KK2B_HM1992#
- class braincell.channel.KK2B_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 (IK2b).
The second 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:
\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 43) / 17)} \\ \tau_p &= \frac{1} {\exp((V' - 81) / 25.6) + \exp(-(V' + 132) / 18)} + 9.9 \\ q_\infty &= \frac{1}{1 + \exp((V' + 58) / 10.6)} \\ \tau_q &= \begin{cases} \left[\exp((V' - 1329) / 200) + \exp(-(V' + 130) / 7.1)\right]^{-1} & V' < -70 \\ 8.9 & V' \geq -70 \end{cases} \end{aligned}\end{split}\]where \(V' = (V - V_{sh}) / \mathrm{mV}\) and the time constants are in milliseconds, further scaled per gate by
gate_phi(). Only \(\tau_q\) differs fromKK2A_HM1992, which uses the same bracket at every voltage and adds a constant 120 ms to it.- 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 to10.0 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, default1.0.temp_ref_p (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Reference temperature forq10_p, default 36 degrees Celsius.q10_q (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Q10 scaling factor for the inactivation gate, default1.0.temp_ref_q (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Reference temperature forq10_q, default 36 degrees Celsius.V_sh (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Threshold shift applied to both gates’ rates, default0.0 mV.
See also
KK2A_HM1992The other \(I_{K2}\) component of the same model; it shares every rate function except
tau_q.KA1_HM1992Transient \(I_A\) component of the same model.
KA2_HM1992The 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 the inactivation time constant is where this pair differs.The two ``tau_q`` branches are far apart at the switch. Just below \(V' = -70\) the expression evaluates to roughly 885 ms, while at and above -70 the class returns 8.9 ms – a jump of two orders of magnitude at a single point. This is the shipped parameterisation, transcribed here rather than smoothed; the code applies the expression strictly below -70 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. Theg_maxdefault is a BrainCell value: the attribution for this key was established from the paper’s current inventory, not by comparing conductance densities.References