TITLE simple NMDA receptors
COMMENT
This is modified from the original NMDA receptor provided by Neuron. The only
difference is the Mg2+ block as well as some parameter values.
Author: Fredrik Edin, 2003
Address: freedin@nada.kth.se
Original comment:
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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).
Extension to model: A probability p of transmitter release. p is a function
of the transmission delay, since, for a given normal delay, deviations will
decrease the probability of successful conductance along the axon.
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 nmdaR_2
RANGE g, s, synon, t1, t2
NONSPECIFIC_CURRENT i
GLOBAL Cdur, Alpha, Beta, Erev, Rinf, Rtau
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cdur = 4.0 (ms) : transmitter duration (rising phase)
Alpha = 0.3 (/ms) : forward (binding) rate
Beta = 0.01 (/ms) : backward (unbinding) rate
Erev = 0 (mV) : reversal potential
mag = 1 (mM)
eta = 3.57 (mM)
gamma = 0.062 (/mV)
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
Rinf : steady state channels open
Rtau (ms) : time constant of channel binding
synon
t1
t2
s
}
STATE {Ron Roff}
INITIAL {
Rinf = Alpha / (Alpha + Beta)
Rtau = 1 / (Alpha + Beta)
synon = 0
t1 = 0
t2 = 0
}
BREAKPOINT {
SOLVE release METHOD cnexp
s = Ron + Roff
g = s * 1(umho) /(1 + mag * exp( - gamma * v ) / eta )
i = g * (v - Erev)
}
DERIVATIVE release {
Ron' = (synon*Rinf - Ron)/Rtau
Roff' = -Beta*Roff
}
: 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
t1 = t1 + 1
if (!on) {
t2 = t2 + 1
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
}
}