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```
COMMENT
kv.mod
Potassium channel, Hodgkin-Huxley style kinetics
Kinetic rates based roughly on Sah et al. and Hamill et al. (1991)
Author: Zach Mainen, Salk Institute, 1995, zach@salk.edu
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
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
v (mV)
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)
celsius (degC)
temp = 23 (degC) : original temp
q10 = 2.3 : temperature sensitivity
vmin = -120 (mV)
vmax = 100 (mV)
}
ASSIGNED {
a (/ms)
b (/ms)
ik (mA/cm2)
gk (pS/um2)
ek (mV)
ninf
ntau (ms)
tadj
}
STATE { n }
INITIAL {
trates(v)
n = ninf
}
BREAKPOINT {
SOLVE states
gk = tadj*gbar*n
ik = (1e-4) * gk * (v - ek)
}
LOCAL nexp
PROCEDURE states() { :Computes state variable n
trates(v) : at the current v and dt.
n = n + nexp*(ninf-n)
VERBATIM
return 0;
ENDVERBATIM
}
PROCEDURE trates(v) { :Computes rate and other constants at current v.
:Call once from HOC to initialize inf at resting v.
LOCAL tinc
TABLE ninf, nexp
DEPEND dt, celsius, temp, Ra, Rb, tha, qa
FROM vmin TO vmax WITH 199
rates(v): not consistently executed from here if usetable_hh == 1
tadj = q10^((celsius - temp)/10)
tinc = -dt * tadj
nexp = 1 - exp(tinc/ntau)
}
PROCEDURE rates(v) { :Computes rate and other constants at current v.
:Call once from HOC to initialize inf at resting v.
a = Ra * (v - tha) / (1 - exp(-(v - tha)/qa))
b = -Rb * (v - tha) / (1 - exp((v - tha)/qa))
ntau = 1/(a+b)
ninf = a*ntau
}
```

Now, what I do not understand are these lines:

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` n = n + nexp*(ninf-n)`

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`nexp = 1 - exp(tinc/ntau)`

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`dn/dt = alpha(v) (1-n) - beta(V)n`

and its adjustment to current temperature, but I still do not see why they are so complex. I tried to googlesearch it for quite some time and I am getting nothing. Can anyone explain this to me please ?