: $Id: gabab.mod,v 1.9 2004/06/17 16:04:05 billl Exp $
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...
For a detailed model of GABAB:
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.
For a review of models of synaptic currents:
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.
This simplified model was introduced in:
Destexhe, A., Bal, T., McCormick, D.A. and Sejnowski, T.J.
Ionic mechanisms underlying synchronized oscillations and propagating
waves in a model of ferret thalamic slices. Journal of Neurophysiology
76: 2049-2070, 1996.
See also http://www.cnl.salk.edu/~alain
Alain Destexhe, Salk Institute and Laval University, 1995
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ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS GABAB
RANGE R, G, g
NONSPECIFIC_CURRENT i
GLOBAL Cmax, Cdur
GLOBAL K1, K2, K3, K4, KD, Erev, warn, cutoff
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cmax = 0.5 (mM) : max transmitter concentration
Cdur = 0.3 (ms) : transmitter duration (rising phase)
:
: 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)
warn = 0 : whether to warn if G too large
cutoff = 10.0 : 1e3 : 1e12
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
Gn
R : fraction of activated receptor
edc
synon
Rinf
Rtau (ms)
Beta (/ms)
}
STATE {
Ron Roff
G : fraction of activated G-protein
}
INITIAL {
R = 0
G = 0
Ron = 0
Roff = 0
synon = 0
Rinf = K1*Cmax/(K1*Cmax + K2)
Rtau = 1/(K1*Cmax + K2)
Beta = K2
}
BREAKPOINT {
: SOLVE bindkin METHOD derivimplicit
: SOLVE bindkin METHOD euler
SOLVE bindkin METHOD cnexp
if (G < cutoff) {
Gn = G*G*G*G : ^n = 4
g = Gn / (Gn+KD)
} else {
if(warn){
printf("gabab.mod WARN: G = %g too large\n", G)
}
g = 1
}
i = g*(v - Erev)
}
DERIVATIVE bindkin {
Ron' = synon*K1*Cmax - (K1*Cmax + K2)*Ron
Roff' = -K2*Roff
R = Ron + Roff
G' = K3 * R - K4 * G
}
: following supports both saturation from single input and
: summation from multiple inputs
: Note: automatic initialization of all reference args to 0 except first
NET_RECEIVE(weight, r0, t0 (ms)) {
if (flag == 1) { : at end of Cdur pulse so turn off
r0 = weight*(Rinf + (r0 - Rinf)*exp(-(t - t0)/Rtau))
t0 = t
synon = synon - weight
Ron = Ron - r0
Roff = Roff + r0
:state_discontinuity(Ron, Ron - r0)
: state_discontinuity(Roff, Roff + r0)
} else{ : at beginning of Cdur pulse so turn on
r0 = weight*r0*exp(-Beta*(t - t0))
t0 = t
synon = synon + weight
Ron = Ron + r0
Roff = Roff - r0
: state_discontinuity(Ron, Ron + r0)
: state_discontinuity(Roff, Roff - r0)
:come again in Cdur
net_send(Cdur, 1)
}
}
