Muscle Channelopathies as Depolarization-Block-Threshold Shifts

Muscle channelopathies are perturbations of membrane excitability — the FitzHugh-Nagumo substrate itself. Myotonia (CLCN1/SCN4A gain) is hyperexcitable: it RAISES the depolarization-block threshold to 1.30 (versus normal 0.80), giving repetitive discharge and delayed relaxation. Periodic paralysis (SCN4A/CACNA1S) LOWERS it to 0.10, so a small depolarizing shift silences the fibre — the opposite sign, like the MG/LEMS pair [V].

The block threshold is the sustained depolarizing drive at which firing collapses (Na inactivation). It moves monotonically with the recovery conductance: myotonia (hyperexcitable) pushes it UP (1.30), periodic paralysis (inactivation-prone) pushes it DOWN (0.10), bracketing normal (0.80). At a depolarizing challenge of 0.70, myotonia still fires (32 spikes) while paralysis is silenced (1) and normal is at its block edge (26). Excitability perturbation [V]; clinical signs [L]; absolute [O].

Excitability is the substrate, so its diseases are too

The kit's membrane model is the FitzHugh-Nagumo relaxation oscillator vendored in the substrate. Skeletal-muscle channelopathies perturb exactly that excitability, so they are the most direct test of the substrate at the membrane level — no added mechanism. The relevant quantity is the depolarization-block threshold: the sustained depolarizing drive above which the membrane stops firing because the fast (sodium-like) channel inactivates. Normal muscle fires in its operating window and blocks only under a strong depolarizing shift.

Two opposite signs from one membrane

Myotonia congenita (loss of the CLCN1 chloride conductance, or SCN4A gain) makes the membrane HYPEREXCITABLE: it resists block, firing repetitively even under a depolarizing challenge that quiets a normal fibre — the electrical correlate of myotonic runs and delayed muscle relaxation. In the model its block threshold rises to 1.30 against normal 0.80.

Periodic paralysis (SCN4A / CACNA1S) is the opposite: the membrane is INACTIVATION-PRONE, so a modest depolarizing shift (a potassium disturbance) tips it into depolarization block — the fibre becomes inexcitable and the muscle is transiently paralysed. Its block threshold falls to 0.10. The two diseases therefore bracket normal from opposite sides, exactly as myasthenia and Lambert-Eaton do at the synapse (§10).

Monotone in the channel defect

Sweeping the recovery conductance, the block threshold moves monotonically — more inactivation-prone, lower threshold:

At a depolarizing challenge of 0.70, the three states separate cleanly: myotonia fires 32 spikes, normal 26 (at its block edge), periodic paralysis 1 (silenced). The DIRECTIONS are the result.

Seam and what is NOT claimed

The specific channel mutation is cited from the genetics/neuro side; the in-class result is the muscle-membrane excitability sign. The clinical signs are cited [L]; the absolute membrane parameters (true conductances, exact thresholds in mV) are not fixed by the substrate [O].