Sensora

Sensora listens to a drizzle of molecules landing on her skin, counting every one to learn how much is out there.

The Physics

How precisely can a cell measure the concentration c of a chemical around it? Molecules arrive by diffusion one by one, so the count is noisy. Berg and Purcell showed in 1977 that a cell of radius a, averaging for a time T, can do no better than a fractional error of order 1/√(Dac T).

Listen longer, or be bigger, to know better. Their paper also argued that a modest number of receptors spread over the surface captures most of the possible signal, and bacteria such as E. coli sense close to this physical limit.

δc / c ~ 1 / √(D a c T)

• δc/c: fractional error in concentration
• D: diffusion coefficient (m²/s)
• a: cell radius (m)
• c: concentration (1/m³)
• T: averaging time (s)

Berg & Purcell, “Physics of chemoreception”, Biophysical Journal 20, 193 (1977).

Honest caveat: This is a scaling law (“~”, not “=”); the careful “perfect instrument” result adds a numerical factor. Bacteria come close to the limit, not exactly to it.

On the shirt

Front: Sensora, the pixel-art character, with “COUNTING EVERY MOLECULE”. Back: the scaling limit, what each symbol means, the listen-longer rule and the 1977 paper. Printed on a unisex tee.