Same concentration, different volume, different signalling noise
Supplied working report; original verdicts not validated.
Review status: Blogger published. This is an archival source note, not a passed proof.
README.md
# Same concentration, different volume, different signalling noise **XXII, Theory 26 / Cellular / Cell signalling** · verdict: **partially supported** Claim (verbatim): > Signalling noise is set by the ratio of molecule number to cell volume, so two cells with the same concentration can differ in noise by an order of magnitude. ## Result Direction holds (noise = 1/sqrt(cV), so a bigger cell is quieter at equal concentration), but an order-of-magnitude noise difference needs a 100x volume difference: a 2x-diameter (8x-volume) cell pair differs by only 2.8x, not 10x. Noise depends on molecule count, not the count/volume ratio. ## Headline A 2x diameter difference gives ~2.8x, not 10x, noise difference. ## Design Coefficient of variation for a Poisson molecule count N ~ Poisson(c V) was computed exactly and confirmed by 20,000-draw simulation across 0.1-316 um^3 at fixed concentration. ## Key statistics - noise_ratio_8x_volume = 2.82843 ratio - noise_ratio_100x_volume = 10 ratio ## Predictions - **P1** (supported): noise = 1/sqrt(cV) falls with V at fixed c - **P2** (not supported): needs 100x volume; 8x volume gives 2.8x ## Limitations - Poisson count noise is the floor; real signalling noise adds bursting, partitioning and extrinsic sources. - The 'ratio of molecule number to volume' wording describes concentration, which is not what sets noise. - Cell-volume differences of 100x are rare among cells of one type, so the stated magnitude is atypical. Provenance: Poisson counting noise: CV = 1/sqrt(N), N = cV. *Working paper — not peer reviewed. AI-assisted. Not medical, clinical, financial or safety advice.*