# 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)
>>>
>>> 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()
>>>
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()


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)
>>>
>>> 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()
>>>
>>> plt.plot(runner.mon.ts, runner.mon['syn.I'][:, 0], label='I')
>>> plt.legend()
>>>
>>> plt.xlabel('Time (ms)')
>>> plt.show()


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.