COMMENT
Revised 12/15/2000 in light of a personal communication
from Misha Tsodyks that u is incremented _before_ x is
converted to y--a point that was not clear in the paper.
If u is incremented _after_ x is converted to y, then
the first synaptic activation after a long interval of
silence will produce smaller and smaller postsynaptic
effect as the length of the silent interval increases,
eventually becoming vanishingly small.
Implementation of a model of short-term facilitation and depression
based on the kinetics described in
Tsodyks et al.
Synchrony generation in recurrent networks
with frequency-dependent synapses
Journal of Neuroscience 20:RC50:1-5, 2000.
Their mechanism represented synapses as current sources.
The mechanism implemented here uses a conductance change instead.
The basic scheme is
x -------> y Instantaneous, spike triggered.
Increment is u*x (see discussion of u below).
x == fraction of "synaptic resources" that have
"recovered" (fraction of xmtr pool that is
ready for release, or fraction of postsynaptic
channels that are ready to be opened, or some
joint function of these two factors)
y == fraction of "synaptic resources" that are in the
"active state." This is proportional to the
number of channels that are open, or the
fraction of max synaptic current that is
being delivered.
tau_1
y -------> z z == fraction of "synaptic resources" that are
in the "inactive state"
tau_rec
z -------> x
where x + y + z = 1
The active state y is multiplied by a synaptic weight to compute
the actual synaptic conductance (or current, in the original form
of the model).
In addition, there is a "facilition" term u that
governs the fraction of x that is converted to y
on each synaptic activation.
-------> u Instantaneous, spike triggered,
happens _BEFORE_ x is converted to y.
Increment is U*(1-u) where U and u both
lie in the range 0 - 1.
tau_facil
u -------> decay of facilitation
This implementation for NEURON offers the user a parameter
u0 that has a default value of 0 but can be used to specify
a nonzero initial value for u.
When tau_facil = 0, u is supposed to equal U.
Note that the synaptic conductance in this mechanism
has the same kinetics as y, i.e. decays with time
constant tau_1.
This mechanism can receive multiple streams of
synaptic input via NetCon objects.
Each stream keeps track of its own
weight and activation history.
The printf() statements are for testing purposes only.
ENDCOMMENT
NEURON {
POINT_PROCESS ltpltd
RANGE e, i, g2, peso, U, tau_facil, tau_rec, tau_1, Rin, Ase
RANGE u0, Pini, Nini, deltap, deltad, f, nip, nid, gamma, eta, VVini
NONSPECIFIC_CURRENT i
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
}
PARAMETER {
: e = -90 mV for inhibitory synapses,
: 0 mV for excitatory
e = 0 (mV)
: tau_1 was the same for inhibitory and excitatory synapses
: in the models used by T et al.
tau_1 = 3 (ms) < 1e-9, 1e9 >
: tau_rec = 100 ms for inhibitory synapses,
: 800 ms for excitatory
tau_rec = 50 (ms) < 1e-9, 1e9 >
: tau_facil = 1000 ms for inhibitory synapses,
: 0 ms for excitatory
tau_facil = 200 (ms) < 0, 1e9 >
: U = 0.05 for inhibitory synapses,
: 0.5 for excitatory
: the (1) is needed for the < 0, 1 > to be effective
: in limiting the values of U and u0
U = 0.36(1) < 0, 1 >
: initial value for the "facilitation variable"
u0 = 0 (1) < 0, 1 >
:PARAMETERS
f = 0.05e-3
deltap = 400
deltad = 400
gamma = 0.2
eta = 2e-3
nip = 0.0987
nid = 0.07
lambdap = 1e-3
lambdad = 2e-3
mp = 3e-3
md = 3e-3
ap = 2
ad = 0.5
taum = 40
Rin=10e7
Ase=2.5e-7
Pini=0
Nini=0
VVini=0
g2=43 (umho)
peso=0.5e-6
}
ASSIGNED {
v (mV)
i (nA)
x
y
}
STATE {
g (umho)
C
Np
Nd
VV (mV)
}
INITIAL {
VV=VVini
g=0
C =0
Np=Pini
Nd=Nini
}
FUNCTION v2(v) { if (v<-65) { v2 = 0 } else {v2 = v+65}
}
BREAKPOINT {
SOLVE state METHOD derivimplicit
i = -g2*VV
}
DERIVATIVE state {
g' = -g/tau_1
C' = gamma*(VV)-eta*C+peso*(v2(v))
Np' = nip*C-(lambdap+g*deltap)*Np+((mp*Np*Np)/(ap+Np*Np))
Nd' = nid*C-(lambdad+g*deltad)*Nd+((md*Nd*Nd)/(ad+Nd*Nd))
VV' = -(VV/taum)+Rin*Ase*g*((1/taum)+f*(deltap*Np-deltad*Nd))
}
NET_RECEIVE(weight (umho), y, z, u, tsyn (ms))
{
INITIAL {
: these are in NET_RECEIVE to be per-stream
y = 0
z = 0
: u = 0
u = u0
tsyn = t
: this header will appear once per stream
:printf("t\t t-tsyn\t y\t z\t u\t newu\t g\t dg\t newg\t newy\n")
}
: first calculate z at event-
: based on prior y and z
z = z*exp(-(t - tsyn)/tau_rec)
z = z + ( y*(exp(-(t - tsyn)/tau_1) - exp(-(t - tsyn)/tau_rec)) / ((tau_1/tau_rec)-1) )
: now calc y at event-
y = y*exp(-(t - tsyn)/tau_1)
x = 1-y-z
: calc u at event--
if (tau_facil > 0) {
u = u*exp(-(t - tsyn)/tau_facil)
} else {
u = U
}
:printf("%g\t%g\t%g\t%g\t%g", t, t-tsyn, y, z, u)
if (tau_facil > 0) {
state_discontinuity(u, u + U*(1-u))
}
: printf("\t%g\t%g\t%g", u, g, weight*x*u)
state_discontinuity(g, g + weight*x*u)
state_discontinuity(y, y + x*u)
tsyn = t
:printf("\t%g\t%g\n", g, y)
:printf("\t%g\t\t%g\t\t%g\t\t%g\n", dt, x, y, z)
}