INa_TM1991

class brainpy.dyn.INa_TM1991(size, keep_size=False, E=50.0, g_max=120.0, phi=1.0, V_sh=-63.0, method='exp_auto', name=None, mode=None)

The sodium current model described by (Traub and Miles, 1991) [1].

The dynamics of this sodium current model is given by:

\[\begin{split}\begin{split} \begin{aligned} I_{\mathrm{Na}} &= g_{\mathrm{max}} m^3 h \\ \frac {dm} {dt} &= \phi(\alpha_m (1-x) - \beta_m) \\ &\alpha_m(V) = 0.32 \frac{(13 - V + V_{sh})}{\exp((13 - V +V_{sh}) / 4) - 1.} \\ &\beta_m(V) = 0.28 \frac{(V - V_{sh} - 40)}{(\exp((V - V_{sh} - 40) / 5) - 1)} \\ \frac {dh} {dt} &= \phi(\alpha_h (1-x) - \beta_h) \\ &\alpha_h(V) = 0.128 * \exp((17 - V + V_{sh}) / 18) \\ &\beta_h(V) = 4. / (1 + \exp(-(V - V_{sh} - 40) / 5)) \\ \end{aligned} \end{split}\end{split}\]

where \(V_{sh}\) is the membrane shift (default -63 mV), and \(\phi\) is the temperature-dependent factor (default 1.).

Parameters:

• size (Union[int, Sequence[int]]) – The size of the simulation target.

• keep_size (bool) – Keep size or flatten the size?

• method (str) – The numerical method

• name (str) – The name of the object.

• g_max (Union[int, float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Initializer, Callable]) – The maximal conductance density (\(mS/cm^2\)).

• E (Union[int, float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Initializer, Callable]) – The reversal potential (mV).

• V_sh (Union[int, float, TypeVar(ArrayType, Array, Variable, TrainVar, Array, ndarray), Initializer, Callable]) – The membrane shift.

References

[1]

Traub, Roger D., and Richard Miles. Neuronal networks of the hippocampus. Vol. 777. Cambridge University Press, 1991.

See also

INa_Ba2002

master_type

alias of HHTypedNeuron