COMMENT
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Simple synaptic mechanism derived for first order kinetics of
binding of transmitter to postsynaptic receptors.
A. Destexhe & Z. Mainen, The Salk Institute, March 12, 1993.
Last modif. Sept 8, 1993.
Reference:
Destexhe, A., Mainen, Z. and Sejnowski, T.J. An efficient method for
computing synaptic conductances based on a kinetic model of receptor binding.
Neural Computation, 6: 14-18, 1994.
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MODIFIED KINETIC MODEL FOR G-PROTEIN GATED SYNAPTIC CHANNELS
For a large family of synaptic receptors, the neurotransmitter does not gate
the ionic channel directly, but through an intracellular second-messenger,
based on the activation of G-proteins. The most probable mechanism for many
of these neurotransmitters is the direct activation/deactivation of a K+
channel by the G-protein itself. In this family of receptors, the cholinergic
(muscarinic M2) and GABAergic (GABA_B) receptors are the most extensively
studied.
For the GABA_B-mediated synaptic response, it is assumed that the transmitter
GABA binds to a receptor which catalyzes the intracellular activation of a
G-protein subunit (G_alpha), which itself diffuses and binds to an associated
K+ channel. The present file contains a first-order model for GABA-B
receptors, which was shown to be equivalent to a more detailed model of the
entire G-protein cascade (Destexhe et al., J. Computational Neuroscience, 1:
195-231, 1994).
Parameters estimated from whole cell recordings of synaptic currents on
hippocampal neurons (Otis et al, J. Physiol. 463: 391-407, 1993). The model
was directly fit to averaged currents (see Destexhe et al., J. Neurophysiol.
72: 803-818, 1994).
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ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS GABAB1
POINTER pre
RANGE C, R, R0, R1, g, gmax, lastrelease, Prethresh
NONSPECIFIC_CURRENT i
GLOBAL Cmax, Cdur, Alpha, Beta, Erev, Deadtime, Rinf, Rtau
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cmax = 1 (mM) : max transmitter concentration
Cdur = 85 (ms) : transmitter duration (rising phase)
Alpha = 0.016 (/ms mM) : forward (binding) rate
Beta = 0.0047 (/ms) : backward (unbinding) rate
Erev = -95 (mV) : reversal potential (potassium)
Prethresh = 0 : voltage level nec for release
Deadtime = 1 (ms) : mimimum time between release events
gmax (umho) : maximum conductance
}
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
}
INITIAL {
R = 0
C = 0
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / ((Alpha * Cmax) + Beta)
lastrelease = -999
}
BREAKPOINT {
SOLVE release
g = gmax * R
i = g*(v - Erev)
}
PROCEDURE release() { LOCAL q
:will crash if user hasn't set pre with the connect statement
q = ((t - lastrelease) - Cdur) : time since last release ended
: ready for another release?
if (q > Deadtime) {
if (pre > Prethresh) { : spike occured?
C = Cmax : start new release
R0 = R
lastrelease = t
}
} else if (q < 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.
}
}