KDR_Ba2002#
- class braincell.channel.KDR_Ba2002(size, g_max=Quantity(10., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=3.0, temp_ref=Quantity(309.15, 'K'), V_sh=Quantity(-50., 'mV'), name=None)#
Bazhenov 2002 delayed-rectifier potassium current.
The fast delayed-rectifier potassium current \(I_K\) of the thalamocortical sleep-oscillation model of (Bazhenov et al., 2002) [1], with \(p^4\) HH gating and an ohmic driving force:
\[\begin{split}\begin{aligned} \alpha_p &= \frac{0.032 \times 5} {\mathrm{exprel}(-(V' - 15) / 5)} \\ \beta_p &= 0.5 \exp(-(V' - 10) / 40) \end{aligned}\end{split}\]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 linoid \(0.032 (15 - V') / (\exp((15 - V')/5) - 1)\);
exprelis used only to remove that expression’s removable singularity, where the code returns \(0.16\ \mathrm{ms}^{-1}\) rather than0/0. The gate integrates \(\dot{p} = \phi (\alpha_p (1 - p) - \beta_p p)\) with \(\phi\) fromgate_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 to10.0 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, default3.0.temp_ref (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Reference temperature forq10, default 36 degrees Celsius.V_sh (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Threshold shift applied to both rates, default-50.0 mV(see Notes).
See also
Notes
The rate functions above are algebraically identical to
K_TM1991’s – the Traub & Miles (1991) \(\alpha_n\) / \(\beta_n\) pair, written here in the mirrored sign convention. Expanding both classes term by term gives the same two expressions, so the kinetics are not restated separately inK_TM1991. The two classes differ only in their shipped defaults:V_sh = -50.0 mVandq10 = 3.0here against-60.0 mVand1.0there. Theirg_maxdefaults are the same,10.0 mS/cm2.That default matches the value the paper’s “Intrinsic currents: thalamus” section gives for thalamocortical relay cells,
g_K = 10 mS/cm^2, which is a stronger fingerprint for this attribution than the rate equations alone. The same section states that the model uses “a fast potassium current, I_K (Traub and Miles, 1991)”, so the authors themselves attribute these kinetics to that book.The 2002 paper does not print these rate expressions. It defers them to Bazhenov, Timofeev, Steriade & Sejnowski (1998), J Neurophysiol 79(5), 2730-2748. This docstring therefore records only that the current is the one used in Bazhenov et al. (2002) [1]; in particular the
V_sh = -50.0 mVshift could not be traced to any equation printed in that paper.With the shipped defaults
tempequalstemp_ref, so the Q10 factor is unity andq10 = 3.0bites only whentempis changed.References