: $Id: gababS.mod,v 1.4 2004/06/17 18:38:24 billl Exp $
TITLE simple GABAb receptors
COMMENT
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Kinetic model of GABA-B receptors
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MODEL OF SECOND-ORDER G-PROTEIN TRANSDUCTION AND FAST K+ OPENING
WITH COOPERATIVITY OF G-PROTEIN BINDING TO K+ CHANNEL
PULSE OF TRANSMITTER
SIMPLE KINETICS WITH NO DESENSITIZATION
Features:
- peak at 100 ms; time course fit to Tom Otis' PSC
- SUMMATION (psc is much stronger with bursts)
Approximations:
- single binding site on receptor
- model of alpha G-protein activation (direct) of K+ channel
- G-protein dynamics is second-order; simplified as follows:
- saturating receptor
- no desensitization
- Michaelis-Menten of receptor for G-protein production
- "resting" G-protein is in excess
- Quasi-stat of intermediate enzymatic forms
- binding on K+ channel is fast
Kinetic Equations:
dR/dt = K1 * T * (1-R-D) - K2 * R
dG/dt = K3 * R - K4 * G
R : activated receptor
T : transmitter
G : activated G-protein
K1,K2,K3,K4 = kinetic rate cst
n activated G-protein bind to a K+ channel:
n G + C <-> O (Alpha,Beta)
If the binding is fast, the fraction of open channels is given by:
O = G^n / ( G^n + KD )
where KD = Beta / Alpha is the dissociation constant
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Parameters estimated from patch clamp recordings of GABAB PSP's in
rat hippocampal slices (Otis et al, J. Physiol. 463: 391-407, 1993).
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PULSE MECHANISM
Kinetic synapse with release mechanism as a pulse.
Warning: for this mechanism to be equivalent to the model with diffusion
of transmitter, small pulses must be used...
see details at http://cns.iaf.cnrs-gif.fr
Written by A. Destexhe, 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 GABABS
POINTER pre
RANGE C, R, G, g, gmax, lastrelease, TimeCount
NONSPECIFIC_CURRENT i
GLOBAL Cmax, Cdur, Prethresh, Deadtime
GLOBAL K1, K2, K3, K4, KD, Erev
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
dt (ms)
Cmax = 0.5 (mM) : max transmitter concentration
Cdur = 0.3 (ms) : transmitter duration (rising phase)
Prethresh = 0 : voltage level nec for release
Deadtime = 1 (ms) : mimimum time between release events
:
: From Kfit with long pulse (5ms 0.5mM)
:
K1 = 0.52 (/ms mM) : forward binding rate to receptor
K2 = 0.0013 (/ms) : backward (unbinding) rate of receptor
K3 = 0.098 (/ms) : rate of G-protein production
K4 = 0.033 (/ms) : rate of G-protein decay
KD = 100 : dissociation constant of K+ channel
n = 4 : nb of binding sites of G-protein on K+
Erev = -95 (mV) : reversal potential (E_K)
gmax (umho) : maximum conductance
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
C (mM) : transmitter concentration
Gn
pre : pointer to presynaptic variable
lastrelease (ms) : time of last spike
TimeCount (ms) : time counter
}
STATE {
R : fraction of activated receptor
G : fraction of activated G-protein
}
INITIAL {
C = 0
lastrelease = -9e9
R = 0
G = 0
TimeCount=-1
}
BREAKPOINT {
SOLVE bindkin METHOD cnexp
Gn = G^n
g = gmax * Gn / (Gn+KD)
i = g*(v - Erev)
}
DERIVATIVE bindkin {
R' = K1 * C * (1-R) - K2 * R
G' = K3 * R - K4 * G
}
NET_RECEIVE(weight ,on) {
if (on) { : at end of Cdur pulse so turn off
on = 0
C = 0
} else {
if (weight==0) { : do nothing
C=0
} else {
C=Cmax
on=1
net_send(Cdur, on)
}
}
}