Taste Adaptation Lab: Hill Dose-Response & Sensory Decay (2D)

Taste & Stimulus

Taste type

Stimulus concentration (×K) 1.00×

Hill coefficient (n) 1.8

Adaptation Kinetics

Adaptation time constant τ_a 6.0 s

Recovery time constant τ_r 12.0 s

Live Readout

Elapsed time

0.0 s

Perceived intensity

Adaptation level

Stimulus

Off

How it works

Initial receptor sensitivity follows a real Hill-equation dose-response curve:

R0(C) = C^n / (K^n + C^n)

C is stimulus concentration (relative to the receptor's half-max K), and n is the Hill coefficient — cooperativity between binding sites. GPCR pathways (sweet, umami, bitter) show steeper, more cooperative curves and slower multi-step cascades; direct ion channels (salty, sour) bind the stimulus ion directly, giving a near-linear curve and a fast rise.

While the stimulus stays on, an adaptation variable A relaxes toward a taste-specific maximum depth with its own exponential time constant τ_a — the same first-order relaxation behind "you stop tasting something after a while":

dA/dt = (A_max − A) / τ_a      (stimulus ON)
dA/dt = (0 − A) / τ_r           (stimulus OFF, recovery)
Perceived intensity = R0 × (1 − A)   while stimulus is ON, else 0

Removing the stimulus drops perceived intensity to zero immediately (nothing left to taste), but the adaptation state A keeps decaying back toward zero on its own, slower, recovery time constant τ_r. Re-applying the stimulus before A has fully recovered starts the next response already partly adapted — real cross-adaptation carry-over.

Left pane — taste bud / receptor cell, glow and bound-ligand density scale with live perceived intensity.
Top-right — the Hill dose-response curve with the live operating point at the current concentration.
Bottom-right — perceived intensity (solid) and adaptation state A (dashed) vs. time.

Perceived intensity Adaptation state A Hill curve operating point