🔬 Cell Signalling — Receptor Cascade & Signal Amplification

Model a G-protein coupled receptor (GPCR) signalling cascade: ligand binds receptor → receptor occupancy → G-protein activation → adenylyl cyclase → cAMP production → PKA phosphorylation. Explore signal amplification, adaptation, and Hill-function ultrasensitivity.

Ligand [L]: 1e-6 M

K_D: 1e-8 M

Hill n: 2.0

PDE activity: 0.3

Receptor occ.: —%

G-protein act.: —%

cAMP: —

PKA: —%

Amplification: —×

EC₅₀: —

Biology / Physics

Receptor occupancy: [RL]/[R_T] = [L]ⁿ/(K_Dⁿ + [L]ⁿ) — the Hill equation. When n > 1 the response is switch-like (ultrasensitive). G-protein activation follows receptor occupancy. cAMP is produced by adenylyl cyclase (proportional to active G-proteins) and degraded by phosphodiesterase (PDE). PKA is activated by cAMP following another Hill function. Signal amplification: a single ligand-bound receptor can activate hundreds of G-proteins, each stimulating production of thousands of cAMP molecules, each activating many PKA enzymes — cascade amplification of ~10,000-fold.