efun(z) {
if (fabs(z) < 1e4) {
efun = 1  z/2
}else{
efun = z/(exp(z)  1)
}
}
