Nav1p1_MA2025_BC

class braincell.channel.Nav1p1_MA2025_BC(size, temp=Quantity(295.15, 'K'), g_max=Quantity(8., 'mS / cm^2'), gateCurrent=0.0, name=None, solver=None, substeps=None)

Non-resurgent Nav1.1 sodium current, basket-cell parameterisation.

The non-resurgent Narsg sodium current derived from the Khaliq et al. (2003) [1] resurgent-current model and used for Kv3/Nav1.1 excitability studies by Akemann, Lundby, Mutoh & Knopfel (2009) [2], reparameterised for the basket-cell model of (Masoli et al., 2025) [3].

This class inherits the 13-state Markov pairs topology, the transition-rate lambdas and the \(\phi\) temperature-scaling formula from Nav1p6_MA2020_GoC (see that class for the full state diagram and rate equations), but overrides three of the fixed kinetic constants and recomputes \(\phi\) with a different base:

\[\phi = 2.7^{(T - 22)/10}, \quad O_{on} = 2.3\ \mathrm{ms^{-1}}, \quad \epsilon = 10^{-12}\ \mathrm{ms^{-1}}, \quad a = \left(\frac{O_{on}}{C_{on}}\right)^{1/4}\]

with \(C_{on}\) unchanged from Nav1p6_MA2020_GoC’s 0.005, so alfac is recomputed to a different value than the base class’s. current() adds an optional gating-current correction on top of the inherited ionic current:

\[\begin{split}\begin{aligned} I &= g_{max}\, O\, (E_{Na} - V) - \mathbb{1}[\text{gateCurrent} \neq 0]\, I_{gate} \\ I_{gate} &= n_c \times 10^6\, e_0\, z_{gate}\, \dot{q} \\ \dot{q} &= f_{01} C_1 + (f_{02}{-}b_{01}) C_2 + (f_{03}{-}b_{02}) C_3 + (f_{04}{-}b_{03}) C_4 - b_{04} C_5 \\ &\ + f_{11} I_1 + (f_{12}{-}b_{11}) I_2 + (f_{13}{-}b_{12}) I_3 + (f_{14}{-}b_{13}) I_4 - b_{14} I_5 \\ n_c &= 10^{12}\, g_{max} / g_{unit} \end{aligned}\end{split}\]

where \(\dot{q}\) is the net probability flux through the activation/inactivation ladders (excluding O, B and I6), \(n_c\) estimates the channel count from g_max and a fixed unitary conductance gunit, and \(e_0\) is the elementary charge.

Parameters:

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

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the \(\phi\) factor, default 22 degrees Celsius.

• g_max (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Maximal conductance density, default 8.0 mS/cm2 (half Nav1p6_MA2020_GoC’s default).

• gateCurrent (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Enables the gating-current correction in current() when nonzero, default 0.0 (disabled).

• 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

Nav1p1_RI2021_SC

Same scheme and constants, stellate-cell model citation.

Nav1p6_MA2025_BC

Resurgent Nav1.6 sibling for the same basket-cell model, with its own (unoverridden) constants.

Notes

Ported from Nav1p1_MA25_BC.mod, whose own header describes the mechanism as “derived from the Narsg channel of Khaliq et al., J. Neurosci. 23(2003)4899” – i.e. via Nav1p6_MA2020_GoC’s origin, not an independently republished scheme.

zgate = 2.5435, gunit = 15e-9 mS and e0 = 1.60217646e-19 C are fixed internal constants set in __init__ and are not exposed as __init__ parameters.

No import deviation is recorded for this mechanism in the bibliography’s MA2025 import-deviations tables.

References

[1]

Khaliq, Z. M., Gouwens, N. W., & Raman, I. M. (2003). The contribution of resurgent sodium current to high-frequency firing in Purkinje neurons: an experimental and modeling study. The Journal of Neuroscience, 23(12), 4899-4912. doi:10.1523/JNEUROSCI.23-12-04899.2003

[2]

Akemann, W., Lundby, A., Mutoh, H., & Knopfel, T. (2009). Effect of voltage sensitive fluorescent proteins on neuronal excitability. Biophysical Journal, 96(10), 3959-3976. doi:10.1016/j.bpj.2009.02.046

[3]

Masoli, S., Rizza, M. F., Soda, T., Sanchez-Ponce, D., Munoz, A., Prestori, F., & D’Angelo, E. (2025). Cerebellar basket cell filtering of Purkinje cell responses elicited by low frequency parallel fibre transmission. Scientific Reports, 15(1), 25192. doi:10.1038/s41598-025-09964-2

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.

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.