COMMENT
Original Hodgkin and Huxley model (J.Physiol. (Lond.) 117:500-544 (1952))
with stochastic conductances, using coupled activation particles (5-state K
channels, 8-state Na channels) and Diffusion approximation (Fox) algorithm
Membrane voltage is in absolute mV and has been reversed in polarity
from the original HH convention and shifted to reflect a resting potential
of -65 mV.
ENDCOMMENT
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(S) = (siemens)
}
NEURON {
SUFFIX hh58F1
USEION na READ ena WRITE ina
USEION k READ ek WRITE ik
NONSPECIFIC_CURRENT il
RANGE gnabar, gkbar, gl, el, NNa, NK, sumN, sumMH
}
PARAMETER {
gnabar = .12 (S/cm2) <0,1e9>
gkbar = .036 (S/cm2) <0,1e9>
gl = .0003 (S/cm2) <0,1e9>
el = -54.3 (mV)
NNa = 5000
NK = 1600
}
ASSIGNED {
v (mV)
celsius (degC)
ena (mV)
ek (mV)
dt (ms)
ina (mA/cm2)
ik (mA/cm2)
il (mA/cm2)
am (/ms)
ah (/ms)
an (/ms)
bm (/ms)
bh (/ms)
bn (/ms)
stsum
M
N
H
R[14] (/ms)
sumN
sumMH
mh0
n0
}
STATE {
mh1
mh2
mh3
mh4
mh5
mh6
mh7
n1
n2
n3
n4
}
BREAKPOINT {
SOLVE states METHOD cnexp
ina = gnabar*mh7*(v - ena)
ik = gkbar*n4*(v - ek)
il = gl*(v - el)
sumN = n0 + n1 + n2 + n3 + n4
sumMH = mh0 + mh1 + mh2 + mh3 + mh4 + mh5 + mh6 + mh7
}
INITIAL {
rates(v)
M=am/bm
H=ah/bh
N=an/bn
stsum=(1+H)*(1+M)^3
mh0=1/stsum
mh1=3*M/stsum
mh2=3*M^2/stsum
mh3=M^3/stsum
mh4=H/stsum
mh5=H*3*M/stsum
mh6=H*3*M^2/stsum
mh7=H*M^3/stsum
stsum=(1+N)^4
n0=1/stsum
n1=4*N/stsum
n2=6*N^2/stsum
n3=4*N^3/stsum
n4=N^4/stsum
rates(v)
}
DERIVATIVE states {
rates(v)
mh1' = (-2*am-bm-ah)*mh1 + 3*am*mh0 + 2*bm*mh2 + bh*mh5 -R[0]+R[1]+R[4]
mh2' = (-am-2*bm-ah)*mh2 + 2*am*mh1 + 3*bm*mh3 + bh*mh6 -R[1]+R[2]+R[5]
mh3' = (-3*bm-ah)*mh3 + am*mh2 + bh*mh7 -R[2]+R[6]
mh4' = (-3*am-bh)*mh4 + bm*mh5 + ah*mh0 + R[7]-R[3]
mh5' = (-2*am-bm-bh)*mh5 + 3*am*mh4 + 2*bm*mh6 + ah*mh1 -R[7]+R[8]-R[4]
mh6' = (-am-2*bm-bh)*mh6 + 2*am*mh5 + 3*bm*mh7 + ah*mh2 -R[8]+R[9]-R[5]
mh7' = (-3*bm-bh)*mh7 + am*mh6 + ah*mh3 -R[9]-R[6]
mh0 = 1-mh1-mh2-mh3-mh4-mh5-mh6-mh7
n1' = (-3*an-bn)*n1 + 4*an*n0 + 2*bn*n2 - R[10] + R[11]
n2' = (-2*an-2*bn)*n2 + 3*an*n1 + 3*bn*n3 -R[11] + R[12]
n3' = (-an-3*bn)*n3 + 2*an*n2 + 4*bn*n4 -R[12] + R[13]
n4' = -4*bn*n4 + an*n3 -R[13]
n0 = 1-n1-n2-n3-n4
}
LOCAL q10
PROCEDURE rates(v(mV)) { :Computes rate and other constants at current v.
LOCAL q10
UNITSOFF
q10 = 3^((celsius - 6.3)/10)
am = q10*0.1*(v+40)/(1-exp(-(v+40)/10))
bm = q10*4*exp(-(v+65)/18)
ah = q10*0.07*exp(-(v+65)/20)
bh = q10/(1+exp(-(v+35)/10))
an = q10*0.01*(v+55)/(1-exp(-(v+55)/10))
bn = q10*0.125*exp(-(v+65)/80)
FROM ii=0 TO 9 {R[ii]=normrand(0,1/sqrt(NNa*dt))}
FROM ii=10 TO 13 {R[ii]=normrand(0,1/sqrt(NK*dt))}
R[0] = R[0]*sqrt(fabs(3*am*mh0+bm*mh1))
R[1] = R[1]*sqrt(fabs(2*am*mh1+2*bm*mh2))
R[2] = R[2]*sqrt(fabs(am*mh2+3*bm*mh3))
R[3] = R[3]*sqrt(fabs(ah*mh0+bh*mh4))
R[4] = R[4]*sqrt(fabs(ah*mh1+bh*mh5))
R[5] = R[5]*sqrt(fabs(ah*mh2+bh*mh6))
R[6] = R[6]*sqrt(fabs(ah*mh3+bh*mh7))
R[7] = R[7]*sqrt(fabs(3*am*mh4+bm*mh5))
R[8] = R[8]*sqrt(fabs(2*am*mh5+2*bm*mh6))
R[9] = R[9]*sqrt(fabs(am*mh6+3*bm*mh7))
R[10] = R[10]*sqrt(fabs(4*an*n0+bn*n1))
R[11] = R[11]*sqrt(fabs(3*an*n1+2*bn*n2))
R[12] = R[12]*sqrt(fabs(2*an*n2+3*bn*n3))
R[13] = R[13]*sqrt(fabs(an*n3+4*bn*n4))
UNITSON
}