Use-Dependent Block: Local Anesthetics & Na⁺ Channels (2D)

Local Anesthetic

Concentration 2.0×

Off-rate kinetics

Stimulation

Firing frequency 2.0 Hz

Recovery time constant τ 5.0 ms

Live Readouts

Blocked channels

Last AP amplitude

100%

Conduction distance

10 / 10 rings

Resting (free)

Open (conducting)

Inactivated

Drug-bound (blocked)

How it works

Local anesthetics don't plug the pore at rest — they follow the modulated-receptor hypothesis (Hille, 1977): the drug's binding site on a voltage-gated Na⁺ channel has low affinity in the resting (R) state and much higher affinity once the channel opens (O) or inactivates (I).

Each channel cycles  R --stimulus--> O --~1ms--> I --τ(recovery)--> R
Binding (state-dependent):  P(bind)   = 1 − exp(−k_on(state)·[drug]·dt)
                             k_on(O,I) ≫ k_on(R)
Unbinding:                  P(unbind) = 1 − exp(−k_off·dt)
A ring only re-fires the next stimulus if the fraction of
UNBLOCKED resting channels exceeds a safety threshold (~35%);
below that, the action potential fails to propagate past it.

Concentration — scales the binding rate; more drug means more channels get trapped bound each time they open.
Firing frequency — faster stimulation leaves less time between spikes for channels to recover (I → R) and for bound drug to dissociate, so block accumulates spike after spike — this is use-dependent block, the reason nerves that fire fast (pain fibers) are blocked before ones that fire slowly.
Recovery time constant τ — how long a channel stays inactivated before it can return to rest; longer τ means more time spent in the high-affinity I state per spike.
Fast vs. slow off-rate — a smaller, more lipophilic drug (lidocaine-like) unbinds quickly between spikes and recovers block at low frequency; a bulkier drug (bupivacaine-like) stays trapped and produces much more persistent block, which is why it's more cardiotoxic in overdose.

Clinically, this is exactly why regional nerve blocks are frequency-selective: unmyelinated C-fibers carrying pain fire rapidly and are blocked first, while touch and motor fibers firing slowly can survive at the same drug concentration.

2D view: each of the 10 rings along the axon is drawn as its true cross-section — 12 channels arranged around the circumference, exactly as in the 3D model, just viewed end-on instead of in perspective. Drag left/right on the axon panel to spin the cross-sections and inspect channels that would otherwise face away from you.

Axon segment · 10 channel rings · 12 Na⁺ channels/ring

drag ↔ to rotate rings

Blocked % (purple) · AP amplitude % (yellow) — last 6 s