brainmodels.synapses.STP

class brainmodels.synapses.STP(pre, post, conn, U=0.15, tau_f=1500.0, tau_d=200.0, tau=8.0, A=1.0, delay=0.0, method='exponential_euler', **kwargs)[source]

Short-term plasticity model.

Model Descriptions

Short-term plasticity (STP) 1 2 3, also called dynamical synapses, refers to a phenomenon in which synaptic efficacy changes 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

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=0.0, method='exponential_euler', **kwargs)[source]

Methods

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

build_inputs([inputs, show_code])

build_monitors([show_code])

cpu()

cuda()

derivative(I, u, x, t)

ints([method])

Collect all integrators in this node and the children nodes.

jax_update(_t, _dt)

load_states(filename[, verbose, check])

Load the model states.

nodes([method, _paths])

Collect all children nodes.

numpy_update(_t, _dt)

register_constant_delay(key, size, delay[, ...])

Register a constant delay.

run(duration[, dt, report, inputs, extra_func])

The running function.

save_states(filename[, all_vars])

Save the model states.

step(t_and_dt, **kwargs)

to(devices)

tpu()

train_vars([method])

The shortcut for retrieving all trainable variables.

unique_name([name, type])

Get the unique name for this object.

update(*args, **kwargs)

The function to specify the updating rule.

vars([method])

Collect all variables in this node and the children nodes.

Attributes

implicit_nodes

Used to wrap the implicit children nodes which cannot be accessed by self.xxx

implicit_vars

Used to wrap the implicit variables which cannot be accessed by self.xxx

target_backend

Used to specify the target backend which the model to run.