brainpy.dyn.channels.IK_DR#

class brainpy.dyn.channels.IK_DR(size, E=- 90.0, g_max=10.0, T=36.0, T_base=3.0, V_sh=- 50.0, method='exp_auto', name=None)[source]#

The delayed rectifier potassium channel current.

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

\[\begin{split}\begin{aligned} I_{\mathrm{K}} &= g_{\mathrm{max}} * p^4 \\ \frac{dp}{dt} &= \phi * (\alpha_p (1-p) - \beta_p p) \\ \alpha_{p} &=\frac{0.032\left(V-V_{sh}-15\right)}{1-\exp \left(-\left(V-V_{sh}-15\right) / 5\right)} \\ \beta_p &= 0.5 \exp \left(-\left(V-V_{sh}-10\right) / 40\right) \end{aligned}\end{split}\]

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

Parameters

  • size (int, sequence of int) – The object size.

  • g_max (float, JaxArray, ndarray, Initializer, Callable) – The maximal conductance density (\(mS/cm^2\)).

  • E (float, JaxArray, ndarray, Initializer, Callable) – The reversal potential (mV).

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

  • V_sh (float, JaxArray, ndarray, Initializer, Callable) – The shift of the membrane potential to spike.

  • method (str) – The numerical integration method.

  • name (str) – The object name.

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=- 90.0, g_max=10.0, T=36.0, T_base=3.0, V_sh=- 50.0, method='exp_auto', name=None)[source]#

Methods

__init__(size[, E, g_max, T, T_base, V_sh, ...])

current(V)

derivative(p, 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.

reset_delay(name, delay_target)

Reset the delay variable.

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.

update_delay(name, delay_data)

Update the delay according to the delay data.

vars([method, level, include_self])

Collect all variables in this node and the children nodes.

Attributes

global_delay_vars

name

steps