gabab1.mod

TITLE simplest model for GABAb receptors

COMMENT
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Simple synaptic mechanism derived for first order kinetics of
binding of transmitter to postsynaptic receptors.

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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Warning: this model of GABAB is phenomenological and is correct only as a very
gross approximation.  It does not account for the typical stimulus-dependence
of GABAB responses (i.e., GABAB appears only for high stimulus intensities). 
For more details and a more recent model, see: 

  Destexhe, A. and Sejnowski, T.J.  G-protein activation kinetics and
  spill-over of GABA may account for differences between inhibitory responses
  in the hippocampus and thalamus.  Proc. Natl. Acad. Sci. USA  92:
  9515-9519, 1995.

  See also: 

  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.

  (electronic copies available at http://cns.iaf.cnrs-gif.fr)

  A. Destexhe & Z. Mainen, The Salk Institute, March 12, 1993.
  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 GABAB1
	POINTER pre
	RANGE C, R, R0, R1, g, gmax, lastrelease, TimeCount
	NONSPECIFIC_CURRENT i
	GLOBAL Cmax, Cdur, Alpha, Beta, Erev, Prethresh, Deadtime, Rinf, Rtau
}
UNITS {
	(nA) = (nanoamp)
	(mV) = (millivolt)
	(umho) = (micromho)
	(mM) = (milli/liter)
}

PARAMETER {
	dt		(ms)
	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
	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
	g = gmax * R
	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.
	}
}