KA1_HM1992

KA1_HM1992#

class braincell.channel.KA1_HM1992(size, g_max=Quantity(30., '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 (IA1).

The first 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:

\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 60) / 8.5)} \\ \tau_p &= \frac{1} {\exp((V' + 35.8) / 19.7) + \exp(-(V' + 79.7) / 12.7)} + 0.37 \\ q_\infty &= \frac{1}{1 + \exp((V' + 78) / 6)} \\ \tau_q &= \begin{cases} \left[\exp((V' + 46) / 5) + \exp(-(V' + 238) / 37.5)\right]^{-1} & V' < -63 \\ 19 & V' \geq -63 \end{cases} \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and the time constants are in milliseconds, further scaled per gate by gate_phi().

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 30.0 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

KA2_HM1992

The other \(I_A\) component of the same model; it differs from this class only in p_inf and g_max (see Notes).

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: KA1_HM1992 and KA2_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 (-60 / 8.5 here, -36 / 20 there) and in the default conductance (30 against 20 mS/cm2). 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; the code applies the expression strictly below -63 and the constant at and above it.

Both Q10 factors default to 1.0, so with the shipped defaults neither gate is temperature-scaled at any temperature; each gate has its own q10/temp_ref pair and is scaled independently. 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