AHP_De1994

AHP_De1994#

class braincell.channel.AHP_De1994(size, n=2, g_max=Quantity(10., 'mS / cm^2'), alpha=48.0, beta=0.09, phi=1.0, name=None)#

Calcium-activated after-hyperpolarization current.

Reproduces the slow Ca2+-activated K+ (AHP) current of the thalamic reticular nucleus spindle-rhythmicity model of (Destexhe et al., 1994) [1]: a two-site calcium-binding gate with no voltage dependence, of the closed form <closed> + n Ca_i <-> <open> (alpha, beta).

\[\begin{split}\begin{aligned} I_{AHP} &= g_{\mathrm{max}} \, p^2 \, (E_K - V) \\ \frac{dp}{dt} &= \phi \left(\alpha_p \, (1 - p) - \beta_p \, p\right) \\ \alpha_p &= \alpha \, \left([\mathrm{Ca}]_i / \mathrm{mM}\right)^n \\ \beta_p &= \beta \end{aligned}\end{split}\]

i.e. a Hodgkin-Huxley-style gate whose forward rate is a power law in intracellular calcium and whose backward rate is a fixed constant.

Parameters:

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

  • n (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Calcium-binding exponent used inside \(\alpha_p\), default 2. Independent of the gate’s conductance exponent (see Notes): changing n alters only the calcium-binding rate law, not the p ** 2 factor in the current.

  • g_max (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Maximal conductance density, default 10.0 mS/cm2.

  • alpha (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Forward (calcium-binding) rate coefficient, default 48.0 (units mM^-n ms^-1).

  • beta (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Backward (unbinding) rate, default 0.09 ms^-1. See Notes: this default is three times the reference value.

  • phi (Array | ndarray | bool | number | bool | int | float | complex | Quantity | Callable) – Rate-scaling factor multiplying both \(\alpha_p\) and \(\beta_p\), default 1.0.

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

Notes

No .mod file under this repository carries a De1994/De19 filename fragment; this class has no in-repo NMODL counterpart to name here.

The gate’s conductance exponent is fixed at power=2 by this class’s gates declaration and is independent of the n constructor parameter, which only exponentiates [Ca]_i inside the forward rate. Both default to 2, which is why the two are easy to conflate; they do not have to agree.

BrainCell’s ``beta`` default is three times the reference value. BrainCell defaults to beta = 0.09 ms^-1, but the reference value is beta = 0.03 ms^-1 – the value used by the authors’ reference implementation, and quoted from the paper by BrainPy. (The 1994 paper itself is paywalled; only its PubMed abstract was read for this documentation pass, so the 0.03 figure could not be checked directly against the published text.) The alpha = 48.0 default is unaffected by this discrepancy: it is exactly beta / cac ** n = 0.03 / 0.025 ** 2 = 48 mM^-2 ms^-1 from the reference implementation’s own beta and cac, and BrainCell reproduces it exactly – evidence that the rest of the parameterisation is faithful even though the beta default drifted.

References

current_owner_type#

alias of Potassium