CaLVA_SU2015_DCN

class braincell.channel.CaLVA_SU2015_DCN(size, perm=Quantity(1., 'cm / s'), temp=Quantity(309.15, 'K'), qdeltat=1.0, name=None)

GHK-drive LVA calcium current of the DCN model (Sudhakar 2015).

A GHK-driven, low-voltage-activated (LVA) calcium current with \(m^2 h\) gating, used for the deep cerebellar nucleus (DCN) neuron model of (Sudhakar et al., 2015) [2]:

\[\begin{split}\begin{aligned} I_{CaLVA} &= -P \cdot m^2 h \cdot \Phi(V, [Ca]_i, [Ca]_o, T) \\ m_\infty &= \frac{1}{1 + \exp(-(V + 56) / -6.2)} \\ \tau_m &= \left(\frac{0.333} {\exp((V + 131) / -16.7) + \exp((V + 15.8) / 18.2)} + 0.204\right) \Big/ q_{\Delta t} \\ h_\infty &= \frac{1}{1 + \exp((V + 80) / 4)} \\ \tau_h &= \frac{1}{q_{\Delta t}} \times \begin{cases} 0.333 \exp((V + 466) / 66) & V < -81 \\ 0.333 \exp((V + 21) / -10.5) + 9.32 & V \geq -81 \end{cases} \end{aligned}\end{split}\]

where \(\Phi\) is the constant-field GHK flux (see ghk_flux()) evaluated with this class’s own inline Faraday/gas-constant literals rather than the shared helper (see Notes), and \(P\) is the permeability parameter.

Parameters:

• size (int | Sequence[int] | integer | Sequence[integer]) – Channel state shape.

• perm (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Permeability entering the GHK flux term. Defaults to 1.0 cm/s.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature entering the GHK flux term and the activation/inactivation time constants. Defaults to 36 degrees Celsius.

• qdeltat (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Divisor applied to \(\tau_m\) and \(\tau_h\); a NEURON-style Q10-free rate scale, not a Gate phi factor. Defaults to 1.0.

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

See also

CaL_SU2015_DCN

Sibling DCN calcium current with the same \(m^2 h\) gating shape and identical rate constants (see Notes), driven ohmically against a fixed reversal potential rather than through GHK.

CaHVA_SU2015_DCN

Sibling DCN calcium current with high-voltage-activated (\(m^3\)) gating instead.

braincell.ion.CdpLVA_SU2015_DCN

Dedicated LVA-current-driven calcium pool BrainCell ships for this current; see Notes for how it relates to root_type.

braincell.channel._base.ghk_flux

Shared GHK flux helper; this class does not call it directly (see Notes).

Notes

Ported from DCN/channel/CaLVA_SU15_DCN.mod, whose TITLE reads “Low voltage activated calcium current (CaLVA) of deep cerebellar nucleus (DCN) neuron”. This class’s rate functions are algebraically identical to CaL_SU2015_DCN’s, whose own mod file (CaL_SU15_DCN.mod) is also titled “LVA calcium current (CaLVA) of deep cerebellar nucleus (DCN) neuron” despite its different CaL symbol name – the two BrainCell classes are the same LVA current family exposed through two different current laws (see CaL_SU2015_DCN’s Notes).

root_type here is the generic Calcium base, identical to CaHVA_SU2015_DCN’s – nothing in this channel class itself restricts it to a particular ion pool. BrainCell separately ships CdpLVA_SU2015_DCN, a dedicated LVA-current-driven calcium pool mirroring the imported NMODL’s separate cali/cal pool (as opposed to CdpHVA_SU2015_DCN’s cai, which the original NEURON mechanism used to let the LVA and HVA currents drive independently trackable calcium pools). Preserving that separation in a BrainCell model is a compositional choice made when attaching this channel to a specific ion instance, not a guarantee enforced by this class’s root_type.

current() evaluates the GHK constant-field equation inline with the mod file’s own hard-coded literals (4.47814e6, -23.20764929) rather than calling ghk_flux(), matching the pattern used by the module-level _cav3p1_nmodl_ghk_flux / _cav3p3_nmodl_ghk_flux helpers elsewhere in this file. NEURON’s raw ical for this mechanism is outward-positive; the sign is flipped in current() to match BrainCell’s repo-wide inward-positive convention.

The origin of the DCN kinetics is the GENESIS model of Steuber, Schultheiss, Silver, De Schutter & Jaeger (2011) [1], translated from GENESIS to NEURON by Luthman, Hoebeek, Maex, Davey, Adams, De Zeeuw & Steuber (2011) and reused, without modification credit, in Sudhakar et al. (2015) [2]. The string “CaLVA” does occur in the Sudhakar et al. (2015) article text, but this docstring does not claim that either paper prints the m_inf/tau_m/h_inf/tau_h constants above.

The original mechanism’s TABLE directive tabulated minf, taum, hinf and tauh over [-150, 100] mV (plus a DEPEND T table); BrainCell removes the table and evaluates all four expressions per-call instead.

References

[1]

Steuber, V., Schultheiss, N. W., Silver, R. A., De Schutter, E., & Jaeger, D. (2011). Determinants of synaptic integration and heterogeneity in rebound firing explored with data-driven models of deep cerebellar nucleus cells. Journal of Computational Neuroscience, 30(3), 633-658. doi:10.1007/s10827-010-0282-z

[2] (1,2)

Sudhakar, S. K., Torben-Nielsen, B., & De Schutter, E. (2015). Cerebellar nuclear neurons use time and rate coding to transmit Purkinje neuron pauses. PLOS Computational Biology, 11(12), e1004641. doi:10.1371/journal.pcbi.1004641

current(V, Ca)

Calculate the current for this ion channel.

This method should be implemented by subclasses to compute the current based on the channel’s specific properties and state.

Parameters:

• *args – Variable length argument list.

• **kwargs – Arbitrary keyword arguments.

Raises:

NotImplementedError – This method must be implemented by subclasses.

root_type

alias of Calcium