KK2A_HM1992

KK2A_HM1992#

class braincell.channel.KK2A_HM1992(size, g_max=Quantity(10., '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 slow potassium current (IK2a).

The first of the two components into which (Huguenard & McCormick, 1992) [1] splits the slowly inactivating potassium current \(I_{K2}\) of thalamic relay neurons, with \(p q\) HH gating (both gates to the first power) and an ohmic driving force:

\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 43) / 17)} \\ \tau_p &= \frac{1} {\exp((V' - 81) / 25.6) + \exp(-(V' + 132) / 18)} + 9.9 \\ q_\infty &= \frac{1}{1 + \exp((V' + 58) / 10.6)} \\ \tau_q &= \frac{1} {\exp((V' - 1329) / 200) + \exp(-(V' + 130) / 7.1)} + 120 \end{aligned}\end{split}\]

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 10.0 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

KK2B_HM1992

The other \(I_{K2}\) component of the same model; it shares every rate function except tau_q.

KA1_HM1992

Transient \(I_A\) component of the same model.

KA2_HM1992

The other \(I_A\) 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. The abstract states that \(I_{K2}\) “was also modeled by assuming two components”, and this pair does implement that split in the inactivation time constant: tau_q here is the continuous expression above, while KK2B_HM1992 evaluates the same bracket only below \(V' = -70\) and returns a constant 8.9 ms 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