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# tsodyks_connection_hom – Synapse type with short term plasticity using homogeneous parameters¶

## 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 iaf_psc_exp_htum, 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)*x(t)*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)*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 than 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)*x(t)*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).

## Parameters¶

U |
real |
Parameter determining the increase in u with each spike [0,1] |

tau_psc |
ms |
Time constant of synaptic current |

tau_fac |
ms |
Time constant for facilitation |

tau_rec |
ms |
Time constant for depression |

x |
real |
Initial fraction of synaptic vesicles in the readily releasable pool [0,1] |

y |
real |
Initial fraction of synaptic vesicles in the synaptic cleft [0,1] |

Remarks:

The weight and the parameters U, tau_psc, tau_fac, and tau_rec are common to all synapses of the model and must be set using SetDefaults on the synapse model.

## 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

## Transmits¶

SpikeEvent