  Organisms must perform sensory-motor behaviors to survive. What bounds or
constraints limit behavioral performance? Previously, we found that the
gradient-climbing speed of a chemotaxing Escherichia coli is near a bound set
by the limited information they acquire from their chemical environments. Here
we ask what limits their sensory accuracy. Past theoretical analyses have shown
that the stochasticity of single molecule arrivals sets a fundamental limit on
the precision of chemical sensing. Although it has been argued that bacteria
approach this limit, direct evidence is lacking. Here, using information theory
and quantitative experiments, we find that E. coli's chemosensing is not
limited by the physics of particle counting. First, we derive the physical
limit on the behaviorally-relevant information that any sensor can get about a
changing chemical concentration, assuming that every molecule arriving at the
sensor is recorded. Then, we derive and measure how much information E. coli's
signaling pathway encodes during chemotaxis. We find that E. coli encode two
orders of magnitude less information than an ideal sensor limited only by shot
noise in particle arrivals. These results strongly suggest that constraints
other than particle arrival noise limit E. coli's sensory fidelity.
