# 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.