= 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.<The gradient-sensing mechanism in bacterial chemotaxis by Robert M. Macnab and Daniel E. Koshland Jr.>[pp. 2509–2512, Abstract and temporal-gradient response experiments]{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.
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