Energy cost of sensing beyond the Berg-Purcell limit
In plain words
In 1977 Berg and Purcell estimated how precisely a cell can measure a chemical concentration in a fixed time. Spending energy in the readout chemistry can do better than simple counting, and the exact trade-off between energy and precision is not settled.
Precise statement
For a receptor or receptor array of size a, concentration c, diffusion constant D and integration time T, the Berg-Purcell estimate is $(dc/c)^2 \sim 1/(D a c T)$, and maximum-likelihood readout lowers it by a factor of 2. Find the tight lower bound on $(dc/c)^2$ as a function of free energy dissipated per measurement by an arbitrary downstream reaction network, including receptor and readout noise, and identify the network architecture that reaches it.
What would settle it
A proof of the bound for general Markov readout networks together with an explicit network that saturates it.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Bounds for specific readout networks were derived around 2012 to 2014; a general tight bound for arbitrary networks is not established as of 2026, to this survey's knowledge.
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