Na_TM1991

Na_TM1991#

class braincell.channel.Na_TM1991(size, g_max=Quantity(120., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=1.0, temp_ref=Quantity(309.15, 'K'), V_sh=Quantity(-63., 'mV'), name=None)#

Traub and Miles 1991 sodium current with \(p^3 q\) HH gating.

The hippocampal pyramidal-cell fast sodium current from the Traub & Miles (1991) [1] reduced model, as packaged in the NEURON HH2.mod mechanism:

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

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and \(\operatorname{exprel}(x) = (\exp(x) - 1) / x\) removes the removable singularity at each Boltzmann midpoint without changing 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 120.0 mS/cm2. This value is a BrainCell default, not a Traub & Miles (1991) [1] figure – HH2.mod itself ships gnabar = 0.1 mho/cm2 (100 mS/cm2).

  • 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 1.0 (no temperature scaling at the reference temperature).

  • 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 -63.0 mV.

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

See also

Na_Ba2002

Same Traub-Miles rate functions with V_sh = -50 mV and q10 = 3.0 instead.

Notes

Ported from HH2.mod. Algebraically these are the same rate functions used by Na_Ba2002; the only numeric differences are this class’s V_sh = -63.0 mV in place of Na_Ba2002’s -50.0 mV, and q10 = 1.0 in place of 3.0.

The -63.0 mV default is the value Destexhe’s network .hoc files assign to vtraub for this current, and it is the offset associated with the Traub-Miles hippocampal pyramidal cell that this class is named for. It is not HH2.mod’s own default, which is -55 mV. This class’s potassium sibling, K_TM1991, ships a different default shift (-60.0 mV) from the same .mod file; the two classes do not share a shift, and neither should be read as implying a single canonical Traub-Miles offset.

References

root_type#

alias of Sodium