CaT_HM1992

CaT_HM1992#

class braincell.channel.CaT_HM1992(size, g_max=Quantity(2., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10_p=3.55, temp_ref_p=Quantity(297.15, 'K'), q10_q=3.0, temp_ref_q=Quantity(297.15, 'K'), V_sh=Quantity(-3., 'mV'), name=None)#

Huguenard & McCormick 1992 low-threshold T-type calcium current.

The thalamic relay-neuron low-threshold (T-type) calcium current \(I_T\) of (Huguenard & McCormick, 1992) [1], with \(p^2 q\) HH gating and an ohmic driving force:

\[\begin{split}\begin{aligned} p_\infty &= \frac{1}{1 + \exp(-(V' + 59) / 6.2)} \\ \tau_p &= \frac{1} {\exp(-(V' + 132) / 16.7) + \exp((V' + 16.8) / 18.2)} + 0.612 \\ q_\infty &= \frac{1}{1 + \exp((V' + 83) / 4)} \\ \tau_q &= \begin{cases} \exp((V' + 467) / 66.6) & V' < -80 \\ \exp(-(V' + 22) / 10.5) + 28 & V' \geq -80 \end{cases} \end{aligned}\end{split}\]

where \(V' = (V - V_{sh}) / \mathrm{mV}\) and \(\tau_p\)/\(\tau_q\) (in milliseconds) are further scaled by gate_phi().

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. Defaults to 2.0 mS/cm2.

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

  • q10_p (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for the activation gate, default 3.55. This value could not be traced to the paper or to any reference NEURON implementation; treat it as a BrainCell/BrainPy default (see Notes).

  • temp_ref_p (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10_p, default 24 degrees Celsius.

  • q10_q (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Q10 scaling factor for the inactivation gate, default 3.0.

  • temp_ref_q (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Reference temperature for q10_q, default 24 degrees Celsius.

  • V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Threshold shift applied to both gates’ rates, default -3.0 mV (see Notes).

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

See also

CaHT_HM1992

Same gating functions with V_sh moved to +25.0 mV, relabelled as a high-threshold current; that relabelling has no source in this paper (see its Notes).

CaT_HP1992

Independently sourced T-type current for reticular nucleus neurons, with the same p^2 q gating shape but a different Boltzmann parameterisation.

Notes

Compared against ITGHK.mod (ModelDB accession 279), Destexhe’s NEURON implementation of this paper, headed “Model of Huguenard & McCormick, J Neurophysiol 68: 1373-1383, 1992”. The mod file’s own shift = 2 mV (screening charge at 2 mM external calcium) is folded into this class’s Boltzmann midpoints only – 57 to 59 in p_inf, 81 to 83 in q_infnot into the time-constant expressions: tau_p carries the mod file’s bare 132/16.8 and tau_q its bare 467/22 with the branch at \(V' = -80\), i.e. exactly ITGHK.mod’s numbers read at shift = 0, not at its own shipped shift = 2 mV. So the equations above match ITGHK.mod’s tau_p, piecewise tau_q and p^2 q gating exactly against a shift = 0 reading, while the steady-state midpoints match the mod file with the 2 mV shift folded in. Do not describe this class as reproducing the mod file “with the 2 mV screening-charge shift folded in” everywhere – that is true of the midpoints and false of the time constants.

A second, unrelated mod file, IT.mod (ModelDB accession 3817), is not a source for any constant here despite modelling the same paper’s data: its header reads “Model based on the data of Huguenard & McCormick… and Huguenard & Prince…”, it shares only m_inf/h_inf with ITGHK.mod, has no real tau_m (activation is taken at steady state), and its piecewise tau_h is commented out in favour of a different bi-exponential fit.

This class applies a further V_sh = -3.0 mV on top of the already-folded 2 mV shift, so the shipped defaults sit 3 mV from ITGHK.mod’s own defaults. This is a documented free parameter, not a citation error.

References

root_type#

alias of Calcium