COMMENT
Summating nmda synapse. This synapse is modified from the standard
Neuron exp2syn mechanism. Changes are restricted to a Mg2+ block.
It can be used to represent several different non-summating synapses
provided their firing rate is not too large and provided they are
close spatially.
Author: Fredrik Edin, 2003
Address: freedin@nada.kth.se
Original comment:
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Two state kinetic scheme synapse described by rise time tau1,
decay time constant tau2, and peak conductance gtrig.
Decay time MUST be greater than rise time.
The solution of A->G->bath with rate constants 1/tau1 and 1/tau2 is
A = a*exp(-t/tau1) and
G = a*tau2/(tau2-tau1)*(-exp(-t/tau1) + exp(-t/tau2))
where tau1 < tau2
(Notice if tau1 -> 0 then we have just single exponential decay.)
The factor is evaluated in the
initial block such that the peak conductance is gtrig.
Because the solution is a sum of exponentials, the
coupled equations can be solved as a pair of independent equations
by the more efficient cnexp method.
Specify an incremental delivery event
(synapse starts delay after the source
crosses threshold. gtrig is incremented by the amount specified in
the delivery event, onset will be set to the proper time)
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ENDCOMMENT
NEURON {
POINT_PROCESS nmdaSUM
RANGE tau1, tau2, e, i
NONSPECIFIC_CURRENT i
RANGE g, s
GLOBAL total
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
}
PARAMETER {
tau1 = .1 (ms)
tau2 = 10 (ms)
e = 0 (mV)
mag = 1 (mM)
eta = 3.57 (mM)
gamma = 0.062 (/mV)
}
ASSIGNED {
v (mV)
i (nA)
g (umho)
s
factor
total (umho)
}
STATE {
A (umho)
B (umho)
}
INITIAL {
LOCAL tp
total = 0
A = 0
B = 0
tp = (tau1*tau2)/(tau2 - tau1) * log(tau2/tau1)
factor = -exp(-tp/tau1) + exp(-tp/tau2)
factor = 1/factor
}
BREAKPOINT {
SOLVE state METHOD cnexp
s = B - A
g = s * 1(umho) /(1 + mag * exp( - (gamma * v)) / eta )
i = g * (v - e)
}
DERIVATIVE state {
A' = -A/tau1
B' = -B/tau2
}
NET_RECEIVE(weight (umho)) {
state_discontinuity(A, A + weight*factor)
state_discontinuity(B, B + weight*factor)
total = total+weight
}