HCN_HM1992

class braincell.channel.HCN_HM1992(size, g_max=Quantity(10., 'mS / cm^2'), E=Quantity(43., 'mV'), temp=Quantity(309.15, 'K'), q10=1.0, temp_ref=Quantity(309.15, 'K'), name=None)

Hyperpolarization-activated current of Huguenard & McCormick (1992).

Reproduces the thalamic relay-neuron \(I_h\) model of (Huguenard & McCormick, 1992) [1]: a single Boltzmann-gated pore driven by an ohmic force against a fixed reversal potential. Dynamics:

\[\begin{split}\begin{aligned} I_h &= g_{\mathrm{max}} \, p \, (E - V) \\ \frac{dp}{dt} &= \phi \frac{p_{\infty} - p}{\tau_p} \\ p_{\infty} &= \frac{1}{1 + \exp((V + 75) / 5.5)} \\ \tau_p &= \frac{1}{\exp(-0.086 V - 14.59) + \exp(0.0701 V - 1.87)} \end{aligned}\end{split}\]

where \(\phi = q_{10}^{(T - T_{\mathrm{ref}}) / 10}\) and the default q10 = 1.0 makes \(\phi \equiv 1\) for any temp.

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 10.0 mS/cm2.

• E (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Reversal potential, default 43.0 mV.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the Q10 factor, default 36 degrees Celsius.

• q10 (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for the p gate, default 1.0.

• temp_ref (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for the Q10 formula, default 36 degrees Celsius.

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

Notes

This class overrides reversal_potential() to return self.E instead of an ion’s reversal potential, so the current is driven against the fixed E parameter, not an ion state – the correct closed form is g_max * p * (E - V), not g_max * p alone.

References

[1]

Huguenard, J. R., & McCormick, D. A. (1992). Simulation of the currents involved in rhythmic oscillations in thalamic relay neurons. Journal of Neurophysiology, 68(4), 1373-1383. doi:10.1152/jn.1992.68.4.1373

reversal_potential(V, *ions)

Return the reversal potential driving the current.

Parameters:

• V (ArrayLike) – Membrane potential. Unused by the default implementation; present so overrides can depend on it.

• *ions (IonInfo) – Ion states, in the declaration order of root_type.

Returns:

Reversal potential, as a voltage. Defaults to that of the first ion, which for a joint root type is the first entry of root_type.__args__. Override to read a fixed self.E or a non-leading ion.

Return type:

ArrayLike

root_type

alias of HHTypedNeuron