TITLE simple NMDA receptors
COMMENT
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Essentially the same as /examples/nrniv/netcon/ampa.mod in the NEURON
distribution - i.e. Alain Destexhe's simple AMPA model - but with
different binding and unbinding rates and with a magnesium block.
Modified by Andrew Davison, The Babraham Institute, May 2000
Simple model for glutamate AMPA receptors
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- FIRST-ORDER KINETICS, FIT TO WHOLE-CELL RECORDINGS
Whole-cell recorded postsynaptic currents mediated by AMPA/Kainate
receptors (Xiang et al., J. Neurophysiol. 71: 2552-2556, 1994) were used
to estimate the parameters of the present model; the fit was performed
using a simplex algorithm (see Destexhe et al., J. Computational Neurosci.
1: 195-230, 1994).
- SHORT PULSES OF TRANSMITTER (0.3 ms, 0.5 mM)
The simplified model was obtained from a detailed synaptic model that
included the release of transmitter in adjacent terminals, its lateral
diffusion and uptake, and its binding on postsynaptic receptors (Destexhe
and Sejnowski, 1995). Short pulses of transmitter with first-order
kinetics were found to be the best fast alternative to represent the more
detailed models.
- ANALYTIC EXPRESSION
The first-order model can be solved analytically, leading to a very fast
mechanism for simulating synapses, since no differential equation must be
solved (see references below).
References
Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. An efficient method for
computing synaptic conductances based on a kinetic model of receptor binding
Neural Computation 6: 10-14, 1994.
Destexhe, A., Mainen, Z.F. and Sejnowski, T.J. Synthesis of models for
excitable membranes, synaptic transmission and neuromodulation using a
common kinetic formalism, Journal of Computational Neuroscience 1:
195-230, 1994.
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ENDCOMMENT
NEURON {
POINT_PROCESS NMDAb
RANGE g, Alpha, Beta, e, gmax
NONSPECIFIC_CURRENT iNMDA : i
GLOBAL Cdur, mg, Cmax
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cmax = 1 (mM) : max transmitter concentration
: Cdur = 30 (ms) : transmitter duration (rising phase)
Cdur = 1.1 (ms) : transmitter duration (rising phase)
: Alpha = 0.072 (/ms /mM) : forward (binding) rate
Alpha = 10 (/ms /mM) : forward (binding) rate
: Beta = 0.0066 (/ms) : backward (unbinding) rate
Beta = 0.0125 (/ms) : backward (unbinding) rate
: e = 45 (mV) : reversal potential
e = 0 (mV) : reversal potential
mg = 1 (mM) : external magnesium concentration
}
ASSIGNED {
v (mV) : postsynaptic voltage
iNMDA (nA) : current = g*(v - e)
g (umho) : conductance
Rinf : steady state channels open
Rtau (ms) : time constant of channel binding
synon
B
gmax : magnesium block
}
STATE {Ron Roff}
INITIAL {
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / (Cmax*Alpha + Beta)
synon = 0
}
BREAKPOINT {
SOLVE release METHOD cnexp
B = mgblock(v)
g = (Ron + Roff)*1(umho) * B
iNMDA = g*(v - e)
}
DERIVATIVE release {
Ron' = (synon*Rinf - Ron)/Rtau
Roff' = -Beta*Roff
}
FUNCTION mgblock(v(mV)) {
TABLE
DEPEND mg
FROM -140 TO 80 WITH 1000
: from Jahr & Stevens
mgblock = 1 / (1 + exp(0.062 (/mV) * -v) * (mg / 3.57 (mM)))
}
: following supports both saturation from single input and
: summation from multiple inputs
: if spike occurs during CDur then new off time is t + CDur
: ie. transmitter concatenates but does not summate
: Note: automatic initialization of all reference args to 0 except first
NET_RECEIVE(weight, on, nspike, r0, t0 (ms)) {
: flag is an implicit argument of NET_RECEIVE and normally 0
if (flag == 0) { : a spike, so turn on if not already in a Cdur pulse
nspike = nspike + 1
if (!on) {
r0 = r0*exp(-Beta*(t - t0))
t0 = t
on = 1
synon = synon + weight
state_discontinuity(Ron, Ron + r0)
state_discontinuity(Roff, Roff - r0)
}
: come again in Cdur with flag = current value of nspike
net_send(Cdur, nspike)
}
if (flag == nspike) { : if this associated with last spike then turn off
r0 = weight*Rinf + (r0 - weight*Rinf)*exp(-(t - t0)/Rtau)
t0 = t
synon = synon - weight
state_discontinuity(Ron, Ron - r0)
state_discontinuity(Roff, Roff + r0)
on = 0
}
gmax = weight
}