tsodyks_synapse

Synapse type with short term plasticity

Description

This synapse model implements synaptic short-term depression and short-term facilitation according to [1]. In particular it solves Eqs (3) and (4) from this paper in an exact manner.

Synaptic depression is motivated by depletion of vesicles in the readily releasable pool of synaptic vesicles (variable x in equation (3)). Synaptic facilitation comes about by a presynaptic increase of release probability, which is modeled by variable U in Eq (4).

The original interpretation of variable y is the amount of glutamate concentration in the synaptic cleft. In [1] this variable is taken to be directly proportional to the synaptic current caused in the postsynaptic neuron (with the synaptic weight w as a proportionality constant). In order to reproduce the results of [1] and to use this model of synaptic plasticity in its original sense, the user therefore has to ensure the following conditions:

1. The postsynaptic neuron must be of type iaf_psc_exp or similar, because these neuron models have a postsynaptic current which decays exponentially.

2. The time constant of each tsodyks_synapse targeting a particular neuron must be chosen equal to that neuron’s synaptic time constant. In particular that means that all synapses targeting a particular neuron have the same parameter tau_psc.

However, there are no technical restrictions using this model of synaptic plasticity also in conjunction with neuron models that have a different dynamics for their synaptic current or conductance. The effective synaptic weight, which will be transmitted to the postsynaptic neuron upon occurrence of a spike at time t is \(u(t) \cdot x(t) \cdot w\), where u(t) and x(t) are defined in Eq (3) and (4), w is the synaptic weight specified upon connection. The interpretation is as follows: The quantity \(u(t) \cdot x(t)\) is the release probability times the amount of releasable synaptic vesicles at time t of the presynaptic neuron’s spike, so this equals the amount of transmitter expelled into the synaptic cleft.

The amount of transmitter then relaxes back to 0 with time constant tau_psc of the synapse’s variable y. Since the dynamics of y(t) is linear, the postsynaptic neuron can reconstruct from the amplitude of the synaptic impulse \(u(t) \cdot x(t) \cdot w\) the full shape of y(t). The postsynaptic neuron, however, might choose to have a synaptic current that is not necessarily identical to the concentration of transmitter y(t) in the synaptic cleft. It may realize an arbitrary postsynaptic effect depending on y(t).

Please note that the initial value of u should be equal to the value of U. Thus, when setting a new value for U before the start of the simulation, make sure to set u to the same value.

References

[1] (1,2,3)

Tsodyks M, Uziel A, Markram H (2000). Synchrony generation in recurrent networks with frequency-dependent synapses. Journal of Neuroscience, 20 RC50. URL: http://infoscience.epfl.ch/record/183402

Parameters

Name	Physical unit	Default value	Description
d	ms	1ms	Synaptic transmission delay
w	real	1	Synaptic weight
tau_psc	ms	3ms
tau_fac	ms	0ms	Setting tau_fac = 0 disables facilitation
tau_rec	ms	800ms
U	real	.5

State variables

Name	Physical unit	Default value	Description
x	real	1
y	real	0
u	real	U
t_last_update	ms	0ms

Source code

The model source code can be found in the NESTML models repository here: tsodyks_synapse.