Axona: Hodgkin–Huxley Spike
Physics of Life & Earth arc, page 189 of 193. Back to The Pixelated Physics Universe
Who they are
Axona's squid armour carries a tentacle axon, and when she fires, a spike of light travels down it.
Axona is a character of the Physics of Life & Earth arc: drawn in pixels, ruled by one piece of real physics, and never allowed to break it.
The physics
Hodgkin and Huxley explained the nerve impulse of the squid giant axon with a circuit: the membrane's capacitance in parallel with sodium, potassium and leak conductances. Sodium channels open fast and close more slowly; potassium opens with a delay. Their equations reproduced the shape of the action potential and its speed. A. L. Hodgkin and A. F. Huxley published it in 1952; it predicted a conduction speed of 18.8 m/s against 21.2 m/s measured.
$$ \begin{gathered} C_m \frac{dV}{dt} = -\bar g_{Na} m^{3}h\,(V - E_{Na}) - \bar g_{K} n^{4}(V - E_K) - g_L (V - E_L) + I \\ \frac{dm}{dt} = \alpha_m(V)(1-m) - \beta_m(V)\,m \qquad (\text{same form for } h \text{ and } n) \end{gathered} $$
| Symbol | Meaning | SI unit |
|---|---|---|
| $C_m$ | membrane capacitance | F |
| $V$ | membrane voltage | V |
| $t$ | time | s |
| $\bar g_{Na},\ \bar g_{K},\ g_L$ | maximum sodium, potassium and leak conductances | S |
| $m,\ h,\ n$ | gating variables (0 to 1) | 1 |
| $E_{Na},\ E_K,\ E_L$ | reversal potentials | V |
| $I$ | applied current | A |
| $\alpha_m,\ \beta_m$ | voltage-dependent opening and closing rates | 1/s |
Honest caveat: The tee uses the modern voltage convention (rest ≈ −65 mV, peak ≈ +40 mV), not the 1952 paper's original sign convention.
Sources
- Hodgkin & Huxley (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve, J. Physiol. 117, 500
- Nobel Prize in Physiology or Medicine 1963, NobelPrize.org
Crossovers
Axona meets Kinessa (8 nm per Step). Axona's spike runs on ion channels moving charge across a membrane. Kinessa's motor runs on ATP, stepping 8 nm at a time along a microtubule. Both are biology driven by physics at the nanoscale.
Axona meets The Spark Herald (Electromagnetism / Lightning Command). Axona models a nerve as a circuit: membrane capacitance in parallel with ion conductances. The Spark Herald's Maxwell equations govern every current in it.
Wear the lore
Concept keywords: Hodgkin–Huxley Spike, Axona, Physics of Life & Earth, physics lore, Pixelated Physics