brainpy.dyn.channels.INa#

class brainpy.dyn.channels.INa(size, E=50.0, g_max=90.0, T=36.0, V_sh=- 50.0, method='exp_auto', name=None)[source]#

The sodium current model.

The sodium current model is adopted from (Bazhenov, et, al. 2002) 1. It’s dynamics is given by:

\[\begin{split}\begin{aligned} I_{\mathrm{Na}} &= g_{\mathrm{max}} * p^3 * q \\ \frac{dp}{dt} &= \phi ( \alpha_p (1-p) - \beta_p p) \\ \alpha_{p} &=\frac{0.32\left(V-V_{sh}-13\right)}{1-\exp \left(-\left(V-V_{sh}-13\right) / 4\right)} \\ \beta_{p} &=\frac{-0.28\left(V-V_{sh}-40\right)}{1-\exp \left(\left(V-V_{sh}-40\right) / 5\right)} \\ \frac{dq}{dt} & = \phi ( \alpha_q (1-h) - \beta_q h) \\ \alpha_q &=0.128 \exp \left(-\left(V-V_{sh}-17\right) / 18\right) \\ \beta_q &= \frac{4}{1+\exp \left(-\left(V-V_{sh}-40\right) / 5\right)} \end{aligned}\end{split}\]

where \(\phi\) is a temperature-dependent factor, which is given by \(\phi=3^{\frac{T-36}{10}}\) (\(T\) is the temperature in Celsius).

Model Examples

Parameters
  • g_max (float) – The maximal conductance density (\(mS/cm^2\)).

  • E (float) – The reversal potential (mV).

  • T (float) – The temperature (Celsius, \(^{\circ}C\)).

  • V_sh (float) – The shift of the membrane potential to spike.

References

1

Bazhenov, Maxim, et al. “Model of thalamocortical slow-wave sleep oscillations and transitions to activated states.” Journal of neuroscience 22.19 (2002): 8691-8704.

__init__(size, E=50.0, g_max=90.0, T=36.0, V_sh=- 50.0, method='exp_auto', name=None)[source]#

Methods

__init__(size[, E, g_max, T, V_sh, method, name])

current(V)

dp(p, t, V)

dq(q, t, V)

get_delay_data(name, delay_step, *indices)

Get delay data according to the provided delay steps.

ints([method])

Collect all integrators in this node and the children nodes.

load_states(filename[, verbose])

Load the model states.

nodes([method, level, include_self])

Collect all children nodes.

register_delay(name, delay_step, delay_target)

Register delay variable.

register_implicit_nodes(nodes)

register_implicit_vars(variables)

reset(V)

Reset function which reset the whole variables 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(t, dt, V)

The function to specify the updating rule.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

global_delay_targets

global_delay_vars

name

steps