 Solution

For the same concentration gradient, the front-to-back difference scales with cell length. A much smaller bacterial cell samples a correspondingly smaller spatial signal, while stochastic arrival and binding of individual chemoattractant molecules make receptor measurements noisy. For illustration, a $2\mu \mathrm{m}$ cell in the $0.5$ cm capillary would experience only $0.04\mathrm{nM}$ across its length, compared with $0.4\mathrm{nM}$ for the longer cell. This illustrates a size penalty; it does not assume that bacterial and human detection thresholds are identical.

Many swimming bacteria, including Escherichia coli, use temporal sensing in bacterial chemotaxis: they compare recent receptor stimulation with an adapted baseline as they move. Increasing attractant suppresses reorientation and prolongs runs; decreasing attractant increases tumbling. Repeated runs and reorientations therefore generate a biased random walk up the gradient, without requiring a simultaneous comparison between the front and back. Chemotaxis feedback regulation supplies the adaptation needed to remain sensitive to changes rather than responding only to absolute concentration.

A discriminating experiment changes concentration rapidly and uniformly around the bacteria: a response then occurs without a spatial difference across the cell. The classic temporal-step experiments found increased tumbling after attractant decreases and smoother swimming after increases.^[ref] In a new experiment, compare up-steps and down-steps with constant-concentration and sham-mixing controls, holding temperature and medium composition fixed. Measure run durations and tumble frequency, rather than only average swimming speed. Such a test supports temporal comparison but does not by itself identify every molecular component or show that all bacterial species use the same mechanism.