TITLE minimal model of GABAa receptors
COMMENT
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Minimal kinetic model for GABA-A receptors
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Model of Destexhe, Mainen & Sejnowski, 1994:
(closed) + T <-> (open)
The simplest kinetics are considered for the binding of transmitter (T)
to open postsynaptic receptors. The corresponding equations are in
similar form as the Hodgkin-Huxley model:
dr/dt = alpha * [T] * (1-r) - beta * r
I = gmax * [open] * (V-Erev)
where [T] is the transmitter concentration and r is the fraction of
receptors in the open form.
If the time course of transmitter occurs as a pulse of fixed duration,
then this first-order model can be solved analytically, leading to a very
fast mechanism for simulating synaptic currents, since no differential
equation must be solved (see Destexhe, Mainen & Sejnowski, 1994).
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Based on voltage-clamp recordings of GABAA receptor-mediated currents in rat
hippocampal slices (Otis and Mody, Neuroscience 49: 13-32, 1992), this model
was fit directly to experimental recordings in order to obtain the optimal
values for the parameters (see Destexhe, Mainen and Sejnowski, 1996).
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This mod file includes a mechanism to describe the time course of transmitter
on the receptors. The time course is approximated here as a brief pulse
triggered when the presynaptic compartment produces an action potential.
The pointer "pre" represents the voltage of the presynaptic compartment and
must be connected to the appropriate variable in oc.
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See details in:
Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. An efficient method for
computing synaptic conductances based on a kinetic model of receptor binding
Neural Computation 6: 10-14, 1994.
Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Kinetic models of
synaptic transmission. In: Methods in Neuronal Modeling (2nd edition;
edited by Koch, C. and Segev, I.), MIT press, Cambridge, 1996.
Written by Alain Destexhe, Laval University, 1995
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ENDCOMMENT
NEURON {
POINT_PROCESS GABAa
RANGE R, g, gmax
NONSPECIFIC_CURRENT i
GLOBAL Cmax, Cdur, Alpha, Beta, Erev, Rinf, Rtau
RANGE i
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cmax = 1 (mM) : max transmitter concentration
Cdur = 0.1 (ms) : transmitter duration (rising phase)
Alpha = 5:4 (/ms mM) : forward (binding) rate
Beta = 0.7:0.18 (/ms) : backward (unbinding) rate
Erev = -80 (mV) : reversal potential
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
Rinf : steady state channels open
Rtau (ms) : time constant of channel binding
synon
gmax
}
STATE {Ron Roff}
INITIAL {
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / ((Alpha * Cmax) + Beta)
synon = 0
}
BREAKPOINT {
SOLVE release METHOD cnexp
g = (Ron + Roff)*1(umho)
i = g*(v - Erev)
}
DERIVATIVE release {
Ron' = (synon*Rinf - Ron)/Rtau
Roff' = -Beta*Roff
}
: following supports both saturation from single input and
: summation from multiple inputs
: if spike occurs during CDur then new off time is t + CDur
: ie. transmitter concatenates but does not summate
: Note: automatic initialization of all reference args to 0 except first
NET_RECEIVE(weight, on, nspike, r0, t0 (ms)) {
: flag is an implicit argument of NET_RECEIVE and normally 0
if (flag == 0) { : a spike, so turn on if not already in a Cdur pulse
nspike = nspike + 1
if (!on) {
r0 = r0*exp(-Beta*(t - t0))
t0 = t
on = 1
synon = synon + weight
state_discontinuity(Ron, Ron + r0)
state_discontinuity(Roff, Roff - r0)
}
: come again in Cdur with flag = current value of nspike
net_send(Cdur, nspike)
}
if (flag == nspike) { : if this associated with last spike then turn off
r0 = weight*Rinf + (r0 - weight*Rinf)*exp(-(t - t0)/Rtau)
t0 = t
synon = synon - weight
state_discontinuity(Ron, Ron - r0)
state_discontinuity(Roff, Roff + r0)
on = 0
}
gmax=weight
}