# Short-term plasticity (STP) synapse models¶

template<typename targetidentifierT>
class Quantal_StpConnection : public Connection<targetidentifierT>
#include <quantal_stp_connection.h>

Name: quantal_stp_synapse - Probabilistic synapse model with short term plasticity.

Description:

This synapse model implements synaptic short-term depression and short-term facilitation according to the quantal release model described by Fuhrmann et al. [1] and Loebel et al. [2].

Each presynaptic spike will stochastically activate a fraction of the available release sites. This fraction is binomialy distributed and the release probability per site is governed by the Fuhrmann et al. (2002) model. The solution of the differential equations is taken from Maass and Markram 2002 [3].

The connection weight is interpreted as the maximal weight that can be obtained if all n release sites are activated.

Parameters:

The following parameters can be set in the status dictionary:

 U real Maximal fraction of available resources [0,1], default=0.5 u real Available fraction of resources [0,1], default=0.5 p real Probability that a vesicle is available, default = 1.0 n integer Total number of release sites, default = 1 a integer Number of available release sites, default = n tau_rec ms Time constant for depression, default=800 ms tau_rec ms Time constant for facilitation, default=0 (off)

References:

1

Fuhrmann G, Segev I, Markram H, Tsodyks MV (2002). Coding of temporal information by activity-dependent synapses. Journal of neurophysiology, 87(1):140-8. DOI: https://doi.org/10.1152/jn.00258.2001

2

Loebel A, Silberberg G, Helbig D, Markram H, Tsodyks MV, Richardson MJE (2009). Multiquantal release underlies the distribution of synaptic efficacies in the neocortex. Frontiers in Computational Neuroscience, 3, 27. DOI: https://doi.org/10.3389/neuro.10.027.2009

3

Maass W, Markram H (2002). Synapses as dynamic memory buffers. Neural Networks, 15(2):155-161. DOI: https://doi.org/10.1016/S0893-6080(01)00144-7

Transmits: SpikeEvent

FirstVersion: December 2013

Author: Marc-Oliver Gewaltig, based on tsodyks2_synapse

SeeAlso: tsodyks2_synapse, synapsedict, stdp_synapse, static_synapse

template<typename targetidentifierT>
class Tsodyks2Connection : public Connection<targetidentifierT>
#include <tsodyks2_connection.h>

Name: tsodyks2_synapse - Synapse type with short term plasticity.

Description:

This synapse model implements synaptic short-term depression and short-term facilitation according to [1] and [2]. It solves Eq (2) from [1] and modulates U according to eq. (2) of [2].

This connection merely scales the synaptic weight, based on the spike history and the parameters of the kinetic model. Thus, it is suitable for all types of synaptic dynamics, that is current or conductance based.

The parameter A_se from the publications is represented by the synaptic weight. The variable x in the synapse properties is the factor that scales the synaptic weight.

Parameters:

The following parameters can be set in the status dictionary:

 U real Maximum probability of release (U1) [0,1], default=0.5 u real Maximum probability of release (U_se) [0,1], default=0.5 x real Current scaling factor of the weight, default=U tau_fac ms Time constant for facilitation, default = 0(off) tau_rec ms Time constant for depression, default = 800ms

Remarks:

Under identical conditions, the tsodyks2_synapse produces slightly lower peak amplitudes than the tsodyks_synapse. However, the qualitative behavior is identical. The script test_tsodyks2_synapse.py in the examples compares the two synapse models.

References:

1

Tsodyks MV, Markram H (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. PNAS, 94(2):719-23. DOI: https://doi.org/10.1073/pnas.94.2.719

2

Fuhrman, G, Segev I, Markram H, Tsodyks MV (2002). Coding of temporal information by activity-dependent synapses. Journal of Neurophysiology, 87(1):140-8. DOI: https://doi.org/10.1152/jn.00258.2001

3

Maass W, Markram H (2002). Synapses as dynamic memory buffers. Neural Networks, 15(2):155-61. DOI: https://doi.org/10.1016/S0893-6080(01)00144-7

Transmits: SpikeEvent

FirstVersion: October 2011

Author: Marc-Oliver Gewaltig, based on tsodyks_synapse by Moritz Helias

SeeAlso: tsodyks_synapse, synapsedict, stdp_synapse, static_synapse

template<typename targetidentifierT>
class TsodyksConnection : public Connection<targetidentifierT>
#include <tsodyks_connection.h>

Name: 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 iaf_tum_2000, 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:

The following parameters can be set in the status dictionary:

 U real Maximum probability of release [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]

References:

1

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

FirstVersion: March 2006

Author: Moritz Helias

SeeAlso: synapsedict, stdp_synapse, static_synapse, iaf_psc_exp, iaf_tum_2000

class TsodyksHomCommonProperties : public CommonPropertiesHomW
#include <tsodyks_connection_hom.h>

Name: tsodyks_synapse_hom - Synapse type with short term plasticity using homogeneous parameters, i.e. all synapses have the same 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_tum_2000, 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 Maximum probability of release [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

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

FirstVersion: March 2006

Author: Susanne Kunkel, Moritz Helias

SeeAlso: synapsedict, tsodyks_synapse, stdp_synapse_hom, static_synapse_hom_w, iaf_psc_exp, iaf_tum_2000 Class containing the common properties for all synapses of type TsodyksConnectionHom.