: $Id: bg.inc,v 1.3 1996/04/05 23:20:18 billl Exp $
TITLE Borg-Graham Channel Model
COMMENT
Modeling the somatic electrical response of hippocampal pyramidal neurons,
MS thesis, MIT, May 1987.
Each channel has activation and inactivation particles as in the original
Hodgkin Huxley formulation. The activation particle mm and inactivation
particle hh go from on to off states according to kinetic variables alpha
and beta which are voltage dependent. The form of the alpha and beta
functions were dissimilar in the HH study. The BG formulae are:
alpha = base_rate * Exp[(v - v_half)*valence*gamma*F/RT]
beta = base_rate * Exp[(-v + v_half)*valence*(1-gamma)*F/RT]
where,
baserate : no affect on Inf. Lowering this increases the maximum
value of Tau
basetau : (in msec) minimum Tau value.
chanexp : number for exponentiating the state variable; e.g.
original HH Na channel use m^3, note that chanexp = 0
will turn off this state variable
erev : reversal potential for the channel
gamma : (between 0 and 1) does not affect the Inf but makes the
Tau more asymetric with increasing deviation from 0.5
celsius : temperature at which experiment was done (Tau will
will be adjusted using a q10 of 3.0)
valence (z) : determines the steepness of the Inf sigmoid. Higher
valence gives steeper sigmoid.
vhalf : (a voltage) determines the voltage at which the value
of the sigmoid function for Inf is 1/2
vmin, vmax : limits for construction of the table. Generally,
these should be set to the limits over which either
of the 2 state variables are varying.
vrest : (a voltage) voltage shift for vhalf
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
RANGE gmax, g, i
GLOBAL erev, Inf, Tau, Mult, Add, vmin, vmax, vrest
} : end NEURON
CONSTANT {
FARADAY = 96489.0 : Faraday's constant
R= 8.31441 : Gas constant
} : end CONSTANT
UNITS {
(mA) = (milliamp)
(mV) = (millivolt)
(umho) = (micromho)
} : end UNITS
COMMENT
** Parameter values should come from files specific to particular channels
PARAMETER {
erev = 0 (mV)
gmax = 0 (mho/cm^2)
vrest = 0 (mV)
mvalence = 0
mgamma = 0
mbaserate = 0
mvhalf = 0
mbasetau = 0
mtemp = 0
mq10 = 3
mexp = 0
hvalence = 0
hgamma = 0
hbaserate = 0
hvhalf = 0
hbasetau = 0
htemp = 0
hq10 = 3
hexp = 0
cao (mM)
cai (mM)
celsius (degC)
dt (ms)
v (mV)
vmax = 100 (mV)
vmin = -100 (mV)
} : end PARAMETER
ENDCOMMENT
ASSIGNED {
i (mA/cm^2)
g (mho/cm^2)
Inf[2] : 0 = m and 1 = h
Tau[2] : 0 = m and 1 = h
Mult[2] : 0 = m and 1 = h
Add[2] : 0 = m and 1 = h
} : end ASSIGNED
STATE { m h }
INITIAL {
mh(v)
if (usetable==0) {
m = Inf[0] h = Inf[1]
} else {
m = Add[0]/(1-Mult[0]) h = Add[1]/(1-Mult[1])
}
}
BREAKPOINT {
LOCAL hexp_val, index, mexp_val
SOLVE states
hexp_val = 1
mexp_val = 1
: Determining h's exponent value
if (hexp > 0) {
FROM index=1 TO hexp {
hexp_val = h * hexp_val
}
}
: Determining m's exponent value
if (mexp > 0) {
FROM index = 1 TO mexp {
mexp_val = m * mexp_val
}
}
: mexp hexp
: Note that mexp_val is now = m and hexp_val is now = h
g = gmax * mexp_val * hexp_val
iassign()
} : end BREAKPOINT
: ASSIGNMENT PROCEDURES
: Must be overwritten by user routines in parameters.multi
: PROCEDURE iassign () { i = g*(v-erev) ina=i }
: PROCEDURE iassign () { i = g*ghkca(v) ica=i }
:-------------------------------------------------------------------
: I suppose we have 2 choices, to use the DERIVATIVE function or
: to explicitly state m+ and h+. If you were to use the DERIVATIVE
: function, then you will do as follows:
: DERIVATIVE deriv {
: m' = (-m + minf) / mtau
: h' = (-h + hinf) / htau
: }
: Else, since m' = (m+ - m) / dt, setting the 2 equations together,
: we can solve for m+ and eventually get :
: m+ = (m * mtau + dt * minf) / (mtau + dt)
: and same for h+:
: h+ = (h * htau + dt * hinf) / (htau + dt)
: This is the one we will use, so ...
PROCEDURE states() {
: Setup the mh table values
mh (v*1(/mV))
m = m * Mult[0] + Add[0]
h = h * Mult[1] + Add[1]
VERBATIM
return 0;
ENDVERBATIM
}
:-------------------------------------------------------------------
: NOTE : 0 = m and 1 = h
PROCEDURE mh (v) {
LOCAL a, b, j, mqq10, hqq10
TABLE Add, Mult DEPEND dt, hbaserate, hbasetau, hexp, hgamma, htemp, hvalence, hvhalf, mbaserate, mbasetau, mexp, mgamma, mtemp, mvalence, mvhalf, celsius, mq10, hq10, vrest, vmin, vmax FROM vmin TO vmax WITH 200
mqq10 = mq10^((celsius-mtemp)/10.)
hqq10 = hq10^((celsius-htemp)/10.)
: Calculater Inf and Tau values for h and m
FROM j = 0 TO 1 {
a = alpha (v, j)
b = beta (v, j)
Inf[j] = a / (a + b)
VERBATIM
switch (_lj) {
case 0:
/* Make sure Tau is not less than the base Tau */
if ((Tau[_lj] = 1 / (_la + _lb)) < mbasetau) {
Tau[_lj] = mbasetau;
}
Tau[_lj] = Tau[_lj] / _lmqq10;
break;
case 1:
if ((Tau[_lj] = 1 / (_la + _lb)) < hbasetau) {
Tau[_lj] = hbasetau;
}
Tau[_lj] = Tau[_lj] / _lhqq10;
if (hexp==0) {
Tau[_lj] = 1.; }
break;
}
ENDVERBATIM
Mult[j] = exp(-dt/Tau[j])
Add[j] = Inf[j]*(1. - exp(-dt/Tau[j]))
}
} : end PROCEDURE mh (v)
:-------------------------------------------------------------------
FUNCTION alpha(v,j) {
if (j == 1) {
if (hexp==0) {
alpha = 1
} else {
alpha = hbaserate * exp((v - (hvhalf+vrest)) * hvalence * hgamma * FRT(htemp)) }
} else {
alpha = mbaserate * exp((v - (mvhalf+vrest)) * mvalence * mgamma * FRT(mtemp))
}
} : end FUNCTION alpha (v,j)
:-------------------------------------------------------------------
FUNCTION beta (v,j) {
if (j == 1) {
if (hexp==0) {
beta = 1
} else {
beta = hbaserate * exp((-v + (hvhalf+vrest)) * hvalence * (1 - hgamma) * FRT(htemp)) }
} else {
beta = mbaserate * exp((-v + (mvhalf+vrest)) * mvalence * (1 - mgamma) * FRT(mtemp))
}
} : end FUNCTION beta (v,j)
:-------------------------------------------------------------------
FUNCTION FRT(temperature) {
FRT = FARADAY * 0.001 / R / (temperature + 273.15)
} : end FUNCTION FRT (temperature)
:-------------------------------------------------------------------
FUNCTION ghkca (v) { : Goldman-Hodgkin-Katz eqn
LOCAL nu, efun
nu = v*2*FRT(celsius)
if(fabs(nu) < 1.e-6) {
efun = 1.- nu/2.
} else {
efun = nu/(exp(nu)-1.) }
ghkca = -FARADAY*2.e-3*efun*(cao - cai*exp(nu))
} : end FUNCTION ghkca()