CaHVA_MA2020_GoC

class braincell.channel.CaHVA_MA2020_GoC(size, g_max=Quantity(0.46, 'mS / cm^2'), temp=Quantity(303.15, 'K'), name=None)

Golgi cell high-voltage-activated calcium current.

The high-voltage-activated (HVA) calcium current of the cerebellar Golgi cell model of (Masoli et al., 2020) [2]. Its kinetics are those of the cerebellar granule cell model of (D’Angelo et al., 2001) [1], reused unchanged for the Golgi cell. Gating is \(s^2 u\) in alpha/beta form with an ohmic driving force:

\[\begin{split}\begin{aligned} I_{Ca} &= g_{max} \, s^2 u \, (E_{Ca} - V) \\ \alpha_s &= 0.04944 \exp((V' + 29.06) / 15.873) \\ \beta_s &= 0.08298 \exp((V' + 18.66) / -25.641) \\ \alpha_u &= 0.0013 \exp((V' + 48) / -18.183) \\ \beta_u &= 0.0013 \exp((V' + 48) / 83.33) \end{aligned}\end{split}\]

where \(V' = V / \mathrm{mV}\) and the rates are per millisecond. Both gates are further scaled by gate_phi() with \(Q_{10} = 3\) referred to 20 degrees Celsius (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 0.46 mS/cm2, the mod file’s gcabar = 0.00046 mho/cm2 (see Notes).

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the gates’ Q10 factor. Defaults to 30 degrees Celsius, matching the mod file’s celsius = 30.

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

See also

CaHVA_MA2020_GrC

The same mechanism imported from the granule cell deposit; identical constants, different model citation, and one different import deviation (see its Notes).

braincell.channel._base.OhmicHH

Template supplying the ohmic driving force used above.

Notes

Ported from GoC/channel/CaHVA_MA20_GoC.mod. An earlier revision of this docstring named the source file CaHVA_MA20_GoC.mod, which does not exist; the shipped file uses the two-digit year code, and that is corrected here. The file’s TITLE reads “Cerebellum Granule Cell Model” and its COMMENT credits “E.D’Angelo, T.Nieus, A. Fontana” – both inherited from the granule cell original, which is where these kinetics come from; the file is that mechanism re-deposited for the Golgi cell model cited as [2]. That credit names authors 1, 2 and 7 of the eight-author origin paper, so it is not turned into a citation: entry [1] below lists all eight.

The mod file applies its Q10 factor inside each of the four rate functions, as Q10 = 3^((celsius - 20)/10) multiplying alp_s, bet_s, alp_u and bet_u. BrainCell hoists it to the gate level instead, as Gate(q10=3.0, temp_ref=20 degC). For the alpha/beta form the two are algebraically identical: with \(\alpha = Q_{10} a\) and \(\beta = Q_{10} b\), \(\alpha (1 - x) - \beta x = Q_{10} (a (1 - x) - b x)\), which is exactly what phi multiplies. The rate methods here therefore return the unscaled a/b.

The mod file’s eca = 129.33 (mV) is not read by this class: the reversal potential is supplied by the attached Calcium ion object.

Import deviation – interpolation table removed. The original TABLE directive tabulated s_inf, tau_s, u_inf and tau_u over [-100, 30] mV, clamping to the boundary value outside that range; BrainCell evaluates the continuous formulas per call, so any BrainCell/NEURON divergence outside that window is expected.

Not an integration-method substitution. Unlike its granule cell twin, this mechanism was already cnexp upstream, so no derivimplicit -> cnexp change was made for it.

Import deviation – NMODL default-precision rewrite. Kalpha_s is written 15.87301587302 in the mod source and 15.873 here, because BrainCell aligns with the roughly six-significant-figure defaults NEURON’s generated C emits rather than with the source text. Ordinary in-formula literals are not subject to this rewrite and keep their source values.

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

g_max’s default is the gcabar of the cell-model deposit this mechanism was imported from – a value tuned for that model, not a conductance reported by the origin paper.

References

[1] (1,2)

D’Angelo, E., Nieus, T., Maffei, A., Armano, S., Rossi, P., Taglietti, V., Fontana, A., & Naldi, G. (2001). Theta-frequency bursting and resonance in cerebellar granule cells: experimental evidence and modeling of a slow K+-dependent mechanism. The Journal of Neuroscience, 21(3), 759-770. doi:10.1523/JNEUROSCI.21-03-00759.2001

[2] (1,2)

Masoli, S., Ottaviani, A., Casali, S., & D’Angelo, E. (2020). Cerebellar Golgi cell models predict dendritic processing and mechanisms of synaptic plasticity. PLOS Computational Biology, 16(12), e1007937. doi:10.1371/journal.pcbi.1007937

root_type

alias of Calcium