### Spike-Time Dependent Plasticity in a parallel network

Posted:

**Thu Feb 05, 2015 5:05 pm**As the title suggests, I am trying to add spike-time dependent plasticity to a parallel network.

Basically what I need to do is modify the synaptic weights every time an action potential occurs based upon the relative time of the presynaptic and postsynaptic spikes of the spiking neuron in question.

My intuition tells me that this needs to be done in the NET_RECEIVE block of my synapse code, but I'm unsure as to how. Assume we have five neurons A1, A2, B, C1, and C2 connected in such that A1 and A2 synapse onto B and B onto C1 and C2, using NetCon objects A1B, A2B, BC1, and BC2. When neuron B spikes, I need to check the most recent spike times of all cells that synapse onto it as well as all cells it synapses onto. If A1 or A2 recently fired, their synaptic weights will be increased, while if C1 or C2 recently fired, their synaptic weights will be decreased.

Am I on the right track?

Basically what I need to do is modify the synaptic weights every time an action potential occurs based upon the relative time of the presynaptic and postsynaptic spikes of the spiking neuron in question.

My intuition tells me that this needs to be done in the NET_RECEIVE block of my synapse code, but I'm unsure as to how. Assume we have five neurons A1, A2, B, C1, and C2 connected in such that A1 and A2 synapse onto B and B onto C1 and C2, using NetCon objects A1B, A2B, BC1, and BC2. When neuron B spikes, I need to check the most recent spike times of all cells that synapse onto it as well as all cells it synapses onto. If A1 or A2 recently fired, their synaptic weights will be increased, while if C1 or C2 recently fired, their synaptic weights will be decreased.

Am I on the right track?

Code: Select all

```
TITLE simple AMPA receptors (discrete connections)
COMMENT
-----------------------------------------------------------------------------
Simple model for glutamate AMPA receptors
=========================================
- 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.
See also:
http://www.cnl.salk.edu/~alain
http://cns.fmed.ulaval.ca
-----------------------------------------------------------------------------
ENDCOMMENT
INDEPENDENT {t FROM 0 TO 1 WITH 1 (ms)}
NEURON {
POINT_PROCESS AMPA_S
RANGE C, R, R0, R1, g, Cmax
NONSPECIFIC_CURRENT i
GLOBAL Cdur, Alpha, Beta, Erev, blockTime, Rinf, Rtau
}
UNITS {
(nA) = (nanoamp)
(mV) = (millivolt)
(umho) = (micromho)
(mM) = (milli/liter)
}
PARAMETER {
Cmax = 0.5 (mM) : max transmitter concentration (set = 1 to match ~/netcon/ampa.hoc)
Cdur = 0.3 (ms) : transmitter duration (rising phase)
Alpha = 0.94 (/ms mM) : forward (binding) rate
Beta = 0.18 (/ms) : backward (unbinding) rate
Erev = 0 (mV) : reversal potential
blockTime = 2 (ms) : time window following dbs event during which non-dbs events are blocked
}
ASSIGNED {
v (mV) : postsynaptic voltage
i (nA) : current = g*(v - Erev)
g (umho) : conductance
C (mM) : transmitter concentration
R : fraction of open channels
R0 : open channels at start of time period
Rinf : steady state channels open
Rtau (ms) : time constant of channel binding
on : rising phase of PSC
gmax : max conductance
tLast
nspike
collisionBlock
}
INITIAL {
R = 0
C = 0
Rinf = Cmax*Alpha / (Cmax*Alpha + Beta)
Rtau = 1 / ((Alpha * Cmax) + Beta)
on = 0
R0 = 0
nspike = 0
collisionBlock = 0
}
BREAKPOINT {
SOLVE release
i = R*(v - Erev)
}
PROCEDURE release() {
if (on) { : transmitter being released?
R = gmax*Rinf + (R0 - gmax*Rinf) * exptable (- (t - tLast) / Rtau)
} else { : no release occuring
R = R0 * exptable (- Beta * (t - tLast))
}
VERBATIM
return 0;
ENDVERBATIM
}
: 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, ncType, ncPrb) {LOCAL ok, tmp :ncType 0=presyn cell, 1=dbs activated axon
INITIAL {
}
: 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
ok = 0
if (ncType == 1) {
collisionBlock = collisionBlock + 1
net_send(blockTime, -1)
ok = 1
}
else
if (collisionBlock == 0) {
ok = 1
}
if (ok) {
if (!on) {
on = 1
tLast = t
R0 = R
gmax = weight :weight not additive from separate sources as in original ampa.mod
}
nspike = nspike + 1 : come again in Cdur with flag = current value of nspike
net_send(Cdur, nspike)
}
}
else
if (flag == nspike) { : if this associated with last spike then turn off
if (on) {
on = 0
tLast = t
R0 = R
gmax = 0
}
}
else
if (flag == -1) {
collisionBlock = collisionBlock - 1
}
}
FUNCTION exptable(x) {
TABLE FROM -10 TO 10 WITH 2000
if ((x > -10) && (x < 10)) {
exptable = exp(x)
} else {
exptable = 0.
}
}
```