Cav3p2_RI2021_SC

class braincell.channel.Cav3p2_RI2021_SC(size, g_max=Quantity(0.0008, 'mS / cm^2'), V_sh=Quantity(0., 'mV'), temp=Quantity(309.15, 'K'), name=None)

Stellate cell Cav3.2 low-threshold T-type calcium current.

The Cav3.2 (T-type, alpha1H) low-threshold calcium current of the cerebellar stellate cell model of (Rizza et al., 2021) [4]. It is Destexhe’s 1992 NEURON implementation of the low-threshold calcium current of (Huguenard & McCormick, 1992) [1], with the biophysical properties refitted to recordings of human recombinant Cav3.2 channels in HEK-293 cells by (Vitko et al., 2005) [2] and transformed from those 23-25 degrees Celsius data to 36 degrees Celsius using Q10 factors credited to (Coulter, Huguenard & Prince, 1989) [3] (see Notes). Gating is \(m^2 h\) with an ohmic driving force:

\[\begin{split}\begin{aligned} I_{Ca} &= g_{max} \, m^2 h \, (E_{Ca} - V) \\ m_\infty &= \frac{1}{1 + \exp(-(V' + 54.8) / 7.4)} \\ h_\infty &= \frac{1}{1 + \exp((V' + 85.5) / 7.18)} \\ \tau_m &= \frac{1}{\phi_m}\left(1.9 + \frac{1}{e^{(V' + 37)/11.9} + e^{-(V' + 131.6)/21}}\right) \\ \tau_h &= 13.7 + \frac{1}{\phi_h} \cdot \frac{1942 + e^{(V' + 164)/9.2}} {1 + e^{(V' + 89.3)/3.7}} \\ \phi_m &= 5^{(36 - 24)/10}, \quad \phi_h = 3^{(36 - 24)/10} \end{aligned}\end{split}\]

where \(V' = V + V_{sh}\) read in millivolts and the time constants are in milliseconds. \(\phi_m\) is supplied by the m gate’s fixed phi, while \(\phi_h\) is written directly into f_h_tau() and the h gate’s phi is left at 1 – because the additive 13.7 sits outside the division and so does not fit the template’s uniform tau / phi shape. Both factors are constants, not functions of temp; see Notes.

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 8.0e-4 mS/cm2, which is not the mod file’s gcabar converted (see Notes).

• V_sh (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Voltage shift added to \(V\) before every rate, the mod file’s shift. Defaults to 0.0 mV.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature. Accepted and stored, but read by no method of this class (see Notes). Defaults to 36 degrees Celsius.

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

See also

Cav3p2_MA2024_PC

The same mechanism re-imported for the human Purkinje cell model; identical kinetics, different model citation.

Cav3p2_MA2025_BC

The same mechanism re-imported for the basket cell model; identical kinetics, different model citation.

CaT_HM1992

The other import in this module tracing to (Huguenard & McCormick, 1992), by way of a different Destexhe implementation and with different constants.

braincell.channel._base.OhmicHH

Template supplying the ohmic driving force used above.

Notes

Ported from SC/channel/Cav3p2_RI21_SC.mod, whose header reads “Model of Huguenard & McCormick, J Neurophysiol 68: 1373-1383, 1992”, “Written by Alain Destexhe, Salk Institute, Sept 18, 1992” and “Biophysical properties of the T current were from recordings of human recombinant Cav3.2 T-channel in HEK-293 cells – see Vitko et al.” It also records the rename “Suffix from CaT3_2 to Cav3_2”. The Destexhe authorship line names the mechanism’s implementer and is deliberately not turned into a citation; entry [1] is the paper his implementation models. Note that the Boltzmann and tau constants above are the Vitko refit, not the numbers of the original 1992 parameterisation.

What the Q10 citation does and does not support. The mod file’s INITIAL block comments the 24-to-36 degrees Celsius transformation as “assuming Q10 of 5 and 3 for m and h (as in Coulter et al., J Physiol 414: 587, 1989)”. Entry [3] is a Q10 source only: it reports that the low-threshold current’s kinetic properties were temperature sensitive with Q10 values greater than 2.5, and does not print the specific 5 and 3 used here. That split is Destexhe’s parameterisation derived from those data, and this docstring does not present [3] as a source of kinetics.

The temperature conversion is baked in, and ``temp`` is dead. The mod file computes phi_m = 5^(12/10) and phi_h = 3^(12/10) once, from the fixed literals 36 and 24 rather than from NEURON’s celsius. BrainCell reproduces that exactly: the m gate carries phi=5.0 ** ((36.0 - 24.0) / 10.0) and f_h_tau() recomputes the matching phi_h inline. Consequently the temp constructor parameter is stored on the instance and never read – neither gate declares a q10, and this mechanism has no GHK term for temp to enter. Changing temp changes nothing.

``g_max``’s default does not match the mod file. The mod file declares gcabar = .0008 (mho/cm2), i.e. 0.8 mS/cm2; this class defaults to 8.0e-4 mS/cm2, the same numeric literal carrying the millisiemens unit, which is a thousand times smaller. Sibling imports in this module resolve the same mho/cm2 declaration the other way – CaHVA_MA2020_GoC turns 0.00046 mho/cm2 into 0.46 mS/cm2, and Cav1p2_MA2020_GoC keeps 0.0002 S/cm2 outright. The divergence is recorded here rather than corrected: this is a documentation-only description of the shipped default. It is invisible to the NEURON comparison suite, which always passes g_max explicitly in S/cm2. Note also that even a correctly converted default would be the cell-model deposit’s tuned gcabar, not a conductance reported by any of the origin papers.

The mod file’s fixed calcium concentrations are not read here. It declares cai = 2.4e-4 (mM) and cao = 2 (mM), computes its own reversal potential from them by the Nernst equation, and notes that cai was “adjusted for eca=120 mV”. OhmicHH instead takes \(E_{Ca}\) from the attached Calcium ion object, so the comparison path has to pin those concentrations externally to reproduce the mod file’s driving force.

Taken together – the hard-coded 36 degrees Celsius conversion, the externally pinned concentrations and the irregular tau_h shape – this mod file is not a clean reusable temperature- and concentration-general mechanism. The implementation here preserves its quirks deliberately, so that BrainCell matches NEURON one for one; a more general rewrite would have to break that correspondence.

NEURON’s raw ica here is gcabar * m*m*h * (v - carev), i.e. outward-positive; OhmicHH computes g_max * m^2 h * (E - V), the same current under BrainCell’s repo-wide inward-positive convention.

The RI2021 import-deviations tables list no TABLE removal, no derivimplicit -> cnexp substitution and no rate-refresh relocation for this mechanism.

References

[1] (1,2)

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

[2]

Vitko, I., Chen, Y., Arias, J. M., Shen, Y., Wu, X.-R., & Perez-Reyes, E. (2005). Functional characterization and neuronal modeling of the effects of childhood absence epilepsy variants of CACNA1H, a T-type calcium channel. The Journal of Neuroscience, 25(19), 4844-4855. doi:10.1523/JNEUROSCI.0847-05.2005

[3] (1,2,3)

Coulter, D. A., Huguenard, J. R., & Prince, D. A. (1989). Calcium currents in rat thalamocortical relay neurones: kinetic properties of the transient, low-threshold current. The Journal of Physiology, 414(1), 587-604. doi:10.1113/jphysiol.1989.sp017705

[4]

Rizza, M. F., Locatelli, F., Masoli, S., Sanchez-Ponce, D., Munoz, A., Prestori, F., & D’Angelo, E. (2021). Stellate cell computational modeling predicts signal filtering in the molecular layer circuit of cerebellum. Scientific Reports, 11(1), 3873. doi:10.1038/s41598-021-83209-w

root_type

alias of Calcium