Kir2p3_MA2024_PC

class braincell.channel.Kir2p3_MA2024_PC(size, g_max=Quantity(0.9, 'mS / cm^2'), temp=Quantity(303.15, 'K'), name=None)

Kir2.3 inward-rectifier current of the Purkinje cell model.

Hyperpolarization-activated inward-rectifier potassium current imported from the human Purkinje cell model of Masoli et al. (2024) [2]. A single first-order d gate of power 1 drives an ohmic current, with the gate written in alpha/beta form:

\[\begin{split}\begin{aligned} \alpha_d &= 0.13289 \, \exp(-(V + 83.94) / 24.3902) \\ \beta_d &= 0.16994 \, \exp((V + 83.94) / 35.714) \end{aligned}\end{split}\]

where \(V\) is in millivolts and the rates are per millisecond. The template forms \(d_\infty = \alpha_d / (\alpha_d + \beta_d)\) and \(\tau_d = 1 / (\alpha_d + \beta_d)\) from these; half activation falls near -87.5 mV, and \(d_\infty\) rises towards 1 as the membrane hyperpolarizes. 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 0.9 mS/cm2, which is exactly the source mechanism’s gkbar = 0.0009 mho/cm2.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the gate’s q10 factor, default 30 degrees Celsius. See the note below on the Purkinje port’s divergent mechanism-local celsius default.

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

See also

Kir2p3_MA2020_GrC

Granule-cell port of the same mechanism.

Kir2p3_MA2025_BC

Basket-cell port of the same mechanism.

Kir2p3_RI2021_SC

Stellate-cell port of the same mechanism.

Notes

Ported from PC/channel/Kir2p3_MA24_PC.mod. That file and the granule, basket and stellate ports are byte-identical apart from their SUFFIX line and one PARAMETER default described below. The four BrainCell classes are likewise identical, so the rate constants above are shared verbatim with Kir2p3_MA2020_GrC, Kir2p3_MA2025_BC and Kir2p3_RI2021_SC. What differs is only the deposit each was imported from, and therefore the model paper cited below.

Recorded divergence: the mechanism-local temperature default. PC/channel/Kir2p3_MA24_PC.mod writes celsius = 10 (degC) in its PARAMETER block where the granule, basket and stellate ports all write celsius = 30 (degC). BrainCell’s temp default is 30 degrees Celsius in all four classes, so this class alone does not reproduce its own source file’s number. In NEURON celsius is a simulator-wide global that the host model normally sets, which is why a mechanism-local default carries little weight; the difference is recorded here rather than resolved, and the code is left unchanged. At 30 degrees Celsius the gate’s q10 factor is 3; at 10 degrees Celsius it would be 1/3.

The rectification lives in the gate, not in the current. The current expression is the plain ohmic g_max * d * (E_K - V) supplied by OhmicHH; there is no Mg2+ or polyamine block term anywhere in the mechanism. The inward-rectifier behaviour comes entirely from \(d_\infty\) increasing as the membrane hyperpolarizes.

Where the q10 factor is applied. The gate declares q10 = 3.0 at a reference of 20 degrees Celsius, so HH.compute_derivative() scales the whole \(\alpha_d (1 - d) - \beta_d d\) term by \(\phi = 3^{(T - 20)/10}\). The .mod file instead multiplies Q10 into alp_d and bet_d. The two forms are algebraically identical, but it means f_d_alpha() and f_d_beta() return the q10-free rates rather than the mechanism’s alpha_d/beta_d.

Provenance, and what the header does not establish. The .mod COMMENT carries a reference string that is the published title of D’Angelo et al. (2001) truncated mid-subtitle. 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 Purkinje-cell paper [2] names the model this parameterisation was imported from, not the origin of the equations.

Conductance default. 0.9 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. The original mechanism’s NMODL TABLE over [-100, 100] mV, covering d_inf and tau_d, is not reproduced: both expressions are evaluated per call. NEURON used the boundary value outside that window, so any BrainCell-versus-NEURON divergence below -100 mV or above 100 mV is expected rather than a port error. The integration method was also changed from derivimplicit to cnexp; with one independent gate ODE that substitution is exact.

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