Kca2p2_MA2020_GoC

class braincell.channel.Kca2p2_MA2020_GoC(size, g_max=Quantity(38., 'mS / cm^2'), q10_base=3.0, diff=3.0, temp=Quantity(295.15, 'K'), name=None, solver=None, substeps=None)

Kca2.2 (SK2) calcium-activated K current, Golgi cell.

Template-based import of Kca2p2_MA20_GoC.mod, part of the cerebellar Golgi cell model of (Masoli et al., 2020) [3], with kinetics from the recombinant SK-channel gating scheme of (Hirschberg et al., 1998) [1] as implemented for the Golgi cell by (Solinas et al., 2007) [2]. A seven-state, purely calcium-dependent Markov scheme: four closed states in series (C1-C4) with two open states (O1, O2) branching off C3 and C4. C1 is the algebraically eliminated state.

\[\begin{split}\begin{aligned} I &= g_{\mathrm{max}} \, (O_1 + O_2) \, (E_K - V) \\ C_1 \underset{k_{c1}}{\overset{k_{c2}[\mathrm{Ca}]_i}{ \rightleftharpoons}} C_2 \underset{k_{c2}}{\overset{k_{c3}[\mathrm{Ca}]_i}{ \rightleftharpoons}} C_3 \underset{k_{c3}}{\overset{k_{c4}[\mathrm{Ca}]_i}{ \rightleftharpoons}} C_4 \\ C_3 \underset{k_{o1}^{-}}{\overset{k_{o1}^{+}}{ \rightleftharpoons}} O_1, \qquad C_4 \underset{k_{o2}^{-}}{\overset{k_{o2}^{+}}{ \rightleftharpoons}} O_2 \end{aligned}\end{split}\]

where every forward (calcium-binding) rate is \(\phi \cdot k / d\) with \(d\) the diff diffusion factor and \([\mathrm{Ca}]_i\) in mM, every backward (unbinding) rate is \(\phi \cdot k\), and \(\phi = q_{10}^{(T - 296.15\,\mathrm{K}) / 10}\) uses \(23\,^{\circ}\mathrm{C}\) (296.15 K) as the reference temperature regardless of the temp default below.

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 38.0 mS/cm2.

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

• diff (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Calcium diffusion-shell divisor applied to every forward (calcium-binding) rate, 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

Kca2p2_MA2025_BC

Same kinetics, basket-cell model citation.

Kca2p2_MA2020_GrC

Same kinetics, granule-cell model citation.

Kca2p2_MA2024_PC

Same kinetics, Purkinje-cell model citation.

Kca2p2_RI2021_SC

Same kinetics, stellate-cell model citation.

Notes

Ported from Kca2p2_MA20_GoC.mod. current is overridden to sum only the two open states, O1 and O2; C1-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 \(22\,^{\circ}\mathrm{C}\). The two temperatures are independent: the reference is the condition the rate constants below were tuned at, and the default is simply this class’s default operating temperature, one degree below that reference. This is unlike Kca3p1_MA2020_GoC, whose analogous q10_base/temp parameters are accepted but never read.

References

[1]

Hirschberg, B., Maylie, J., Adelman, J. P., & Marrion, N. V. (1998). Gating of recombinant small-conductance Ca-activated K+ channels by calcium. The Journal of General Physiology, 111(4), 565-581. doi:10.1085/jgp.111.4.565

[2]

Solinas, S., Forti, L., Cesana, E., Mapelli, J., De Schutter, E., & D’Angelo, E. (2007). Computational reconstruction of pacemaking and intrinsic electroresponsiveness in cerebellar Golgi cells. Frontiers in Cellular Neuroscience, 1, 2. doi:10.3389/neuro.03.002.2007

[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.