# 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