TITLE minimal model of NMDA receptors
COMMENT
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Minimal kinetic model for glutamate NMDA 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] * B(V) * (V-Erev)
where [T] is the transmitter concentration and r is the fraction of
receptors in the open form. B(V) represents the voltage-dependent
Mg++ block (see Jahr & Stevens J Neurosci 10: 1830, 1990; Jahr & Stevens
J Neurosci 10: 3178, 1990).
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 NMDA receptor-mediated currents in rat
hippocampal slices (Hessler et al., Nature 366: 569-572, 1993), 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, 1998, pp. 1-28.
(electronic copy available at http://cns.iaf.cnrs-gif.fr)
Written by Alain Destexhe, Laval University, 1995
27-11-2002: the pulse is implemented using a counter, which is more
stable numerically (thanks to Yann LeFranc)
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ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS NMDA
POINTER pre
RANGE C, R, R0, R1, g, gmax, B, lastrelease, TimeCount
NONSPECIFIC_CURRENT i
RANGE Cmax, Cdur, Alpha, Beta, Erev, mg
RANGE Prethresh, Deadtime, Rinf, Rtau
THREADSAFE
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
dt (ms)
Cmax = 1 (mM) : max transmitter concentration
Cdur = 1 (ms) : transmitter duration (rising phase)
Alpha = 0.072 (/ms mM) : forward (binding) rate
Beta = 0.0066 (/ms) : backward (unbinding) rate
Erev = 0 (mV) : reversal potential
Prethresh = 0 : voltage level nec for release
Deadtime = 1 (ms) : mimimum time between release events
gmax (umho) : max conductance (100 pS single syn)
mg = 1 (mM) : external magnesium concentration
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
C (mM) : transmitter concentration
R : fraction of open channels
R0 : open channels at start of release
R1 : open channels at end of release
Rinf : steady state channels open
Rtau (ms) : time constant of channel binding
pre : pointer to presynaptic variable
lastrelease (ms) : time of last spike
B : magnesium block
TimeCount (ms) : time counter
}
INITIAL {
R = 0
C = 0
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / ((Alpha * Cmax) + Beta)
lastrelease = -1000
R1=0
TimeCount=-1
}
BREAKPOINT {
SOLVE release
B = mgblock(v) : B is the block by magnesium at this voltage
g = gmax * R * B
i = g*(v - Erev)
}
PROCEDURE release() {
:will crash if user hasn't set pre with the connect statement
TimeCount=TimeCount-dt : time since last release ended
: ready for another release?
if (TimeCount < -Deadtime) {
if (pre > Prethresh) { : spike occured?
C = Cmax : start new release
R0 = R
lastrelease = t
TimeCount=Cdur
}
} else if (TimeCount > 0) { : still releasing?
: do nothing
} else if (C == Cmax) { : in dead time after release
R1 = R
C = 0.
}
if (C > 0) { : transmitter being released?
R = Rinf + (R0 - Rinf) * exptable (- (t - lastrelease) / Rtau)
} else { : no release occuring
R = R1 * exptable (- Beta * (t - (lastrelease + Cdur)))
}
VERBATIM
return 0;
ENDVERBATIM
}
FUNCTION exptable(x) {
TABLE FROM -10 TO 10 WITH 2000
if ((x > -10) && (x < 10)) {
exptable = exp(x)
} else {
exptable = 0.
}
}
FUNCTION mgblock(v(mV)) {
TABLE
DEPEND mg
FROM -140 TO 80 WITH 1000
: from Jahr & Stevens
mgblock = 1 / (1 + exp(0.062 (/mV) * -v) * (mg / 3.57 (mM)))
}