What a Cell Pays to Know: Energy per Bit in Bacterial Chemotaxis

An Escherichia coli cell measures attractant concentration by comparing receptor occupancy over time, with precision bounded by the Berg-Purcell molecule-counting limit. This paper prices that measurement. For a 1 micrometre cell, diffusion constant 1.0e-9 m^2/s, 10 micromolar background and a 1 s window at 310 K, the counting bound gives 0.041 percent fractional precision, equivalent to 11.26 bits of concentration information per window. The adaptation machinery is priced from published inputs: the receptor methylation-demethylation cycle turns over at 20.39 events per second per cell (direct turnover measurement; an enzyme-inventory cross-check gives 11.44 per second), and each methylation consumes one S-adenosylmethionine at about 3 ATP equivalents, 58.20 k_B T per event, for a window cost of 5.0779e-18 J. The cell therefore pays 105.4 k_B T per bit (4.5093e-19 J per bit), 152.0 times the Landauer floor k_B T ln 2 at 310 K, an excess of 104.7 k_B T per bit over the minimum the counting statistics alone would allow. Across the stated input ranges the cost spans 3.1 to 6068.6 k_B T per bit, and it rises with integration time because energy grows linearly with the window while information grows only logarithmically. Model calculations from published values are labelled SIMULATED, NOT MEASURED. The deposit includes the paper PDF, the computation script (compute.py) that produces every number in the paper, and its outputs (results.json, results.txt).