STP

class brainpy.state.STP(in_size, name=None, U=0.15, tau_f=Quantity(1500., 'ms'), tau_d=Quantity(200., 'ms'))

Synapse with short-term plasticity.

This class implements a synapse model with short-term plasticity (STP), which captures activity-dependent changes in synaptic efficacy that occur over milliseconds to seconds. The model simultaneously accounts for both short-term facilitation and depression based on the formulation by Tsodyks & Markram (1998).

The model is characterized by the following equations:

\[ \frac{du}{dt} = -\frac{u}{\tau_f} + U \cdot (1 - u) \cdot \delta(t - t_{spike}) \]

\[ \frac{dx}{dt} = \frac{1 - x}{\tau_d} - u \cdot x \cdot \delta(t - t_{spike}) \]

\[ g_{syn} = u \cdot x \]

where:

• \(u\) represents the utilization of synaptic efficacy (facilitation variable)

• \(x\) represents the available synaptic resources (depression variable)

• \(\tau_f\) is the facilitation time constant

• \(\tau_d\) is the depression time constant

• \(U\) is the baseline utilization parameter

• \(\delta(t - t_{spike})\) is the Dirac delta function representing presynaptic spikes

• \(g_{syn}\) is the effective synaptic conductance

Parameters:

• in_size (Size) – Size of the input.

• name (str, optional) – Name of the synapse instance.

• U (ArrayLike, default 0.15) – Baseline utilization parameter (fraction of resources used per action potential).

• tau_f (ArrayLike, default 1500.*u.ms) – Time constant of short-term facilitation in milliseconds.

• tau_d (ArrayLike, default 200.*u.ms) – Time constant of short-term depression (recovery of synaptic resources) in milliseconds.

u

Utilization of synaptic efficacy (facilitation variable).

Type:

HiddenState

x

Available synaptic resources (depression variable).

Type:

HiddenState

See also

STD

Short-term depression only model.

Notes

• Larger values of tau_f produce stronger facilitation effects.

• Larger values of tau_d lead to slower recovery from depression.

• The parameter U controls the initial release probability [1].

• The effective synaptic strength is the product of u and x.

• For a comprehensive treatment of short-term plasticity dynamics, see [2].

References

[1]

Tsodyks, M. V., & Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proceedings of the National Academy of Sciences, 94(2), 719-723.

[2]

Tsodyks, M., Pawelzik, K., & Markram, H. (1998). Neural networks with dynamic synapses. Neural computation, 10(4), 821-835.

Examples

>>> import brainpy
>>> import brainstate
>>> import saiunit as u
>>> # Create an STP synapse with facilitation-dominant parameters
>>> stp = brainpy.state.STP(100, U=0.1, tau_f=1500.*u.ms, tau_d=200.*u.ms)
>>> stp.init_state(batch_size=1)

init_state(batch_size=None, **kwargs)

State initialization function.

reset_state(batch_size=None, **kwargs)

State resetting function.