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 to2.0 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, default3.55. 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 forq10_p, default 24 degrees Celsius.q10_q (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Q10 scaling factor for the inactivation gate, default3.0.temp_ref_q (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Reference temperature forq10_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).
See also
CaHT_HM1992Same gating functions with
V_shmoved to+25.0 mV, relabelled as a high-threshold current; that relabelling has no source in this paper (see its Notes).CaT_HP1992Independently sourced T-type current for reticular nucleus neurons, with the same
p^2 qgating 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 ownshift = 2 mV(screening charge at 2 mM external calcium) is folded into this class’s Boltzmann midpoints only – 57 to 59 inp_inf, 81 to 83 inq_inf– not into the time-constant expressions:tau_pcarries the mod file’s bare 132/16.8 andtau_qits bare 467/22 with the branch at \(V' = -80\), i.e. exactlyITGHK.mod’s numbers read atshift = 0, not at its own shippedshift = 2 mV. So the equations above matchITGHK.mod’stau_p, piecewisetau_qandp^2 qgating exactly against ashift = 0reading, 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 onlym_inf/h_infwithITGHK.mod, has no realtau_m(activation is taken at steady state), and its piecewisetau_his commented out in favour of a different bi-exponential fit.This class applies a further
V_sh = -3.0 mVon top of the already-folded 2 mV shift, so the shipped defaults sit 3 mV fromITGHK.mod’s own defaults. This is a documented free parameter, not a citation error.References