Na_ZH2019_IO

class braincell.channel.Na_ZH2019_IO(size, g_max=Quantity(70., 'mS / cm^2'), name=None)

Inferior olive somatic sodium current, Schweighofer kinetics.

Inferior olive (IO) somatic fast sodium current from the essential-tremor cortico-cerebello-thalamo-cortical loop model of (Zhang & Santaniello, 2019) [2]:

\[\begin{split}\begin{aligned} \alpha_m &= x/(1 - \exp(-x)),\ x = (V + 41) / 10 \\ \beta_m &= 9 \exp(-(V + 66) / 20) \\ \alpha_h &= 5 \exp(-(V + 60) / 15) \\ \beta_h &= 10 y/(1 - \exp(-y)),\ y = (V + 50) / 10 \end{aligned}\end{split}\]

with \(V\) in mV, \(m_\infty = \alpha_m / (\alpha_m + \beta_m)\), \(\tau_m = 0.001\) ms (effectively instantaneous), \(h_\infty = \alpha_h / (\alpha_h + \beta_h)\), \(\tau_h = 250 / (\alpha_h + \beta_h)\). Gating is \(m^3 h\). Both \(x/(1-\exp(-x))\) terms are evaluated by the module-level helper _x_over_one_minus_exp_neg_stable, which substitutes the Taylor form 1 + x/2 for |x| < 1e-6 and the closed form otherwise – this is the numerically stable replacement for the removable singularity at \(x = 0\), not the naive textbook fraction.

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 70.0 mS/cm2.

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

Notes

Ported from Na_ZH19_IO.mod. Kinetics originate in the single-compartment inferior olive model of Schweighofer, Doya & Kawato (1999) [1], reaching this class through the NEURON port of Torben-Nielsen, Segev & Yarom (2012), and reused by (Zhang & Santaniello, 2019) [2].

Na_ZH19_IO.mod guards the removable singularities in alpha_m and beta_h with an explicit if (fabs(v + 41.0) < 1e-6) / if (fabs(v + 50.0) < 1e-6) branch that substitutes the perturbed literal 41.000001 / 50.000001. BrainCell replaces both branches with _x_over_one_minus_exp_neg_stable instead of reproducing the perturbed-literal branch; this is exact away from the singularity and better-behaved at it, but it is a BrainCell substitution, not a reproduction of the .mod file’s own guard.

The upstream rates(v) call was relocated from BREAKPOINT into DERIVATIVE states, so m/h steady states and time constants are refreshed before the cnexp state update rather than after it – a semantic change carried over from the source .mod file, not introduced by this port.

References

[1]

Schweighofer, N., Doya, K., & Kawato, M. (1999). Electrophysiological properties of inferior olive neurons: A compartmental model. Journal of Neurophysiology, 82(2), 804-817. doi:10.1152/jn.1999.82.2.804

[2] (1,2)

Zhang, X., & Santaniello, S. (2019). Role of cerebellar GABAergic dysfunctions in the origins of essential tremor. Proceedings of the National Academy of Sciences of the United States of America, 116(27), 13592-13601. doi:10.1073/pnas.1817689116

root_type

alias of Sodium