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)

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

• STP for Working Memory Capacity

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, png, hires.png, pdf)

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, png, hires.png, pdf)

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)

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.
get_delay_data(name, delay_step, *indices)	Get delay data according to the provided delay steps.
ints([method])	Collect all integrators in this node and the children nodes.
load_states(filename[, verbose])	Load the model states.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(name, delay_step, delay_target)	Register delay variable.
register_implicit_nodes(nodes)
register_implicit_vars(variables)
reset()	Reset function which reset the whole variables in the model.
reset_delay(name, delay_target)	Reset the delay variable.
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(t, dt)	The function to specify the updating rule.
update_delay(name, delay_data)	Update the delay according to the delay data.
vars([method, level, include_self])	Collect all variables in this node and the children nodes.

Attributes

derivative
global_delay_vars
name
steps