Na_Ba2002

Na_Ba2002#

class braincell.channel.Na_Ba2002(size, g_max=Quantity(90., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=3.0, temp_ref=Quantity(309.15, 'K'), V_sh=Quantity(-50., 'mV'), name=None)#

Bazhenov 2002 sodium current with \(p^3 q\) HH gating.

The thalamocortical-cell fast sodium current used in the slow-wave sleep oscillation model of (Bazhenov et al., 2002) [1], with the mirrored-sign Traub-Miles rate forms (see Notes):

\[\begin{split}\begin{aligned} \alpha_p &= \frac{0.32 \times 4} {\operatorname{exprel}(-(V' - 13) / 4)} \\ \beta_p &= \frac{0.28 \times 5} {\operatorname{exprel}((V' - 40) / 5)} \\ \alpha_q &= 0.128 \exp(-(V' - 17) / 18) \\ \beta_q &= \frac{4}{1 + \exp(-(V' - 40) / 5)} \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and \(\operatorname{exprel}(x) = (\exp(x) - 1) / x\), used only to remove the removable singularity at each Boltzmann midpoint; it does not change the function value. Gating is \(p^3 q\).

Parameters:

  • size (int | Sequence[int] | integer | Sequence[integer]) – Channel state shape.

  • g_max (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Maximal conductance density, default 90.0 mS/cm2 – matches the TC-cell value reported in (Bazhenov et al., 2002) [1].

  • temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the Q10 factor, default 36 degrees Celsius.

  • q10 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for both gates, default 3.0.

  • temp_ref (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for the Q10 formula, default 36 degrees Celsius.

  • V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Threshold shift applied to both gates’ rates, default -50.0 mV.

  • name (str | None) – Optional channel name.

See also

Na_TM1991

Same Traub-Miles rate functions with V_sh = -63 mV and q10 = 1.0 instead.

Notes

Algebraically these are the same Traub & Miles (1991) rate functions used by Na_TM1991, written with the sign of V - V_sh mirrored; the only numeric differences are this class’s V_sh = -50.0 mV in place of Na_TM1991’s -63.0 mV, and q10 = 3.0 in place of 1.0. (Bazhenov et al., 2002) [1] attribute the current’s kinetics to Traub & Miles (1991) but do not print the alpha/beta expressions themselves – the paper’s Methods defer them to Bazhenov et al. (1998). This docstring’s equations are transcribed from this class’s own rate methods, confirmed algebraically equivalent to the Traub-Miles forms, not copied from the 2002 paper’s text.

References

root_type#

alias of Sodium