Kca1p1_MA2020_GoC

class braincell.channel.Kca1p1_MA2020_GoC(size, g_max=Quantity(10., 'mS / cm^2'), q10_base=3.0, temp=Quantity(295.15, 'K'), name=None, solver=None, substeps=None)

Kca1.1 (BK/mslo) Ca- and voltage-activated K current, Golgi cell.

Template-based import of Kca1p1_MA20_GoC.mod, part of the cerebellar Golgi cell model of (Masoli et al., 2020) [3], with parameters from the allosteric BK-channel gating scheme of (Cox, Cui, & Aldrich, 1997) [1] as adapted for calcium buffering in Purkinje cells by (Anwar, Hong, & De Schutter, 2012) [2]. Ten states arranged as a 5x2 grid: a closed ladder C0-C4 and an open ladder O0-O4, each ladder stepping through 0-4 bound calcium ions, with five vertical closed-to-open transitions, one per occupancy level. C0 is the algebraically eliminated state.

\[\begin{split}\begin{aligned} I &= g_{\mathrm{max}} \, (O_0 + O_1 + O_2 + O_3 + O_4) \, (E_K - V) \\ C_i \underset{(i+1) K_c k_1}{\overset{(4-i)[\mathrm{Ca}]_i k_1}{ \rightleftharpoons}} C_{i+1}, &\qquad O_i \underset{(i+1) K_o k_1}{\overset{(4-i)[\mathrm{Ca}]_i k_1}{ \rightleftharpoons}} O_{i+1}, \qquad i = 0,\dots,3 \\ C_i \underset{\mathrm{pb}_i \, \beta(V)}{\overset{ \mathrm{pf}_i \, \alpha(V)}{\rightleftharpoons}} O_i, &\qquad i = 0,\dots,4 \\ \alpha(V) &= \exp\!\left(\frac{Q_o F V}{R T}\right), \qquad \beta(V) = \exp\!\left(\frac{Q_c F V}{R T}\right) \end{aligned}\end{split}\]

where \([\mathrm{Ca}]_i\) is expressed in mM, \(k_1\), \(K_c\), \(K_o\) are fixed rate/dissociation constants; each unbinding step is standard mass-action, so its rate scales with the number of calcium ions bound in the state being left, i.e. \((i+1)\) for the departure from \(C_{i+1}\) or \(O_{i+1}\). Every rate additionally carries the multiplicative factor \(\phi = q_{10}^{(T - 296.15\,\mathrm{K}) / 10}\) (\(23\,^{\circ}\mathrm{C}\) reference), \(F\) is the Faraday constant, \(R\) the gas constant, and \(Q_o\), \(Q_c\) are the Horrigan-Aldrich gating charges for the opening and closing conformational change.

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 10.0 mS/cm2.

• q10_base (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Q10 temperature coefficient, default 3.0.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature, default 22 degrees Celsius. See Notes for the 22/23 degree distinction.

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

• solver (str | None) – Markov-chain integration scheme.

• substeps (int | None) – Number of solver substeps per integration step.

See also

Kca1p1_MA2025_BC

Same kinetics, basket-cell model citation.

Kca1p1_MA2020_GrC

Same kinetics, granule-cell model citation.

Kca1p1_MA2024_PC

Same kinetics, Purkinje-cell model citation.

Kca1p1_RI2021_SC

Same kinetics, stellate-cell model citation.

Notes

Ported from Kca1p1_MA20_GoC.mod. current is overridden to sum all five open states, O0 through O4; C0-C4 do not conduct.

_phi evaluates the Q10 scaling relative to a fixed \(23\,^{\circ}\mathrm{C}\) reference (ref_celsius=23.0), while the temp constructor default is \(22\,^{\circ}\mathrm{C}\), one degree below that reference. This is unlike Kca3p1_MA2020_GoC, whose analogous q10_base/temp parameters are accepted but never read.

self.L0 = 1806 is assigned in __init__ alongside the other Horrigan-Aldrich constants but is never read by any rate method or by current; it is documented here rather than removed, since removing an assigned-but-unused attribute is a behavior change out of scope for a documentation pass.

References

[1]

Cox, D. H., Cui, J., & Aldrich, R. W. (1997). Allosteric gating of a large conductance Ca-activated K+ channel. The Journal of General Physiology, 110(3), 257-281. doi:10.1085/jgp.110.3.257

[2]

Anwar, H., Hong, S., & De Schutter, E. (2012). Controlling Ca2+-activated K+ channels with models of Ca2+ buffering in Purkinje cells. The Cerebellum, 11(3), 681-693. doi:10.1007/s12311-010-0224-3

[3]

Masoli, S., Ottaviani, A., Casali, S., & D’Angelo, E. (2020). Cerebellar Golgi cell models predict dendritic processing and mechanisms of synaptic plasticity. PLOS Computational Biology, 16(12), e1007937. doi:10.1371/journal.pcbi.1007937

current(V, K, Ca)

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.

current_owner_type

alias of Potassium

reset_state(V, K, Ca, batch_size=None)

Reset the state of the ion channel.

This method should reset all state variables of the channel to their initial values.

Parameters:

• *args – Variable length argument list.

• **kwargs – Arbitrary keyword arguments.