Nav_MA2020_GrC

class braincell.channel.Nav_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, granule-cell parameterisation.

A 13-state Raman & Bean (2001) [2]-style resurgent sodium Markov scheme, refitted to the transient/persistent/resurgent granule-cell recordings and kinetic scheme of Magistretti et al. (2006) [1] and imported here for the granule-cell model of (Masoli et al., 2020) [3]. Five closed states C1-C5 form an activation ladder mirrored by five inactivated states I1-I5; C5 opens into O, which can transition into a blocked state OB or into the shared deep-inactivated state I6 (also reachable from I5); I6 is algebraically eliminated as dependent_state.

All transition rates share one temperature factor and a small set of voltage-dependent and constant primitives:

\[\begin{split}\begin{aligned} \phi &= 3^{(T - 20)/10} \\ \alpha(V) &= \phi\, A_\alpha\, e^{V/V_\alpha}, \quad \beta(V) = \phi\, A_\beta\, e^{-V/V_\beta}, \quad \theta(V) = \phi\, A_\theta\, e^{-V/V_\theta} \\ \gamma &= \phi A_\gamma, \quad \delta = \phi A_\delta, \quad \varepsilon = \phi A_\varepsilon \\ C_{on} &= \phi A_{Con}, \quad C_{off} = \phi A_{Coff}, \quad O_{on} = \phi A_{Oon}, \quad O_{off} = \phi A_{Ooff} \\ a &= (O_{on}/C_{on})^{1/4}, \quad b = (O_{off}/C_{off})^{1/4} \end{aligned}\end{split}\]

with \(V\) in mV (unitless argument to the exponentials) and \(T\) the temperature in degrees Celsius. The closed and inactivated ladders share the same scaling weights \(n_1{=}5.422,\ n_2{=}3.279,\ n_3{=}1.83,\ n_4{=}0.738\):

\[\begin{split}\begin{aligned} f_{0k} &= n_k\, \alpha(V), & b_{0k} &= n_{5-k}\, \beta(V), & k&=1,\dots,4 \\ f_{1k} &= n_k\, \alpha(V)\, a, & b_{1k} &= n_{5-k}\, \beta(V)\, b, & k&=1,\dots,4 \\ f_{ik} &= C_{on}\, a^{\,k-1}, & b_{ik} &= C_{off}\, b^{\,k-1}, & k&=1,\dots,5 \\ f_{0O} &= \gamma, & b_{0O} &= \delta \\ f_{ip} &= \varepsilon, & b_{ip} &= \theta \\ f_{1n} &= \gamma, & b_{1n} &= \delta \\ f_{in} &= O_{on}, & b_{in} &= O_{off} \end{aligned}\end{split}\]

where subscript 0k/1k index the Ck<->Ck+1/ Ik<->Ik+1 ladder steps, ik the Ck<->Ik cross-links, 0O the C5<->O opening step, ip the O<->OB blocking step, and 1n/in the I5<->I6/O<->I6 deep-inactivation 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

NaFHF_MA2020_GrC

Same 13-state scheme with an additional slow-blocked branch (L3-L6) enabled.

Nav1p6_MA2020_GoC

Same general resurgent-Markov family, fitted instead to Purkinje-cell kinetics with its own constants.

Notes

Ported from Nav_MA20_GrC.mod, whose header attributes the scheme to “Raman 13 state model. Adapted from Magistretti et al, 2006.” This class does not subclass Nav1p6_MA2020_GoC; it is an independent implementation with its own __init__ and rate constants. \(\phi\) is referenced to 20 degrees Celsius here, unlike the Nav1.6/Nav1.1 Golgi/Purkinje/basket/stellate family, which references 22 degrees Celsius.

Discrepancy between code and bibliography record. This class ships ACon = 0.005 and AOoff = 0.005. The bibliography’s cross-checked fingerprint for the MA2020 granule sodium pair states that Nav_MA2020_GrC and NaFHF_MA2020_GrC share ACon = 0.025 and AOoff = 0.002 – those values are correct for NaFHF_MA2020_GrC (confirmed against its own code) but not for this class. The values documented above are read directly from this class’s __init__ and are the ones in effect at runtime.

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