brainpy.dyn.neurons.WangBuzsakiModel#

class brainpy.dyn.neurons.WangBuzsakiModel(size, keep_size=False, ENa=55.0, gNa=35.0, EK=- 90.0, gK=9.0, EL=- 65, gL=0.1, V_th=20.0, phi=5.0, C=1.0, V_initializer=OneInit(value=- 65.0), h_initializer=OneInit(value=0.6), n_initializer=OneInit(value=0.32), noise=None, method='exp_auto', name=None, mode=NormalMode)[source]#

Wang-Buzsaki model 9, an implementation of a modified Hodgkin-Huxley model.

Each model is described by a single compartment and obeys the current balance equation:

\[C_{m} \frac{d V}{d t}=-I_{\mathrm{Na}}-I_{\mathrm{K}}-I_{\mathrm{L}}-I_{\mathrm{syn}}+I_{\mathrm{app}}\]

where \(C_{m}=1 \mu \mathrm{F} / \mathrm{cm}^{2}\) and \(I_{\mathrm{app}}\) is the injected current (in \(\mu \mathrm{A} / \mathrm{cm}^{2}\) ). The leak current \(I_{\mathrm{L}}=g_{\mathrm{L}}\left(V-E_{\mathrm{L}}\right)\) has a conductance \(g_{\mathrm{L}}=0.1 \mathrm{mS} / \mathrm{cm}^{2}\), so that the passive time constant \(\tau_{0}=C_{m} / g_{\mathrm{L}}=10 \mathrm{msec} ; E_{\mathrm{L}}=-65 \mathrm{mV}\).

The spike-generating \(\mathrm{Na}^{+}\) and \(\mathrm{K}^{+}\) voltage-dependent ion currents \(\left(I_{\mathrm{Na}}\right.\) and \(I_{\mathrm{K}}\) ) are of the Hodgkin-Huxley type (Hodgkin and Huxley, 1952). The transient sodium current \(I_{\mathrm{Na}}=g_{\mathrm{Na}} m_{\infty}^{3} h\left(V-E_{\mathrm{Na}}\right)\), where the activation variable \(m\) is assumed fast and substituted by its steady-state function \(m_{\infty}=\alpha_{m} /\left(\alpha_{m}+\beta_{m}\right)\) ; \(\alpha_{m}(V)=-0.1(V+35) /(\exp (-0.1(V+35))-1), \beta_{m}(V)=4 \exp (-(V+60) / 18)\). The inactivation variable \(h\) obeys a first-order kinetics:

\[\frac{d h}{d t}=\phi\left(\alpha_{h}(1-h)-\beta_{h} h\right)\]

where \(\alpha_{h}(V)=0.07 \exp (-(V+58) / 20)\) and \(\beta_{h}(V)=1 /(\exp (-0.1(V+28)) +1) \cdot g_{\mathrm{Na}}=35 \mathrm{mS} / \mathrm{cm}^{2}\) ; \(E_{\mathrm{Na}}=55 \mathrm{mV}, \phi=5 .\)

The delayed rectifier \(I_{\mathrm{K}}=g_{\mathrm{K}} n^{4}\left(V-E_{\mathrm{K}}\right)\), where the activation variable \(n\) obeys the following equation:

\[\frac{d n}{d t}=\phi\left(\alpha_{n}(1-n)-\beta_{n} n\right)\]

with \(\alpha_{n}(V)=-0.01(V+34) /(\exp (-0.1(V+34))-1)\) and \(\beta_{n}(V)=0.125\exp (-(V+44) / 80)\) ; \(g_{\mathrm{K}}=9 \mathrm{mS} / \mathrm{cm}^{2}\), and \(E_{\mathrm{K}}=-90 \mathrm{mV}\).

Parameters
  • size (sequence of int, int) – The size of the neuron group.

  • ENa (float, JaxArray, ndarray, Initializer, callable) – The reversal potential of sodium. Default is 50 mV.

  • gNa (float, JaxArray, ndarray, Initializer, callable) – The maximum conductance of sodium channel. Default is 120 msiemens.

  • EK (float, JaxArray, ndarray, Initializer, callable) – The reversal potential of potassium. Default is -77 mV.

  • gK (float, JaxArray, ndarray, Initializer, callable) – The maximum conductance of potassium channel. Default is 36 msiemens.

  • EL (float, JaxArray, ndarray, Initializer, callable) – The reversal potential of learky channel. Default is -54.387 mV.

  • gL (float, JaxArray, ndarray, Initializer, callable) – The conductance of learky channel. Default is 0.03 msiemens.

  • V_th (float, JaxArray, ndarray, Initializer, callable) – The threshold of the membrane spike. Default is 20 mV.

  • C (float, JaxArray, ndarray, Initializer, callable) – The membrane capacitance. Default is 1 ufarad.

  • phi (float, JaxArray, ndarray, Initializer, callable) – The temperature regulator constant.

  • V_initializer (JaxArray, ndarray, Initializer, callable) – The initializer of membrane potential.

  • h_initializer (JaxArray, ndarray, Initializer, callable) – The initializer of h channel.

  • n_initializer (JaxArray, ndarray, Initializer, callable) – The initializer of n channel.

  • method (str) – The numerical integration method.

  • name (str) – The group name.

References

9

Wang, X.J. and Buzsaki, G., (1996) Gamma oscillation by synaptic inhibition in a hippocampal interneuronal network model. Journal of neuroscience, 16(20), pp.6402-6413.

__init__(size, keep_size=False, ENa=55.0, gNa=35.0, EK=- 90.0, gK=9.0, EL=- 65, gL=0.1, V_th=20.0, phi=5.0, C=1.0, V_initializer=OneInit(value=- 65.0), h_initializer=OneInit(value=0.6), n_initializer=OneInit(value=0.32), noise=None, method='exp_auto', name=None, mode=NormalMode)[source]#

Methods

__init__(size[, keep_size, ENa, gNa, EK, ...])

clear_input()

Function to clear inputs in the neuron group.

dV(V, t, h, n, I_ext)

dh(h, t, V)

dn(n, t, V)

get_batch_shape([batch_size])

get_delay_data(identifier, delay_step, *indices)

Get delay data according to the provided delay steps.

load_states(filename[, verbose])

Load the model states.

m_inf(V)

nodes([method, level, include_self])

Collect all children nodes.

offline_fit(target, fit_record)

offline_init()

online_fit(target, fit_record)

online_init()

register_delay(identifier, delay_step, ...)

Register delay variable.

register_implicit_nodes(*nodes, **named_nodes)

register_implicit_vars(*variables, ...)

reset([batch_size])

Reset function which reset the whole variables in the model.

reset_local_delays([nodes])

Reset local delay variables.

reset_state([batch_size])

Reset function which reset the states in the model.

save_states(filename[, variables])

Save the model states.

train_vars([method, level, include_self])

The shortcut for retrieving all trainable variables.

unique_name([name, type_])

Get the unique name for this object.

update(tdi[, x])

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

derivative

global_delay_data

mode

Mode of the model, which is useful to control the multiple behaviors of the model.

name

Name of the model.

varshape

The shape of variables in the neuron group.