Kv1p1_MA2024_PC

class braincell.channel.Kv1p1_MA2024_PC(size, g_max=Quantity(4., 'mS / cm^2'), temp=Quantity(295.15, 'K'), gateCurrent=0.0, name=None)

Kv1.1 low-threshold potassium current of the Purkinje model.

Non-inactivating, low-threshold potassium current carried by Kv1.1 subunits, imported from the human Purkinje cell model of Masoli et al. (2024) [3]. Gating is a single n gate of power 4 in alpha/beta form:

\[\begin{split}\begin{aligned} \alpha_n &= 0.12889 \, \exp((V + 45) / 33.90877) \\ \beta_n &= 0.12889 \, \exp(-(V + 45) / 12.42101) \end{aligned}\end{split}\]

where \(V\) is in millivolts and the rates are per millisecond. Because the two prefactors are equal, \(n_\infty = \alpha_n / (\alpha_n + \beta_n)\) is exactly 0.5 at -45 mV, and the \(n^4\) conductance reaches half its maximum near -29.9 mV – consistent with the Vhalf = -28.8 +- 2.3 mV that the .mod header quotes from the Zerr et al. (1998) recordings [1].

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 4.0 mS/cm2, which is exactly the source mechanism’s gbar = 0.004 S/cm2.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the gate’s q10 factor, default 22 degrees Celsius. This equals the gate’s reference temperature, so the default temperature factor is exactly 1.

• gateCurrent (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Gating-current switch, default 0.0 (dimensionless, off). Any non-zero value enables the gating-current term described below.

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

See also

Kv1p1_MA2020_GoC

Golgi-cell port of the same mechanism.

Kv1p1_MA2020_GrC

Granule-cell port of the same mechanism.

Kv1p1_MA2025_BC

Basket-cell port of the same mechanism.

Kv1p1_RI2021_SC

Stellate-cell port of the same mechanism.

Notes

Ported from PC/channel/Kv1p1_MA24_PC.mod. That file and the Golgi, granule, basket and stellate ports are identical apart from their SUFFIX line and one line of indentation, and the five BrainCell classes are identical too: the rate constants and the gating-current constants above are shared verbatim with Kv1p1_MA2020_GoC, Kv1p1_MA2020_GrC, Kv1p1_MA2025_BC and Kv1p1_RI2021_SC. What differs is only the deposit each was imported from, and therefore the model paper cited below.

Why this class overrides current. The mechanism emits an optional Kv gating current alongside the ionic current, so OhmicHH is not enough. current() returns

\[g_{\max} \, n^4 \, (E_K - V) - I_{\text{gate}}\]

with

\[I_{\text{gate}} = n_c \cdot 10^{6} \cdot e_0 \cdot 4 \, z_n \cdot \frac{\mathrm{d}n}{\mathrm{d}t}, \qquad n_c = 10^{12} \, \frac{g_{\max}}{g_{\text{unit}}}\]

where \(g_{\text{unit}} = 16\) pS is the unitary channel conductance, \(z_n = 2.7978\) the n-gate valence, \(e_0 = 1.60217646 \times 10^{-19}\) C the elementary charge and \(\mathrm{d}n/\mathrm{d}t\) the same \(\phi(\alpha_n (1 - n) - \beta_n n)\) the gate integrates. NEURON emits this term as a separate NONSPECIFIC_CURRENT; BrainCell folds it into the single current() return, and the subtraction reflects the package’s inward-positive sign convention against NMODL’s outward-positive one. The term is selected with u.math.where rather than a Python branch, so gateCurrent may be an array and the choice stays traceable.

Where the q10 factor is applied. The gate declares q10 = 2.7 at a reference of 22 degrees Celsius, so HH.compute_derivative() scales the rate balance by \(\phi = 2.7^{(T - 22)/10}\). The .mod file instead divides its taun by the same factor. The two forms are algebraically identical.

Provenance. The .mod header states that the six rate parameters were obtained by least-squares fits to \(G/G_{\max}(V)\) and \(\tau(V)\) data from human Kv1.1 expressed in Xenopus oocytes by Zerr et al. (1998) [1], and names the RIKEN implementation published by Akemann et al. (2009) [2] as its model reference. The Purkinje-cell paper [3] names the model this parameterisation was imported from, not the origin of the equations.

Conductance default. 4.0 mS/cm2 is the deposit’s tuned value, carried across from the .mod file. It is not a value printed in any of the cited papers.

Import deviations: none. This mechanism carries no NMODL TABLE and was already integrated with cnexp upstream, so neither the table-removal nor the derivimplicit substitution recorded for other channels in this model applies here.

References

[1] (1,2)

Zerr, P., Adelman, J. P., & Maylie, J. (1998). Episodic ataxia mutations in Kv1.1 alter potassium channel function by dominant negative effects or haploinsufficiency. The Journal of Neuroscience, 18(8), 2842-2848. doi:10.1523/JNEUROSCI.18-08-02842.1998

[2]

Akemann, W., Lundby, A., Mutoh, H., & Knopfel, T. (2009). Effect of voltage sensitive fluorescent proteins on neuronal excitability. Biophysical Journal, 96(10), 3959-3976. doi:10.1016/j.bpj.2009.02.046

[3] (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

current(V, K)

Calculate the current for this ion channel.

This method should be implemented by subclasses to compute the current based on the channel’s specific properties and state.

Parameters:

• *args – Variable length argument list.

• **kwargs – Arbitrary keyword arguments.

Raises:

NotImplementedError – This method must be implemented by subclasses.

root_type

alias of Potassium