K_TM1991

K_TM1991#

class braincell.channel.K_TM1991(size, g_max=Quantity(10., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=1.0, temp_ref=Quantity(309.15, 'K'), V_sh=Quantity(-60., 'mV'), name=None)#

Traub and Miles 1991 delayed-rectifier potassium current.

The delayed-rectifier potassium current of the hippocampal pyramidal cell model of (Traub & Miles, 1991) [1], with \(p^4\) HH gating and an ohmic driving force:

\[\begin{split}\begin{aligned} \alpha_p &= \frac{0.032 \times 5} {\mathrm{exprel}((15 - V') / 5)} \\ \beta_p &= 0.5 \exp((10 - V') / 40) \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\), \(\mathrm{exprel}(x) = (e^{x} - 1)/x\), and both rates are in \(\mathrm{ms}^{-1}\). Away from \(V' = 15\) the activation rate is exactly the published linoid \(0.032 (15 - V') / (\exp((15 - V')/5) - 1)\); exprel is used only to remove that expression’s removable singularity, where the code returns \(0.16\ \mathrm{ms}^{-1}\) rather than 0/0. The gate integrates \(\dot{p} = \phi (\alpha_p (1 - p) - \beta_p p)\) with \(\phi\) from gate_phi().

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. Defaults to 10.0 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 the activation gate, default 1.0, i.e. no temperature correction at any temperature (see Notes).

  • temp_ref (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10, default 36 degrees Celsius.

  • V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Threshold shift applied to both rates, default -60.0 mV – not -63.0 mV (see Notes).

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

See also

KDR_Ba2002

The same two rate functions with V_sh = -50.0 mV and q10 = 3.0, as used by Bazhenov et al. (2002).

braincell.channel.sodium.Na_TM1991

Sodium counterpart from the same source mechanism, which ships V_sh = -63.0 mV.

Notes

Compared against HH2.mod from ModelDB accession 3670, Destexhe’s NEURON implementation, whose header reads “Equations modified by Traub, for Hippocampal Pyramidal cells, in: Traub & Miles, Neuronal Networks of the Hippocampus, Cambridge, 1991”. With v2 = v - vtraub in the mod file and \(V' = (V - V_{sh})/\mathrm{mV}\) here, the two rate functions above and the \(p^4\) gating match the mod file term for term.

The shift default is -60 mV, and the two BrainCell ``TM1991`` classes do not agree with each other. braincell.channel.sodium.Na_TM1991 ships V_sh = -63.0 mV while this class ships -60.0 mV, although both derive from the same mechanism; the 3 mV divergence is a BrainCell choice, not something inherited from the source. Any sentence about “the Traub & Miles -63 mV shift” is wrong for this class. HH2.mod’s own PARAMETER block ships a third value, vtraub = -55 mV; the rate equations are unaffected either way, since the shift enters only through v2/\(V'\).

The g_max default coincides with HH2.mod’s gkbar = 0.01 mho/cm^2 (= 10 mS/cm2), but it is documented here as a BrainCell default rather than as a value printed in the book.

HH2.mod applies tadj = 3^((celsius - 36)/10), which is unity at 36 degrees Celsius; the shipped q10 = 1.0 with temp_ref at 36 degrees Celsius agrees there, but stays unity at every other temperature as well, so raising temp does not speed this gate unless q10 is also changed.

References

root_type#

alias of Potassium