brainpy.dyn.synapses.STP#

class brainpy.dyn.synapses.STP(pre, post, conn, U=0.15, tau_f=1500.0, tau_d=200.0, tau=8.0, A=1.0, delay_step=None, method='exp_auto', name=None)[source]#

Short-term plasticity model.

Model Descriptions

Short-term plasticity (STP) 1 2 3, also called dynamical synapses, refers to the changes of synaptic strengths over time in a way that reflects the history of presynaptic activity. Two types of STP, with opposite effects on synaptic efficacy, have been observed in experiments. They are known as Short-Term Depression (STD) and Short-Term Facilitation (STF).

In the model proposed by Tsodyks and Markram 4 5, the STD effect is modeled by a normalized variable \(x (0 \le x \le 1)\), denoting the fraction of resources that remain available after neurotransmitter depletion. The STF effect is modeled by a utilization parameter \(u\), representing the fraction of available resources ready for use (release probability). Following a spike,

  • (i) \(u\) increases due to spike-induced calcium influx to the presynaptic terminal, after which

  • (ii) a fraction \(u\) of available resources is consumed to produce the post-synaptic current.

Between spikes, \(u\) decays back to zero with time constant \(\tau_f\) and \(x\) recovers to 1 with time constant \(\tau_d\).

In summary, the dynamics of STP is given by

\[\begin{split}\begin{aligned} \frac{du}{dt} & = -\frac{u}{\tau_f}+U(1-u^-)\delta(t-t_{sp}),\nonumber \\ \frac{dx}{dt} & = \frac{1-x}{\tau_d}-u^+x^-\delta(t-t_{sp}), \\ \frac{dI}{dt} & = -\frac{I}{\tau_s} + Au^+x^-\delta(t-t_{sp}), \end{aligned}\end{split}\]

where \(t_{sp}\) denotes the spike time and \(U\) is the increment of \(u\) produced by a spike. \(u^-, x^-\) are the corresponding variables just before the arrival of the spike, and \(u^+\) refers to the moment just after the spike. The synaptic current generated at the synapse by the spike arriving at \(t_{sp}\) is then given by

\[\Delta I(t_{spike}) = Au^+x^-\]

where \(A\) denotes the response amplitude that would be produced by total release of all the neurotransmitter (\(u=x=1\)), called absolute synaptic efficacy of the connections.

Model Examples

STD

>>> import brainpy as bp
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = bp.dyn.LIF(1)
>>> neu2 = bp.dyn.LIF(1)
>>> syn1 = bp.dyn.STP(neu1, neu2, bp.connect.All2All(), U=0.2, tau_d=150., tau_f=2.)
>>> net = bp.dyn.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.dyn.DSRunner(net, inputs=[('pre.input', 28.)], monitors=['syn.I', 'syn.u', 'syn.x'])
>>> runner.run(150.)
>>>
>>>
>>> # plot
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 7)
>>>
>>> fig.add_subplot(gs[0, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.u'][:, 0], label='u')
>>> plt.plot(runner.mon.ts, runner.mon['syn.x'][:, 0], label='x')
>>> plt.legend()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()

(Source code)

STF

>>> import brainpy as bp
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = bp.dyn.LIF(1)
>>> neu2 = bp.dyn.LIF(1)
>>> syn1 = bp.dyn.STP(neu1, neu2, bp.connect.All2All(), U=0.1, tau_d=10, tau_f=100.)
>>> net = bp.dyn.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.dyn.DSRunner(net, inputs=[('pre.input', 28.)], monitors=['syn.I', 'syn.u', 'syn.x'])
>>> runner.run(150.)
>>>
>>>
>>> # plot
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 7)
>>>
>>> fig.add_subplot(gs[0, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.u'][:, 0], label='u')
>>> plt.plot(runner.mon.ts, runner.mon['syn.x'][:, 0], label='x')
>>> plt.legend()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()

(Source code)

Model Parameters

Parameter

Init Value

Unit

Explanation

tau_d

200

ms

Time constant of short-term depression.

tau_f

1500

ms

Time constant of short-term facilitation.

U

.15

The increment of \(u\) produced by a spike.

A

1

The response amplitude that would be produced by total release of all the neurotransmitter

delay

0

ms

The decay time of the current \(I\) output onto the post-synaptic neuron groups.

Model Variables

Member name

Initial values

Explanation

u

0

Release probability of the neurotransmitters.

x

1

A Normalized variable denoting the fraction of remain neurotransmitters.

I

0

Synapse current output onto the post-synaptic neurons.

References

1

Stevens, Charles F., and Yanyan Wang. “Facilitation and depression at single central synapses.” Neuron 14, no. 4 (1995): 795-802.

2

Abbott, Larry F., J. A. Varela, Kamal Sen, and S. B. Nelson. “Synaptic depression and cortical gain control.” Science 275, no. 5297 (1997): 221-224.

3

Abbott, L. F., and Wade G. Regehr. “Synaptic computation.” Nature 431, no. 7010 (2004): 796-803.

4

Tsodyks, Misha, Klaus Pawelzik, and Henry Markram. “Neural networks with dynamic synapses.” Neural computation 10.4 (1998): 821-835.

5

Tsodyks, Misha, and Si Wu. “Short-term synaptic plasticity.” Scholarpedia 8, no. 10 (2013): 3153.

__init__(pre, post, conn, U=0.15, tau_f=1500.0, tau_d=200.0, tau=8.0, A=1.0, delay_step=None, method='exp_auto', name=None)[source]#

Methods

__init__(pre, post, conn[, U, tau_f, tau_d, ...])

check_post_attrs(*attrs)

Check whether post group satisfies the requirement.

check_pre_attrs(*attrs)

Check whether pre group satisfies the requirement.

clear_input()

get_delay_data(identifier, delay_step, *indices)

Get delay data according to the provided delay steps.

load_states(filename[, verbose])

Load the model states.

nodes([method, level, include_self])

Collect all children nodes.

offline_fit(target, fit_record)

offline_init()

online_fit(target, fit_record)

online_init()

register_delay(identifier, delay_step, ...)

Register delay variable.

register_implicit_nodes(*nodes, **named_nodes)

register_implicit_vars(*variables, ...)

reset()

Reset function which reset the whole variables in the model.

reset_local_delays([nodes])

Reset local delay variables.

reset_state([batch_size])

Reset function which reset the states in the model.

save_states(filename[, variables])

Save the model states.

train_vars([method, level, include_self])

The shortcut for retrieving all trainable variables.

unique_name([name, type_])

Get the unique name for this object.

update(tdi)

The function to specify the updating rule.

update_local_delays([nodes])

Update local delay variables.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

derivative

global_delay_data

mode

Mode of the model, which is useful to control the multiple behaviors of the model.

name

Name of the model.