Kv1p5_MA2024_PC

class braincell.channel.Kv1p5_MA2024_PC(size, g_max=Quantity(0.00013195, 'S / cm^2'), temp=Quantity(310.15, 'K'), Tauact=1.0, Tauinactf=1.0, Tauinacts=1.0, name=None)

Kv1.5 ultrarapid delayed-rectifier current (IKur), K path only.

Hodgkin-Huxley model of the cardiac ultrarapid delayed rectifier IKur, fitted to human atrial myocyte recordings by Feng et al. (1998) [1] and imported into BrainCell from the human Purkinje cell model of Masoli et al. (2024) [2]. Three gates – m (power 3), n and u – combine with a voltage-dependent conductance factor, so current() returns

\[g_{\max} \left(0.1 + \frac{1}{1 + \exp(-(V - 15)/13)}\right) m^3 n u \, (E_K - V)\]

with the gate kinetics

\[\begin{split}\begin{aligned} m_\infty &= \frac{1}{1 + \exp(-(V + 30.3)/9.6)} \\ \tau_m &= \frac{1}{3(\alpha_m + \beta_m)} T_{\text{act}}, \quad \alpha_m = \frac{0.65 \, q_{10}} {\exp(-(V + 10)/8.5) + \exp(-(V - 30)/59)}, \quad \beta_m = \frac{0.65 \, q_{10}}{2.5 + \exp((V + 82)/17)} \\ n_\infty &= 0.25 + \frac{1}{1.35 + \exp((V + 7)/14)} \\ \tau_n &= \frac{1}{3(\alpha_n + \beta_n)} T_{\text{inactf}}, \quad \alpha_n = \frac{0.001 \, q_{10}} {2.4 + 10.9 \exp(-(V + 90)/78)}, \quad \beta_n = 0.001 \, q_{10} \exp((V - 168)/16) \\ u_\infty &= 0.1 + \frac{1}{1.1 + \exp((V + 7)/14)} \\ \tau_u &= 6800 \, T_{\text{inacts}} \end{aligned}\end{split}\]

where \(V\) is in millivolts, \(\tau\) in milliseconds and \(q_{10} = 2.2^{(T - 37)/10}\) with \(T\) in degrees Celsius. 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, default 0.13195e-3 siemens/cm2. This is the BrainCell name for the NEURON gKur parameter and is exactly its .mod value.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature entering \(q_{10}\), default 37 degrees Celsius. This equals the \(q_{10}\) reference temperature, so the default factor is exactly 1.

• Tauact (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Activation time-scale multiplier for \(\tau_m\), default 1.0 (dimensionless).

• Tauinactf (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Fast-inactivation time-scale multiplier for \(\tau_n\), default 1.0 (dimensionless).

• Tauinacts (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Slow-inactivation time-scale multiplier for \(\tau_u\), default 1.0 (dimensionless).

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

See also

braincell.channel.Kv1p5_MA2020_GrC

Granule-cell subclass that inherits these gate kinetics and adds the nonspecific cation current component.

Kv1p1_MA2024_PC

Low-threshold Kv1 current of the same Purkinje cell model.

Notes

Ported from PC/channel/Kv1p5_MA24_PC.mod.

This is a cardiac mechanism, not a cerebellar one. The .mod TITLE reads “Cardiac IKur current & nonspec cation current with identical kinetics”, and its kinetics were fitted to human atrial myocyte recordings [1], not to any cerebellar recording. The Purkinje-cell citation [2] names the model BrainCell imported this parameterisation from, not the origin of the kinetics.

Only the potassium path is converted. The Purkinje .mod file computes a nonspecific cation current ino with kinetics identical to ik, but its USEION no WRITE ino line is commented out, so ino survives only as a RANGE variable with no current owner. BrainCell converts the default ik path alone; this class has no gnonspec parameter and emits no nonspecific current. The granule-cell sibling braincell.channel.Kv1p5_MA2020_GrC, whose .mod file leaves that line enabled, subclasses this one and adds the second component.

q10 asymmetry in f_u_tau(). Temperature scaling is not attached through the gate objects: none of the three gates sets phi or q10, so HH.gate_phi() resolves to 1.0 for m, n and u alike. Instead the private _q10 method computes \(2.2^{(T - 37)/10}\) and multiplies it into the alpha/beta rates used by f_m_tau() and f_n_tau() only. f_u_tau() returns the constant 6800 * Tauinacts milliseconds: it is voltage-independent, it receives no \(q_{10}\) scaling, and unlike its two siblings it also carries no factor of \(1/3\). This reproduces the .mod file’s utau = 6800*Tauinacts exactly and is the mechanism’s own code path, not a BrainCell convention and not a closed-form temperature dependence printed in either cited paper.

Conductance default. 0.13195e-3 siemens/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 integration method was changed from derivimplicit to cnexp; the three gate ODEs are independent, so the substitution is exact. This mechanism carries no NMODL TABLE, so no table-removal deviation applies.

References

[1] (1,2)

Feng, J., Xu, D., Wang, Z., & Nattel, S. (1998). Ultrarapid delayed rectifier current inactivation in human atrial myocytes: properties and consequences. American Journal of Physiology-Heart and Circulatory Physiology, 275(5), H1717-H1725. doi:10.1152/ajpheart.1998.275.5.H1717

[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

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