: $Id: synq.inc,v 1.8 1996/02/14 20:45:23 billl Exp $
COMMENT
Basic synapse routines from Alain Destexhe and Zach Meinen with queue added.
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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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During the arrival of the presynaptic spike (detected by threshold
crossing), it is assumed that there is a brief pulse (duration=Cdur)
of neurotransmitter C in the synaptic cleft (the maximal concentration
of C is Cmax). Then, C is assumed to bind to a receptor Rc according
to the following first-order kinetic scheme:
Rc + C ---(Alpha)--> Ro (1)
<--(Beta)---
where Rc and Ro are respectively the closed and open form of the
postsynaptic receptor, Alpha and Beta are the forward and backward
rate constants. If R represents the fraction of open gates Ro,
then one can write the following kinetic equation:
dR/dt = Alpha * C * (1-R) - Beta * R (2)
and the postsynaptic current is given by:
Isyn = gmax * R * (V-Erev) (3)
where V is the postsynaptic potential, gmax is the maximal conductance
of the synapse and Erev is the reversal potential.
If C is assumed to occur as a pulse in the synaptic cleft, such as
C _____ . . . . . . Cmax
| |
_____| |______ . . . 0
t0 t1
then one can solve the kinetic equation exactly, instead of solving
one differential equation for the state variable and for each synapse,
which would be greatly time consuming...
Equation (2) can be solved as follows:
1. during the pulse (from t=t0 to t=t1), C = Cmax, which gives:
R(t-t0) = Rinf + [ R(t0) - Rinf ] * exp (- (t-t0) / Rtau ) (4)
where
Rinf = Alpha * Cmax / (Alpha * Cmax + Beta)
and
Rtau = 1 / (Alpha * Cmax + Beta)
2. after the pulse (t>t1), C = 0, and one can write:
R(t-t1) = R(t1) * exp (- Beta * (t-t1) ) (5)
There is a pointer called "pre" which must be set to the variable which
is supposed to trigger synaptic release. This variable is usually the
presynaptic voltage but it can be the presynaptic calcium concentration,
or other. Prethresh is the value of the threshold at which the release is
initiated.
Once pre has crossed the threshold value given by Prethresh, a pulse
of C is generated for a duration of Cdur, and the synaptic conductances
are calculated accordingly to eqs (4-5). Another event is not allowed to
occur for Deadtime milliseconds following after pre rises above threshold.
The user specifies the presynaptic location in hoc via the statement
connect pre_GABA[i] , v.section(x)
where x is the arc length (0 - 1) along the presynaptic section (the currently
specified section), and i is the synapse number (Which is located at the
postsynaptic location in the usual way via
postsynaptic_section {loc_GABA(i, x)}
Notice that loc_GABA() must be executed first since that function also
allocates space for the synapse.
*****************************************************************************
NEURON {
POINT_PROCESS NAME
}
PARAMETER {
Cmax = 1 (mM) : max transmitter concentration
Cdur = 1.08 (ms) : transmitter duration (rising phase)
Alpha = 1 (/ms mM) : forward (binding) rate
Beta = 0.02 (/ms) : backward (unbinding) rate
Erev = -80 (mV) : reversal potential
Prethresh = 0 : voltage level nec for release
Deadtime = 1 (ms) : mimimum time between release events
gmax (umho) : maximum conductance
}
INCLUDE "synq.inc"
*****************************************************************************
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINTER pre
RANGE C, R, R0, R1, g, gmax, lastrelease, spk
NONSPECIFIC_CURRENT i
GLOBAL Cmax, Cdur, Alpha, Beta, Erev, Prethresh, Deadtime, Rinf, Rtau
}
INCLUDE "queue.inc" : queue routines
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
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
spk : flag for spk occuring
lastrelease (ms) : time of last spike
}
INITIAL {
initq() : ****
R = 0
C = 0
R0 = 0
R1 = 0
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / ((Alpha * Cmax) + Beta)
lastrelease = -9e4
}
BREAKPOINT {
SOLVE releaser
g = gmax * R
i = g*(v - Erev)
}
PROCEDURE releaser() { LOCAL q
:will crash if user hasn't set pre with the connect statement
if (! spk && pre > Prethresh) { : new spike occured?
spk = 1
pushq(t+delay) }
if (spk && pre < Prethresh) { : spike over?
spk = 0
}
q = ((t - lastrelease) - Cdur) : time since last release ended
: ready for another release?
if (q >= Deadtime + dt) {
if (t >= queu[head]) { : **** a current spike time
popq() : ****
C = Cmax : start new release
R0 = R
lastrelease = t
}
} else { : still releasing?
if (t > queu[head]) { popq() } : **** throw away value from missed spikes
}
if (q < Deadtime && q > 0 && 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.
}
}
Simulation Platform