NaFHF_MA2020_GrC

class braincell.channel.NaFHF_MA2020_GrC(size, temp=Quantity(305.15, 'K'), g_max=Quantity(13., 'mS / cm^2'), name=None, solver=None, substeps=None)

Resurgent Nav sodium current with slow block, granule-cell model.

The same 13-state Raman & Bean (2001) [2]-style resurgent sodium Markov scheme documented on Nav_MA2020_GrC – fitted to the granule-cell kinetics of Magistretti et al. (2006) [1] and imported for the granule-cell model of (Masoli et al., 2020) [3] – extended with a second, slower blocked-state ladder L3-L6 branching off C3, C4, C5 and O. It is the same mechanism as Nav_MA2020_GrC with this slow-blocked branch enabled, not an independently derived model.

The shared primitives (\(\phi\), \(\alpha\), \(\beta\), \(\theta\), \(\gamma\), \(\delta\), \(\varepsilon\), \(C_{on}\), \(C_{off}\), \(O_{on}\), \(O_{off}\), \(a\), \(b\)) and the C1-C5/I1-I5/O/ OB/I6 transition-rate formulas are exactly as given on Nav_MA2020_GrC. The added L3-L6 branch uses two further constant rate factors \(L_{on} = \phi A_{Lon}\) and \(L_{off} = \phi A_{Loff}\) and fixed scale factors \(c = 20.0\), \(d = 0.075\):

\[\begin{split}\begin{aligned} f_{33} &= n_3\, \alpha(V)\, c, & b_{33} &= n_2\, \alpha(V)\, d \\ f_{34} &= n_4\, \alpha(V)\, c, & b_{34} &= n_1\, \alpha(V)\, d \\ f_{3n} &= \gamma, & b_{3n} &= \delta \\ f_{l3} &= L_{on}, & b_{l3} &= L_{off} \\ f_{l4} &= L_{on}\, c, & b_{l4} &= L_{off}\, d \\ f_{l5} &= L_{on}\, c^2, & b_{l5} &= L_{off}\, d^2 \\ f_{l6} &= L_{on}\, c^2, & b_{l6} &= L_{off}\, d^2 \end{aligned}\end{split}\]

where f33/b33 and f34/b34 are the C3<->C4/ C4<->C5 steps of the L-branch’s own closed-ladder mirror (L3/L4/L5 gate through the same alfa/beta primitives as C3-C5 but scaled by c/d), f3n/b3n is the L5<->L6 step, and fl3-fl6/bl3-bl6 are the C3<->L3, C4<->L4, C5<->L5 and O<->L6 cross-links.

Parameters:

• size (int | Sequence[int] | integer | Sequence[integer]) – Channel state shape.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving \(\phi\), default 32 degrees Celsius.

• g_max (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Maximal conductance density, default 13.0 mS/cm2.

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

• solver (str | None) – Override for Markov’s default ODE solver.

• substeps (int | None) – Override for Markov’s default substep count.

See also

Nav_MA2020_GrC

Same scheme without the slow-blocked branch; the shared primitives and ladder formulas are documented there.

Notes

Ported from NaFHF_MA20_GrC.mod. Its own COMMENT block is empty, which is not a provenance gap: it inherits Nav_MA20_GrC.mod’s “Based on Raman 13 state model. Adapted from Magistretti et al, 2006.” attribution, per the bibliography.

This class ships ACon = 0.025 and AOoff = 0.002 – unlike Nav_MA2020_GrC, these values match the bibliography’s cross-checked fingerprint for the MA2020 granule sodium pair exactly. See Nav_MA2020_GrC’s Notes for the discrepancy recorded against its own ACon/AOoff values.

No import deviation is recorded for this mechanism in the bibliography’s MA2020 import-deviations tables.

References

[1]

Magistretti, J., Castelli, L., Forti, L., & D’Angelo, E. (2006). Kinetic and functional analysis of transient, persistent and resurgent sodium currents in rat cerebellar granule cells in situ: an electrophysiological and modelling study. The Journal of Physiology, 573(1), 83-106. doi:10.1113/jphysiol.2006.106682

[2]

Raman, I. M., & Bean, B. P. (2001). Inactivation and recovery of sodium currents in cerebellar Purkinje neurons: evidence for two mechanisms. Biophysical Journal, 80(2), 729-737. doi:10.1016/S0006-3495(01)76052-3

[3]

Masoli, S., Tognolina, M., Laforenza, U., Moccia, F., & D’Angelo, E. (2020). Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage. Communications Biology, 3(1), 222. doi:10.1038/s42003-020-0953-x

current(V, Na)

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.

init_state(V, Na, batch_size=None)

Initialize the state of the ion channel.

This method should set up the initial state of all variables for the channel.

Parameters:

• *args – Variable length argument list.

• **kwargs – Arbitrary keyword arguments.

reset_state(V, Na, 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.

root_type

alias of Sodium