KNI_Ya1989

KNI_Ya1989#

class braincell.channel.KNI_Ya1989(size, g_max=Quantity(0.004, 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=1.0, temp_ref=Quantity(309.15, 'K'), tau_max=Quantity(4000., 'ms'), V_sh=Quantity(0., 'mV'), name=None)#

Yamada 1989 slow non-inactivating potassium current.

The muscarine-sensitive M current \(I_M\) of (Yamada, Koch, & Adams, 1989) [1] – a slow, non-inactivating potassium current with a single activation gate to the first power and an ohmic driving force:

\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 35) / 10)} \\ \tau_p &= \frac{\tau_{max}} {3.3 \exp((V' + 35) / 20) + \exp(-(V' + 35) / 20)} \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and \(\tau_{max}\) is the tau_max parameter read in milliseconds. \(\tau_p\) is further scaled by gate_phi(). There is no inactivation gate: the conductance is \(g_{max} p\).

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 0.004 mS/cm2 (see Notes).

  • 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, default 1.0, i.e. no temperature correction (see Notes).

  • temp_ref (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10, default 36 degrees Celsius.

  • tau_max (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Peak time constant scaling \(\tau_p\). Defaults to 4000.0 ms (see Notes).

  • V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Threshold shift applied to both rates, default 0.0 mV.

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

See also

KK2A_HM1992

Slowly inactivating thalamic potassium current, for

contrast

this class does not inactivate at all.

Notes

Compared against IM.mod from ModelDB accession 3817, whose header reads “Model taken from Yamada, W.M., Koch, C. and Adams, P.R. Multiple channels and calcium dynamics. In: Methods in Neuronal Modeling, edited by C. Koch and I. Segev, MIT press, 1989, p 97-134.” The mod file computes exactly the two functions above and a single, non-inactivating, linear-in-\(m\) potassium conductance; this class implements them with one Gate of power 1. The current is the M current of the bullfrog sympathetic ganglion B-type cell, which is the chapter’s subject.

Two shipped defaults diverge from that reference implementation. IM.mod ships taumax = 1000 ms and gkbar = 1e-6 mho/cm^2 (= 0.001 mS/cm2), whereas this class defaults to tau_max = 4000.0 ms and g_max = 0.004 mS/cm2. Both are BrainCell defaults and neither is a value from the chapter.

The temperature handling diverges too. IM.mod assumes Q10 = 2.3 referenced to 36 degrees Celsius; this class defaults to q10 = 1.0, so as shipped there is no temperature correction at any temperature.

Sources disagree on the chapter’s final page: the machine-readable bibliographic record gives 97-133, used in the entry below, while IM.mod’s header gives 97-134. The discrepancy is recorded rather than adjudicated.

References

root_type#

alias of Potassium