# 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. 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