Kdr_ZH2019_IO

Kdr_ZH2019_IO#

class braincell.channel.Kdr_ZH2019_IO(size, g_max=Quantity(18., 'mS / cm^2'), name=None)#

Delayed rectifier of the inferior-olive model (Zhang 2019).

The somatic delayed-rectifier potassium current of the single-compartment inferior olive (IO) neurons in the essential-tremor cortico-cerebello-thalamo-cortical loop model of (Zhang & Santaniello, 2019) [2], with \(n^4\) HH gating and an ohmic driving force:

\[\begin{split}\begin{aligned} \alpha_n &= 10 \, S\!\left(\frac{V + 41}{10}\right), \quad S(x) = \frac{x}{1 - \exp(-x)} \\ \beta_n &= 12.5 \exp(-(V + 51) / 80) \\ n_\infty &= \frac{\alpha_n}{\alpha_n + \beta_n}, \qquad \tau_n = \frac{10}{\alpha_n + \beta_n} \end{aligned}\end{split}\]

where \(V\) is in millivolts – this class applies no voltage shift – the rates are in \(\mathrm{ms}^{-1}\) and \(\tau_n\) is in milliseconds. Expanding \(S\) gives the familiar linoid \(\alpha_n = (V + 41)/(1 - \exp(-(V + 41)/10))\) everywhere except at its singular point (see Notes). The reversal potential comes from the potassium ion object, not from the class.

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 18.0 mS/cm2, exactly the source mechanism’s gbar.

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

See also

braincell.channel.Na_ZH2019_IO

Sodium current of the same inferior-olive import family and the same bibliographic origin.

braincell.channel.hyperpolarization_activated.HCN_ZH2019_IO

H current of the same family.

Notes

Ported from IO/channel/Kdr_ZH19_IO.mod, whose header reads “K_dr channel from Schweighofer et al 1999. The referred model is an inferior olive neuron” with porter credit “B. Torben-Nielsen @ HUJI, 21-10-2010”. The kinetics therefore originate with Schweighofer, Doya, & Kawato (1999) [1] and reached this class through the NEURON port of Torben-Nielsen, Segev, & Yarom (2012), which Zhang & Santaniello (2019) [2] reused without further modification credit. The 2012 port paper is named in this prose only, per house style, and not as a numbered reference.

The inferior olive neurons in both of those models are single-compartment (nseg = 1); the multi-compartment part of that lineage is a separate Purkinje-cell population. This class must not be described as part of a multi-compartment inferior olive mechanism.

Singularity guard: the mod file’s branch is not reproduced. Kdr_ZH19_IO.mod guards the removable singularity of \(\alpha_n\) with if (fabs(v + 41.0) < 1e-6) and, inside that branch, substitutes the perturbed literal 41.00001. BrainCell instead routes the expression through the stable helper \(S(x) = x/(1 - \exp(-x))\), which returns \(1 + x/2\) when abs(x) < 1e-6. Because the guard now applies to the scaled argument \(x = (V + 41)/10\), it triggers for abs(V + 41) < 1e-5 mV and yields \(\alpha_n \approx 10\ \mathrm{ms}^{-1}\) there. The substitution is exact away from the singular point and better-behaved at it, but it is a BrainCell choice: the import README explicitly excludes those in-formula literals from its NMODL default-precision rewrites.

Import deviation. As for every mechanism of this ZH19/IO family, the rates(v) call moved from the NMODL BREAKPOINT into DERIVATIVE states, so ninf/taun are refreshed before the cnexp state update rather than after it. That is a semantic change, not a cosmetic one.

Two further details of the source, recorded so they are not mistaken for port errors: the mod file’s ek = -75 mV PARAMETER is absent here because the reversal potential is supplied by the ion object, and its taun numerator carries the upstream comment “: was 5”, i.e. the factor 10 above replaced an earlier 5 before this port.

References

root_type#

alias of Potassium