Aplysia Gill-Withdrawal Reflex: Quantal Vesicle Release — 2D

Stimulate

Parameters

Stimulus interval (ISI) 1.5 s

Docking-site recovery τ 8 s

Serotonin facilitation gain 2.5×

Live Readouts

Docked sites

12/12

Quantal EPSP

0.0 mV

Gill withdrawal

5-HT facilitation

off

Quanta released (last stim)

Total stimuli fired

How it works

This is a quantal, single-vesicle counterpart to the continuous-pool 3D version of Kandel's Aplysia gill-withdrawal circuit. Instead of tracking a smooth vesicle-pool fraction, it simulates 12 individual presynaptic docking (active-zone) sites, each independently empty or occupied — Katz's original quantal hypothesis of neurotransmitter release, made literal.

Each empty site fills with hazard rate 1/τ  (docking of a fresh vesicle)
Each occupied site releases independently, probability p_eff, per stimulus
Expected occupancy still obeys:  dV/dt = (1−V)/τ − p·δ(stim)   (V = occupied/12)
p_eff(t) = p₀ · [1 + (G−1)·e^(−t/τ_5HT)]   after a tail shock

Habituation emerges from the same site-depletion statistics as before — repeated touches fire more sites than τ can refill, so fewer sites are occupied at each successive stimulus and fewer quanta are released. Sensitization still comes from serotonin (5-HT) released by the facilitatory interneuron, which raises the per-site release probability p_eff for several seconds.

What's genuinely different from the 3D model: each released vesicle becomes a real neurotransmitter quantum that undergoes its own 2D drift-diffusion transport (a directed random walk, mean-squared displacement ⟨r²⟩ = 4Dt around the drift) across the synaptic cleft before it can bind a postsynaptic receptor — so the EPSP you see is a live sum of discrete, independently-arriving quantal events, not an instantaneous analytic scalar.

Touch Siphon — fires one test pulse without starting the train, so you can probe synaptic strength at any moment.
Start Habituating Train — fires repeated touches at the chosen ISI; watch docked sites (orange squares at the terminal) empty out and the gill's withdrawal shrink.
ISI slider — shorter intervals outrun site recovery and habituate faster; long intervals let sites refill between touches.
Recovery τ — mean time for an empty docking site to capture a fresh vesicle from the reserve pool (the roaming yellow dots).
Sensitizing Tail Shock — releases serotonin (yellow burst, diffusing down from the interneuron) that raises release probability for ~6 s, temporarily overriding habituation.

Sensory neuron / docking sites Motor neuron → gill Facilitatory interneuron (5-HT) Reserve vesicles / quanta in transit

Aplysia Gill-Withdrawal Reflex: Quantal Vesicle Release (2D)