# brainmodels.synapses.ExpCUBA

class brainmodels.synapses.ExpCUBA(pre, post, conn, g_max=1.0, delay=0.0, tau=8.0, method='exp_auto', name=None)[source]

Current-based exponential decay synapse model.

Model Descriptions

The single exponential decay synapse model assumes the release of neurotransmitter, its diffusion across the cleft, the receptor binding, and channel opening all happen very quickly, so that the channels instantaneously jump from the closed to the open state. Therefore, its expression is given by

$g_{\mathrm{syn}}(t)=g_{\mathrm{max}} e^{-\left(t-t_{0}\right) / \tau}$

where $$\tau_{delay}$$ is the time constant of the synaptic state decay, $$t_0$$ is the time of the pre-synaptic spike, $$g_{\mathrm{max}}$$ is the maximal conductance.

Accordingly, the differential form of the exponential synapse is given by

\begin{split}\begin{aligned} & g_{\mathrm{syn}}(t) = g_{max} g \\ & \frac{d g}{d t} = -\frac{g}{\tau_{decay}}+\sum_{k} \delta(t-t_{j}^{k}). \end{aligned}\end{split}

For the current output onto the post-synaptic neuron, its expression is given by

$I_{\mathrm{syn}}(t) = g_{\mathrm{syn}}(t)$

Model Examples

>>> import brainpy as bp
>>> import brainmodels
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = brainmodels.neurons.LIF(1)
>>> neu2 = brainmodels.neurons.LIF(1)
>>> syn1 = brainmodels.synapses.ExpCUBA(neu1, neu2, bp.connect.All2All(), g_max=5.)
>>> net = bp.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.StructRunner(net, inputs=[('pre.input', 25.)], monitors=['pre.V', 'post.V', 'syn.g'])
>>> runner.run(150.)
>>>
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> plt.plot(runner.mon.ts, runner.mon['pre.V'], label='pre-V')
>>> plt.plot(runner.mon.ts, runner.mon['post.V'], label='post-V')
>>> plt.legend()
>>>
>>> plt.plot(runner.mon.ts, runner.mon['syn.g'], label='g')
>>> plt.legend()
>>> plt.show()


Model Parameters

 Parameter Init Value Unit Explanation delay 0 ms The decay length of the pre-synaptic spikes. tau_decay 8 ms The time constant of decay. g_max 1 µmho(µS) The maximum conductance.

Model Variables

 Member name Initial values Explanation g 0 Gating variable. pre_spike False The history spiking states of the pre-synaptic neurons.

References

1

Sterratt, David, Bruce Graham, Andrew Gillies, and David Willshaw. “The Synapse.” Principles of Computational Modelling in Neuroscience. Cambridge: Cambridge UP, 2011. 172-95. Print.

__init__(pre, post, conn, g_max=1.0, delay=0.0, tau=8.0, method='exp_auto', name=None)[source]

Methods

 __init__(pre, post, conn[, g_max, delay, ...]) check_post_attrs(*attrs) Check whether post group satisfies the requirement. check_pre_attrs(*attrs) Check whether pre group satisfies the requirement. child_ds([method, include_self]) Return the children instance of dynamical systems. derivative(g, t) ints([method]) Collect all integrators in this node and the children nodes. load_states(filename[, verbose, check_missing]) Load the model states. nodes([method, _paths]) Collect all children nodes. register_constant_delay(key, size, delay[, ...]) Register a constant delay, whose update method will be appended into the self.steps in this host class. register_implicit_nodes(nodes) register_implicit_vars(variables) save_states(filename[, all_vars]) Save the model states. train_vars([method]) 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. vars([method]) Collect all variables in this node and the children nodes.