COMMENT
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Kinetic model of GABA-A receptors
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7-state gating model from Jones and Westbrook (Neuron 15, 181 - 191, 1995)
D1 D2
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C1 -- C2 -- C3
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O1 O2
Or 16-state gating scheme from Haas and MacDonald (J Physiol 514.1, 27 - 45, 1999)
D2 D3 -- D4
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C1 -- C2 -- C3 -- C4
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O1 O2 O3
/\ /\ /\
C5 C6 C7 C8 C9 C10
Reversal potential Egaba is changing according to [Cl-]i change (due to Cl- influx). Bicarbonate (HCO3) flows through the GABAR too, and therefore Egaba is also [HCO3]i/[HCO3]o -dependent. igaba = icl + ihco3 (we assume icl and ihco3 to be mutually independent)
Based on gabaA_Cl.mod, modified to use GHK current equation.
ENDCOMMENT
TITLE detailed GABAergic conductance with changing Cl- concentration
NEURON {
POINT_PROCESS gaghk
USEION cl READ cli, clo WRITE icl VALENCE -1
USEION hco3 READ hco3i, hco3o WRITE ihco3 VALENCE -1
RANGE icl, ihco3, i
RANGE GABAdur, GABA, taugaba, GABAINIT
RANGE f1, f2
RANGE kon, koff, koff2, k34, k43, alfa1, beta1, alfa2, beta2, alfa3, beta3
RANGE a1o, a1c, b1o, b1c, a2o, a2c, b2o, b2c, a3o, a3c, b3o, b3c
RANGE d1, r1, d2, r2, d3, r3, d4, r4
RANGE C1, C2, C3, C4, C5, C6, C7, C8, C9, C1O
RANGE O1, O2, O3, D1, D2, D3, D4
RANGE Prel, Pcl, Phco3, Rnumber
RANGE ecl, ehco3, egaba
RANGE gcl, ghco3, grel
}
UNITS {
(mA) = (milliamp)
(nA) = (nanoamp)
(mV) = (millivolt)
(uS) = (micromho)
(mM) = (milli/liter)
(uM) = (micro/liter)
F = (faraday) (coulombs)
R = (k-mole) (joule/degC)
}
PARAMETER {
: these must be specified at the hoc level, or through clever use
: of the INITIAL block
: hco3o = 26 (mM) : extracellular HCO3- concentration
: hco3i = 16 (mM) : intracellular HCO3- concentration
Prel = 0.18 : Phco3/Pcl relative permeability
Rnumber = 50 : number of GABAARs in the synaptic compartment
Pcl = 8e-14 (cm3/s) : maximum Cl- single channel permeability for GABAAR
: the value assigned here will have no effect; must be specified at the hoc level
celsius = 37 (degC)
GABAdur = 1 (ms) : transmitter duration (rising phase)
taugaba = 0.2 (ms)
: Rates
kon = .003 (/uM /ms) : binding (.007 Haas)
koff = .150 (/ms) : unbinding (170 Haas)
koff2 = .300 (/ms) : unbinding
alfa1 = 1.111 (/ms) : closing
beta1 = .200 (/ms) : opening
alfa2 = .142 (/ms) : closing
beta2 = 2.500 (/ms) : opening
alfa3 = .150 (/ms) : closing
beta3 = .076 (/ms) : opening
d1 = .013 (/ms) : slow desensitizing
r1 = .00013 (/ms) : resensitizing
d2 = .750 (/ms) : fast desensitizing (750 - 1000), 960 (Haas)
r2 = .015 (/ms) : resensitizing (15 - 25), 22 (Haas)
d3 = .008 (/ms) : intermediate desensitizing
r3 = .00081 (/ms) : resensitizing
d4 = .00075 (/ms) : slow desenzitizing
r4 = .00049 (/ms) : resenzitizing
k34 = .710 (/ms)
k43 = .058 (/ms)
a1o = .180 (/ms)
a2o = .180 (/ms)
a1c = 5.100 (/ms)
a2c = 5.100 (/ms)
b1o = .070 (/ms)
b2o = .070 (/ms)
b1c = .630 (/ms)
b2c = .630 (/ms)
a3o = .090 (/ms)
b3o = .035 (/ms)
a3c = 5.100 (/ms)
b3c = .630 (/ms)
}
ASSIGNED {
v (mV) : postsynaptic voltage - we hypothesize that Egaba changes due to increase of [Cl]i
cli (mM)
clo (mM)
icl (nA) : chloride current
ecl (mV) : equilibrium potential for Cl-
hco3i (mM)
hco3o (mM)
ihco3 (nA) : bicarb current
ehco3 (mV) : equilibrium potential for HCO3-
egaba (mV) : reversal potential for GABAR
i (nA) : total current generated by this mechanism = icl + ihco3
GABA (mM) : transmitter concentration
GABAINIT (mM) : increased transmitter concentration after release
time0 (ms)
f1 (/ms) : binding
f2 (/ms) : binding
Phco3 (cm3/s) : max Phco3 = 0.18 * max Pcl
gcl (uS) : GABA - induced conductance for chloride
ghco3 (uS) : GABA - induced conductance for bicarbonate
grel : relative conductance
}
STATE {
: Channel states (all fractions)
C1 : unbound
C2 : single bound
C3 : double bound
C4 : double bound
C5
C6
C7
C8
C9
C1O
O1 : open
O2 : open
O3 : open
D1 : desensitized
D2 : desensitized
D3 : desensitized
D4 : desensitized
}
INITIAL {
GABA = 0
GABAINIT = 0
C1 = 1
C2 = 0
C3 = 0
C4 = 0
C5 = 0
C6 = 0
C7 = 0
C8 = 0
C9 = 0
C1O = 0
O1 = 0
O2 = 0
O3 = 0
D1 = 0
D2 = 0
D3 = 0
D4 = 0
icl = 0
ihco3 = 0
i = 0
Phco3 = Prel * Pcl
}
BREAKPOINT {
if (GABAINIT > 0)
{ GABA = GABAINIT * exp(-(t-time0)/taugaba) }
else {GABA = GABAINIT}
SOLVE kstates METHOD sparse
icl = (1e+06)*(O1+O2+O3) * Pcl * Rnumber * ghk(v, cli, clo, -1) :1e+6 is a factor to convert mA to nA
ihco3 = (1e+06)*(O1+O2+O3) * Phco3 * Rnumber * ghk(v, hco3i, hco3o, -1)
i = icl + ihco3
egaba = ghkvoltage(cli, clo, hco3i, hco3o)
gcl = (1e+06)*(O1+O2+O3) * Pcl * Rnumber * conduct(v, cli, clo) :1e+6 is a factor to convert S to uS
ghco3 = (1e+06)*(O1+O2+O3) * Phco3 * Rnumber *conduct(v, hco3i, hco3o)
if (gcl>0) {grel = ghco3/gcl} else {grel = 0}
}
KINETIC kstates {
f1 = 2 * kon * (1e3) * GABA
f2 = kon * (1e3) * GABA
~ C1 <-> C2 (f1,koff)
~ C2 <-> C3 (f2,koff2)
~ C2 <-> O1 (beta1,alfa1)
~ C3 <-> O2 (beta2,alfa2)
~ C2 <-> D1 (d1,r1)
~ C3 <-> D2 (d2,r2)
: Haas and MacDonald kinetics
~ C3 <-> C4 (k34,k43)
~ C4 <-> O3 (beta3,alfa3)
~ C4 <-> D3 (d3,r3)
~ D3 <-> D4 (d4,r4)
~ O1 <-> C5 (a1c,a1o)
~ O1 <-> C6 (b1c,b1o)
~ O2 <-> C7 (a2c,a2o)
~ O2 <-> C8 (b2c,b2o)
~ O3 <-> C9 (a3c,a3o)
~ O3 <-> C1O (b3c,b3o)
CONSERVE C1+C2+C3+C4+C5+C6+C7+C8+C9+C1O+O1+O2+O3+D1+D2+D3+D4 = 1
}
NET_RECEIVE(weight(mM), nspike) {
: an onset event (generated by NetStim) always has an implicit argument called flag which is set to 0
if (flag == 0) {
nspike = nspike + 1
time0 = t
GABAINIT = weight
: come again in Cdur with flag = current value of nspike (selfevent generated with delay Cdur & flag=nspike)
net_send(GABAdur, nspike)
}
if (flag == nspike) {
: if this associated with last spike then turn off
GABAINIT = 0
}
}
FUNCTION ghk(v(mV), ci(mM), co(mM), z) (millicoul/cm3) {
LOCAL e, w
w = v * (.001) * z*F / (R*(celsius+273.15))
if (fabs(w)>1e-4)
{ e = w / (exp(w)-1) }
else
: denominator is small -> Taylor series
{ e = 1-w/2 }
ghk = - (.001) * z* F * (co-ci*exp(w)) * e
}
FUNCTION ghkvoltage(c1i(mM), c1o(mM), c2i(mM), c2o(mM)) (mV) {
ghkvoltage = - (1000)*(celsius + 273.15)*R/F*log((c1o + Prel*c2o)/(c1i + Prel*c2i))
}
FUNCTION conduct(v(mV), ci(mM), co(mM)) (millicoul/cm3/mV) {
LOCAL w
w = v * (.001) *F / (R*(celsius+273.15))
conduct = (0.001)*(.001)*F^2/(R*(celsius+273.15))*(ci-(co+ci)*exp(w)+(ci-co)*w*exp(w)+co*(exp(w)^2))/((1-exp(w))^2)
}