brainmodels.synapses.DualExpCUBA

class brainmodels.synapses.DualExpCUBA(pre, post, conn, delay=0.0, g_max=1.0, tau_decay=10.0, tau_rise=1.0, method='exponential_euler', **kwargs)[source]

Current-based dual exponential synapse model.

Model Descriptions

The dual exponential synapse model 1, also named as difference of two exponentials model, is given by:

\[g_{\mathrm{syn}}(t)=g_{\mathrm{max}} \frac{\tau_{1} \tau_{2}}{ \tau_{1}-\tau_{2}}\left(\exp \left(-\frac{t-t_{0}}{\tau_{1}}\right) -\exp \left(-\frac{t-t_{0}}{\tau_{2}}\right)\right)\]

where \(\tau_1\) is the time constant of the decay phase, \(\tau_2\) is the time constant of the rise phase, \(t_0\) is the time of the pre-synaptic spike, \(g_{\mathrm{max}}\) is the maximal conductance.

However, in practice, this formula is hard to implement. The equivalent solution is two coupled linear differential equations 2:

\[\begin{split}\begin{aligned} &g_{\mathrm{syn}}(t)=g_{\mathrm{max}} g \\ &\frac{d g}{d t}=-\frac{g}{\tau_{\mathrm{decay}}}+h \\ &\frac{d h}{d t}=-\frac{h}{\tau_{\text {rise }}}+ \delta\left(t_{0}-t\right), \end{aligned}\end{split}\]

The current onto the post-synaptic neuron is given by

\[I_{syn}(t) = g_{\mathrm{syn}}(t).\]

Model Examples

Model Parameters

Parameter

Init Value

Unit

Explanation

delay

0

ms

The decay length of the pre-synaptic spikes.

tau_decay

10

ms

The time constant of the synaptic decay phase.

tau_rise

1

ms

The time constant of the synaptic rise phase.

g_max

1

µmho(µS)

The maximum conductance.

Model Variables

Member name

Initial values

Explanation

g

0

Synapse conductance on the post-synaptic neuron.

s

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.

2

Roth, A., & Van Rossum, M. C. W. (2009). Modeling Synapses. Computational Modeling Methods for Neuroscientists.

__init__(pre, post, conn, delay=0.0, g_max=1.0, tau_decay=10.0, tau_rise=1.0, method='exponential_euler', **kwargs)[source]

Methods

__init__(pre, post, conn[, delay, g_max, ...])

build_inputs([inputs, show_code])

build_monitors([show_code])

cpu()

cuda()

derivative(g, h, 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.