Kv4p3_MA2024_PC

class braincell.channel.Kv4p3_MA2024_PC(size, g_max=Quantity(3.2, 'mS / cm^2'), temp=Quantity(303.15, 'K'), name=None)

A-type transient potassium current of the Purkinje cell model.

Fast-inactivating A-type potassium current, imported from the human Purkinje cell model of Masoli et al. (2024) [2].

Gating is an a gate of power 3 and a b gate of power 1, each with an explicit Boltzmann steady state and a time constant built from an alpha/beta pair:

\[\begin{split}\begin{aligned} a_\infty &= \frac{1}{1 + \exp((V + 38) / (-17))} \\ b_\infty &= \frac{1}{1 + \exp((V + 78.8) / 8.4)} \\ \tau_a &= \frac{1}{\alpha_a + \beta_a}, \qquad \tau_b = \frac{1}{\alpha_b + \beta_b} \end{aligned}\end{split}\]

with, writing \(\sigma(x, y) = 1 / (e^{x/y} + 1)\) for the module-level _sigm helper,

\[\begin{split}\begin{aligned} \alpha_a &= 0.8147 \, \sigma(V + 9.17203,\ -23.3271) \\ \beta_a &= 0.1655 \big/ e^{(V + 18.2791) / 19.4718} \\ \alpha_b &= 0.0368 \, \sigma(V + 111.332,\ 12.8433) \\ \beta_b &= 0.0345 \, \sigma(V + 49.9537,\ -8.90123) \end{aligned}\end{split}\]

where \(V\) is in millivolts, the rates are per millisecond and the time constants are in milliseconds. This class applies no voltage shift, and the reversal potential comes from the potassium ion object rather than 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 3.2 mS/cm2, which is exactly the source mechanism’s gkbar = 0.0032 mho/cm2.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving both gates’ q10 factor, default 30 degrees Celsius. This matches the celsius = 30 (degC) written in the source mechanism’s PARAMETER block.

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

See also

Kv4p3_MA2020_GoC

Golgi-cell port of the same mechanism.

Kv4p3_MA2020_GrC

Granule-cell port of the same mechanism.

Kv4p3_MA2025_BC

Basket-cell port of the same mechanism.

Kv4p3_RI2021_SC

Stellate-cell port of the same mechanism.

Notes

Ported from PC/channel/Kv4p3_MA24_PC.mod. The five cell-type ports of this mechanism are byte-identical apart from their SUFFIX line and their celsius default, and the five BrainCell classes carry the same rate constants: every equation above is shared verbatim with Kv4p3_MA2020_GoC, Kv4p3_MA2020_GrC, Kv4p3_MA2025_BC and Kv4p3_RI2021_SC. What differs is the default temp, the deposit each was imported from, and therefore the model paper cited below.

Kalpha_a is stored here as a bare float and passed straight to _sigm, whereas Kv4p3_MA2020_GoC, Kv4p3_MA2020_GrC and Kv4p3_RI2021_SC attach u.mV to it and convert with .to_decimal(u.mV) at use. The arithmetic is identical – both forms divide a millivolt difference by -23.3271 – but the inconsistency is real, and on this documentation-only branch it is recorded rather than fixed.

Where the q10 factor is applied. Both gates declare q10 = 3.0 at a reference of 25.5 degrees Celsius, so HH.compute_derivative() scales each \((x_\infty - x)/\tau_x\) term by \(\phi = 3^{(T - 25.5)/10}\) (about 1.64 at the default 30 degrees Celsius). The .mod file instead multiplies the same Q10 into alp_a, bet_a, alp_b and bet_b, which divides its tau_a and tau_b by that factor. The two forms are algebraically identical, but it means f_a_tau() and f_b_tau() return q10-free time constants rather than the mechanism’s tau_a and tau_b.

Provenance, and what the header does not establish. The .mod header carries Author: E.D'Angelo, T.Nieus, A. Fontana. That credit line is copy-pasted verbatim across every cell-type port of this mechanism, and it names authors 1, 2 and 7 of an eight-author paper, so it is not treated as a citation here. The kinetics originate in the cerebellar granule cell model of D’Angelo et al. (2001) [1]; the model paper [2] names the deposit this parameterisation was imported from, not the origin of the equations. The commented-out alternatives that remain in the .mod file – linoid forms of each rate, and a “Bardoni Belluzzi” steady-state block – are never evaluated by the mechanism and are not reproduced here.

Conductance default. 3.2 mS/cm2 is the deposit’s tuned value, carried across from the .mod file. It is not a value printed in either cited paper.

Import deviations. Three, all recorded against this symbol. First, the original mechanism’s NMODL TABLE over [-100, 30] mV, covering a_inf, tau_a, b_inf and tau_b, is not reproduced: all four expressions are evaluated per call. NEURON clamped tabulated values to the boundary outside that window, so any BrainCell-versus-NEURON divergence below -100 mV or above 30 mV is expected rather than a port error. Second, the integration method was changed from derivimplicit to cnexp; the two gate ODEs are independent, so the substitution is exact. Third, four parameters are carried at NEURON’s compiled six-significant- figure precision rather than at the .mod source text’s: Kalpha_a -23.32708 becomes -23.3271, Kbeta_a 19.47175 becomes 19.4718, V0beta_a -18.27914 becomes -18.2791 and V0alpha_b -111.33209 becomes -111.332. That rewrite reaches those four parameters only; ordinary in-formula literals keep their source values.

References

[1]

D’Angelo, E., Nieus, T., Maffei, A., Armano, S., Rossi, P., Taglietti, V., Fontana, A., & Naldi, G. (2001). Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow K+-dependent mechanism. The Journal of Neuroscience, 21(3), 759-770. doi:10.1523/JNEUROSCI.21-03-00759.2001

[2] (1,2)

Masoli, S., Sanchez-Ponce, D., Vrieler, N., Abu-Haya, K., Lerner, V., Shahar, T., Nedelescu, H., Rizza, M. F., Benavides-Piccione, R., DeFelipe, J., Yarom, Y., Munoz, A., & D’Angelo, E. (2024). Human Purkinje cells outperform mouse Purkinje cells in dendritic complexity and computational capacity. Communications Biology, 7(1), 5. doi:10.1038/s42003-023-05689-y

root_type

alias of Potassium