# 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.