KA2_HM1992

KA2_HM1992#

class braincell.channel.KA2_HM1992(size, g_max=Quantity(20., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10_p=1.0, temp_ref_p=Quantity(309.15, 'K'), q10_q=1.0, temp_ref_q=Quantity(309.15, 'K'), V_sh=Quantity(0., 'mV'), name=None)#

Huguenard & McCormick 1992 A-type potassium current (IA2).

The second of the two components into which (Huguenard & McCormick, 1992) [1] splits the rapidly inactivating transient potassium current \(I_A\) of thalamic relay neurons, with \(p^4 q\) HH gating and an ohmic driving force:

\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 36) / 20)} \\ \tau_p &= \frac{1} {\exp((V' + 35.8) / 19.7) + \exp(-(V' + 79.7) / 12.7)} + 0.37 \\ q_\infty &= \frac{1}{1 + \exp((V' + 78) / 6)} \\ \tau_q &= \begin{cases} \left[\exp((V' + 46) / 5) + \exp(-(V' + 238) / 37.5)\right]^{-1} & V' < -63 \\ 19 & V' \geq -63 \end{cases} \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and the time constants are in milliseconds, further scaled per gate by gate_phi(). Only \(p_\infty\) differs from KA1_HM1992: its activation curve is 24 mV more depolarized and considerably shallower.

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 20.0 mS/cm2 (see Notes).

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

  • q10_p (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for the activation gate, default 1.0.

  • temp_ref_p (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10_p, default 36 degrees Celsius.

  • q10_q (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for the inactivation gate, default 1.0.

  • temp_ref_q (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10_q, default 36 degrees Celsius.

  • V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Threshold shift applied to both gates’ rates, default 0.0 mV.

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

See also

KA1_HM1992

The other \(I_A\) component of the same model, with a lower activation midpoint and a steeper slope.

KK2A_HM1992

Slowly inactivating \(I_{K2}\) component of the same model.

KK2B_HM1992

The other \(I_{K2}\) component.

Notes

The paper’s published abstract enumerates exactly four currents, which map onto BrainCell as: \(I_T\) -> CaT_HM1992; \(I_A\) -> KA1_HM1992 / KA2_HM1992; \(I_{K2}\) -> KK2A_HM1992 / KK2B_HM1992; and \(I_h\) -> HCN_HM1992.

One divergence between the shipped pair and the paper’s own description, recorded rather than corrected. The abstract says \(I_A\) “was modeled by assuming two components with different time constants of inactivation”. In BrainCell the two components’ inactivation is identical: this class and KA1_HM1992 carry the same q_inf, the same piecewise tau_q and even the same tau_p, and differ only in the activation midpoint and slope and in the default conductance. The \(I_{K2}\) pair does differ in inactivation, as the paper describes for that current.

The tau_q branches do not meet: at \(V' = -63\) the lower branch evaluates to about 23.4 ms while the class returns the constant 19 ms. The discontinuity is in the source parameterisation, not introduced here.

Both Q10 factors default to 1.0, so with the shipped defaults neither gate is temperature-scaled at any temperature. The g_max default is a BrainCell value: the attribution for this key was established from the paper’s current inventory, not by comparing conductance densities.

References

root_type#

alias of Potassium