brainpy.synapses.NMDA

class brainpy.synapses.NMDA(pre, post, conn, output=MgBlock, stp=None, comp_method='dense', g_max=0.15, delay_step=None, tau_decay=100.0, a=0.5, tau_rise=2.0, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)

NMDA synapse model.

Model Descriptions

The NMDA receptor is a glutamate receptor and ion channel found in neurons. The NMDA receptor is one of three types of ionotropic glutamate receptors, the other two being AMPA and kainate receptors.

The NMDA receptor mediated conductance depends on the postsynaptic voltage. The voltage dependence is due to the blocking of the pore of the NMDA receptor from the outside by a positively charged magnesium ion. The channel is nearly completely blocked at resting potential, but the magnesium block is relieved if the cell is depolarized. The fraction of channels \(g_{\infty}\) that are not blocked by magnesium can be fitted to

\[g_{\infty}(V,[{Mg}^{2+}]_{o}) = (1+{e}^{-\alpha V} \frac{[{Mg}^{2+}]_{o}} {\beta})^{-1}\]

Here \([{Mg}^{2+}]_{o}\) is the extracellular magnesium concentration, usually 1 mM. Thus, the channel acts as a “coincidence detector” and only once both of these conditions are met, the channel opens and it allows positively charged ions (cations) to flow through the cell membrane [2].

If we make the approximation that the magnesium block changes instantaneously with voltage and is independent of the gating of the channel, the net NMDA receptor-mediated synaptic current is given by

\[I_{syn} = g_\mathrm{NMDA}(t) (V(t)-E) \cdot g_{\infty}\]

where \(V(t)\) is the post-synaptic neuron potential, \(E\) is the reversal potential.

Simultaneously, the kinetics of synaptic state \(g\) is given by

\[\begin{split}& g_\mathrm{NMDA} (t) = g_{max} g \\ & \frac{d g}{dt} = -\frac{g} {\tau_{decay}}+a x(1-g) \\ & \frac{d x}{dt} = -\frac{x}{\tau_{rise}}+ \sum_{k} \delta(t-t_{j}^{k})\end{split}\]

where the decay time of NMDA currents is usually taken to be \(\tau_{decay}\) =100 ms, \(a= 0.5 ms^{-1}\), and \(\tau_{rise}\) =2 ms.

The NMDA receptor has been thought to be very important for controlling synaptic plasticity and mediating learning and memory functions [3].

Model Examples

• (Wang, 2002) Decision making spiking model

>>> import brainpy as bp
>>> from brainpy import synapses, neurons
>>> import matplotlib.pyplot as plt
>>>
>>> neu1 = neurons.HH(1)
>>> neu2 = neurons.HH(1)
>>> syn1 = synapses.NMDA(neu1, neu2, bp.connect.All2All())
>>> net = bp.Network(pre=neu1, syn=syn1, post=neu2)
>>>
>>> runner = bp.DSRunner(net, inputs=[('pre.input', 5.)], monitors=['pre.V', 'post.V', 'syn.g', 'syn.x'])
>>> runner.run(150.)
>>>
>>> fig, gs = bp.visualize.get_figure(2, 1, 3, 8)
>>> fig.add_subplot(gs[0, 0])
>>> 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()
>>>
>>> fig.add_subplot(gs[1, 0])
>>> plt.plot(runner.mon.ts, runner.mon['syn.g'], label='g')
>>> plt.plot(runner.mon.ts, runner.mon['syn.x'], label='x')
>>> plt.legend()
>>> plt.show()

Parameters:

• pre (NeuDyn) – The pre-synaptic neuron group.

• post (NeuDyn) – The post-synaptic neuron group.

• conn (optional, ArrayType, dict of (str, ndarray), TwoEndConnector) – The synaptic connections.

• comp_method (str) – The connection type used for model speed optimization. It can be sparse and dense. The default is dense.

• delay_step (int, ArrayType, Initializer, Callable) – The delay length. It should be the value of \(\mathrm{delay\_time / dt}\).

• g_max (float, ArrayType, Initializer, Callable) – The synaptic strength (the maximum conductance). Default is 1.

• tau_decay (float, ArrayType) – The time constant of the synaptic decay phase. Default 100 [ms]

• tau_rise (float, ArrayType) – The time constant of the synaptic rise phase. Default 2 [ms]

• a (float, ArrayType) – Default 0.5 ms^-1.

• name (str) – The name of this synaptic projection.

• method (str) – The numerical integration methods.

References

[1]

Brunel N, Wang X J. Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition[J]. Journal of computational neuroscience, 2001, 11(1): 63-85.

[2]

Furukawa, Hiroyasu, Satinder K. Singh, Romina Mancusso, and Eric Gouaux. “Subunit arrangement and function in NMDA receptors.” Nature 438, no. 7065 (2005): 185-192.

[3]

Li, F. and Tsien, J.Z., 2009. Memory and the NMDA receptors. The New England journal of medicine, 361(3), p.302.

[4]

https://en.wikipedia.org/wiki/NMDA_receptor

__init__(pre, post, conn, output=MgBlock, stp=None, comp_method='dense', g_max=0.15, delay_step=None, tau_decay=100.0, a=0.5, tau_rise=2.0, method='exp_auto', name=None, mode=None, stop_spike_gradient=False)

Methods

__init__(pre, post, conn[, output, stp, ...])
add_aft_update(key, fun)	Add the after update into this node
add_bef_update(key, fun)	Add the before update into this node
add_inp_fun(key, fun[, label, category])	Add an input function.
check_post_attrs(*attrs)	Check whether post group satisfies the requirement.
check_pre_attrs(*attrs)	Check whether pre group satisfies the requirement.
clear_input(*args, **kwargs)	Empty function of clearing inputs.
cpu()	Move all variable into the CPU device.
cuda()	Move all variables into the GPU device.
get_aft_update(key)	Get the after update of this node by the given key.
get_bef_update(key)	Get the before update of this node by the given key.
get_delay_data(identifier, delay_pos, *indices)	Get delay data according to the provided delay steps.
get_delay_var(name)
get_inp_fun(key)	Get the input function.
get_local_delay(var_name, delay_name)	Get the delay at the given identifier (name).
has_aft_update(key)	Whether this node has the after update of the given key.
has_bef_update(key)	Whether this node has the before update of the given key.
jit_step_run(i, *args, **kwargs)	The jitted step function for running.
load_state(state_dict, **kwargs)	Load states from a dictionary.
load_state_dict(state_dict[, warn, compatible])	Copy parameters and buffers from state_dict into this module and its descendants.
nodes([method, level, include_self])	Collect all children nodes.
register_delay(identifier, delay_step, ...)	Register delay variable.
register_implicit_nodes(*nodes[, node_cls])
register_implicit_vars(*variables[, var_cls])
register_local_delay(var_name, delay_name[, ...])	Register local relay at the given delay time.
reset(*args, **kwargs)	Reset function which reset the whole variables in the model (including its children models).
reset_local_delays([nodes])	Reset local delay variables.
reset_state(*args, **kwargs)
save_state(**kwargs)	Save states as a dictionary.
setattr(key, value)	rtype: None
state_dict(**kwargs)	Returns a dictionary containing a whole state of the module.
step_run(i, *args, **kwargs)	The step run function.
sum_current_inputs(*args[, init, label])	Summarize all current inputs by the defined input functions .current_inputs.
sum_delta_inputs(*args[, init, label])	Summarize all delta inputs by the defined input functions .delta_inputs.
sum_inputs(*args, **kwargs)
to(device)	Moves all variables into the given device.
tpu()	Move all variables into the TPU device.
tracing_variable(name, init, shape[, ...])	Initialize the variable which can be traced during computations and transformations.
train_vars([method, level, include_self])	The shortcut for retrieving all trainable variables.
tree_flatten()	Flattens the object as a PyTree.
tree_unflatten(aux, dynamic_values)	Unflatten the data to construct an object of this class.
unique_name([name, type_])	Get the unique name for this object.
update([pre_spike])	The function to specify the updating rule.
update_local_delays([nodes])	Update local delay variables.
vars([method, level, include_self, ...])	Collect all variables in this node and the children nodes.

Attributes

after_updates
before_updates
cur_inputs
current_inputs
delta_inputs
g_max
implicit_nodes
implicit_vars
mode	Mode of the model, which is useful to control the multiple behaviors of the model.
name	Name of the model.
supported_modes	Supported computing modes.