Na_HH1952#
- class braincell.channel.Na_HH1952(size, g_max=Quantity(120., 'mS / cm^2'), temp=Quantity(309.15, 'K'), q10=3.0, temp_ref=Quantity(309.15, 'K'), V_sh=Quantity(-45., 'mV'), name=None)#
Hodgkin-Huxley 1952 sodium current with \(p^3 q\) HH gating.
The original squid giant axon fast sodium current of (Hodgkin & Huxley, 1952) [1]:
\[\begin{split}\begin{aligned} \alpha_p &= \frac{1}{\operatorname{exprel}(-(V' - 5) / 10)} \\ \beta_p &= 4 \exp(-(V' + 20) / 18) \\ \alpha_q &= 0.07 \exp(-(V' + 20) / 20) \\ \beta_q &= \frac{1}{1 + \exp(-(V' - 10) / 10)} \end{aligned}\end{split}\]where \(V' = (V - V_{sh}) / \mathrm{mV}\) and \(\operatorname{exprel}(x) = (\exp(x) - 1) / x\) removes the removable singularity at the Boltzmann midpoint without changing the function value. With the default
V_sh = -45 mV(soV' = (V/mV) + 45, placing rest at -65 mV in the modern absolute-potential convention), these expand to exactly the published forms \(\alpha_m = 0.1 (V+40) / (1 - \exp(-(V+40)/10))\), \(\beta_m = 4 \exp(-(V+65)/18)\), \(\alpha_h = 0.07 \exp(-(V+65)/20)\), \(\beta_h = 1 / (1 + \exp(-(V+35)/10))\). Gating is \(p^3 q\).- 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, default120.0 mS/cm2– matches (Hodgkin & Huxley, 1952) [1]’s \(g_{Na}\).temp (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Absolute temperature driving the Q10 factor, default 36 degrees Celsius.q10 (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Q10 scaling factor for both gates, default3.0– the paper’s own factor-of-3-per-10-degree-Celsius correction.temp_ref (
Array|ndarray|bool|number|bool|int|float|complex|Quantity) – Reference temperature for the Q10 formula, default 36 degrees Celsius.V_sh (
Array|ndarray|bool|number|bool|int|float|complex|Quantity|Callable) – Threshold shift applied to both gates’ rates, default-45.0 mV.
Notes
(Hodgkin & Huxley, 1952) [1] measured these rates at 6.3 degrees Celsius, not this class’s
temp_ref = 36degrees Celsius default. Becausetempandtemp_refare equal by default, the Q10 correction is a no-op at construction time; the defaults do not reproduce the original 6.3-degree-Celsius kinetics.References