The Hawaiian bobtail squid (Euprymna scolopes) hosts a pure culture of the luminous bacterium Vibrio fischeri inside crypts of a specialized light organ. Newly hatched squid recruit free-living cells from seawater; the population then grows logistically inside the crypt:
dN/dt = r·N·(1 − N/K_cap) − v·N (logistic growth, v = venting rate)
Each cell constitutively synthesizes and secretes a small diffusible autoinducer (3-oxo-C6-homoserine lactone) via the LuxI enzyme. Because the crypt is a near-closed volume, the signal accumulates in proportion to how many cells are producing it:
dA/dt = k_a·N − δ·A (production ∝ population, decay/efflux at rate δ)
Autoinducer diffuses back into every cell and binds the LuxR receptor. Only once enough receptor–autoinducer complex has formed does LuxR turn on the lux operon (luciferase + accessory genes) — a cooperative, switch-like response modeled with a Hill function:
P_on(A) = A⁴ / (A⁴ + K⁴) (K = quorum threshold, per-cell noise sets which side of the switch each cell lands on)
- Growth rate r — how fast the bacterial population expands inside the crypt.
- Decay rate δ — how quickly autoinducer is diluted or exported; a lower δ lets signal build faster relative to population, tripping the switch earlier.
- Quorum threshold K — the autoinducer level needed before the lux operon activates; raising it delays the light-up.
- Dawn Venting — every morning the squid expels roughly 95% of its bacterial symbionts into the ocean, reseeding tomorrow's population growth (observed in real animals as a diel rhythm).
This is the founding experimental system for quorum sensing (Nealson & Hastings, 1970s) — the same LuxI/LuxR logic, generalized, underlies density-dependent gene regulation across most bacterial species, including virulence and biofilm switches in pathogens.