CaL_SU2015_DCN

class braincell.channel.CaL_SU2015_DCN(size, g_max=Quantity(0.01, 'mS / cm^2'), E=Quantity(139., 'mV'), qdeltat=1.0, name=None)

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

An ohmically-driven calcium current with \(m^2 h\) HH gating against a fixed reversal potential, used for the deep cerebellar nucleus (DCN) neuron model of (Sudhakar et al., 2015) [2]:

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

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 0.01 mS/cm2.

• E (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Fixed reversal potential used in place of an ion-derived value (see Notes). Defaults to 139.0 mV.

• 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

CaLVA_SU2015_DCN

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

CaHVA_SU2015_DCN

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

Notes

Ported from DCN/channel/CaL_SU15_DCN.mod. Its own ``TITLE`` reads “LVA calcium current (CaLVA) of deep cerebellar nucleus (DCN) neuron” – i.e. the mod file named CaL_SU15_DCN.mod describes itself as an LVA / “CaLVA” current, not an L-type current, despite the CaL symbol name. This class’s rate functions are in fact algebraically identical to CaLVA_SU2015_DCN’s: both use m_inf = 1/(1 + exp((V+56)/-6.2)) and the same \(\tau_m\)/\(h_\infty\)/\(\tau_h\) expressions above. The only structural difference between the two classes is the current law – this class overrides reversal_potential() to return the fixed E parameter and derives its driving force ohmically, while CaLVA_SU2015_DCN derives its driving force from a GHK flux against explicit ion concentrations. The default E = 139.0 mV was not independently verified against the mod file’s own PARAMETER block for this task; it is documented here as a shipped BrainCell default, not attributed to a specific value printed in Sudhakar et al. (2015) [2].

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 “CaL” does not occur in the Sudhakar et al. (2015) article text; this docstring records only that the mechanism is part of the model published as [2], not that the paper names or describes it, and it does not claim that either paper prints the constants above.

The original mechanism’s TABLE directive tabulated minf, taum, hinf and tauh over [-150, 100] mV (with no DEPEND T table, unlike CaHVA_SU2015_DCN and CaLVA_SU2015_DCN); 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] (1,2,3,4)

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

reversal_potential(V, *ions)

Return the reversal potential driving the current.

Parameters:

• V (ArrayLike) – Membrane potential. Unused by the default implementation; present so overrides can depend on it.

• *ions (IonInfo) – Ion states, in the declaration order of root_type.

Returns:

Reversal potential, as a voltage. Defaults to that of the first ion, which for a joint root type is the first entry of root_type.__args__. Override to read a fixed self.E or a non-leading ion.

Return type:

ArrayLike

root_type

alias of HHTypedNeuron