KM_MA2020_GrC

class braincell.channel.KM_MA2020_GrC(size, g_max=Quantity(0.25, 'mS / cm^2'), temp=Quantity(303.15, 'K'), name=None)

M-type potassium current of the granule cell model.

Slow, non-inactivating M-type potassium current imported from the cerebellar granule cell model of Masoli et al. (2020) [2]. A single first-order n gate of power 1 drives an ohmic current:

\[\begin{split}\begin{aligned} n_\infty &= \frac{1}{1 + \exp(-(V + 35) / 6)} \\ \alpha_n &= 0.0033 \, \exp((V + 30) / 40) \\ \beta_n &= 0.0033 \, \exp(-(V + 30) / 20) \\ \tau_n &= \frac{1}{\alpha_n + \beta_n} \end{aligned}\end{split}\]

where \(V\) is in millivolts, the rates are per millisecond and \(\tau_n\) is in milliseconds. This class applies no voltage shift, and the reversal potential comes from the potassium ion object rather than from the class.

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 0.25 mS/cm2, which is exactly the source mechanism’s gkbar = 0.00025 mho/cm2.

• temp (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Absolute temperature driving the gate’s q10 factor, default 30 degrees Celsius. This matches the celsius = 30 (degC) written in the source mechanism’s PARAMETER block.

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

See also

KM_MA2020_GoC

Golgi-cell port of the same mechanism.

KM_RI2021_SC

Stellate-cell port of the same mechanism.

Kir2p3_MA2020_GrC

Inward rectifier of the same granule cell model, sharing the same origin paper.

Notes

Ported from GrC/channel/KM_MA20_GrC.mod. That file, the Golgi port GoC/channel/KM_MA20_GoC.mod and the stellate port SC/channel/KM_RI21_SC.mod are byte-identical apart from their SUFFIX line, and so are the three BrainCell classes: the rate constants above are shared verbatim with KM_MA2020_GoC and KM_RI2021_SC. What differs is only the deposit each was imported from, and therefore the model paper cited below.

The mechanism does not use the steady state implied by its own rates. Its n_inf = a_n/(a_n + b_n) line is commented out in the .mod source and replaced by the explicit Boltzmann shown above, so \(n_\infty\) and \(\tau_n\) are independent expressions here.

Where the q10 factor is applied. The gate declares q10 = 3.0 at a reference of 22 degrees Celsius, so HH.compute_derivative() scales the whole \((n_\infty - n)/\tau_n\) term by \(\phi = 3^{(T - 22)/10}\) (about 2.41 at the default 30 degrees Celsius). The .mod file instead multiplies Q10 into alp_n and bet_n, which divides its tau_n by the same factor. The two forms are algebraically identical, but it means f_n_tau() returns the q10-free time constant rather than the mechanism’s tau_n.

Provenance, and what the header does not establish. The .mod header carries Author: A. Fontana and CoAuthor: T.Nieus. That credit line is copy-pasted verbatim across every cell-type port of this mechanism and names people unrelated to the granule-cell key, so it is not treated as a citation here. The kinetics originate in the cerebellar granule cell model of D’Angelo et al. (2001) [1]; the granule-cell paper [2] names the model this parameterisation was imported from, not the origin of the equations. Reference [2] is the granule-cell paper specifically – the companion Golgi-cell paper of the same year belongs to KM_MA2020_GoC, not to this class.

Conductance default. 0.25 mS/cm2 is the deposit’s tuned value, carried across from the .mod file. It is not a value printed in either cited paper.

Import deviations. The original mechanism’s NMODL TABLE over [-100, 30] mV, covering n_inf and tau_n, is not reproduced: both expressions are evaluated per call. NEURON clamped tabulated values to the boundary outside that window, so any BrainCell-versus-NEURON divergence below -100 mV or above 30 mV is expected rather than a port error. The integration method was also changed from derivimplicit to cnexp; with one independent gate ODE that substitution is exact.

References

[1]

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] (1,2,3)

Masoli, S., Tognolina, M., Laforenza, U., Moccia, F., & D’Angelo, E. (2020). Parameter tuning differentiates granule cell subtypes enriching transmission properties at the cerebellum input stage. Communications Biology, 3(1), 222. doi:10.1038/s42003-020-0953-x

root_type

alias of Potassium