  Directional chemosensing is ubiquitous in cell biology, but some cells such
as mating yeast paradoxically degrade the signal they aim to detect. While the
data processing inequality suggests that such signal modification cannot
increase the sensory information, we show using a reaction-diffusion model and
an exactly solvable discrete-state reduction that it can. We identify a
non-Markovian step in the information chain allowing the system to evade the
data processing inequality, reflecting the nonlocal nature of diffusion. Our
results apply to any sensory system in which degradation couples to diffusion.
Experimental data suggest that mating yeast operate in the beneficial regime
where degradation improves sensing.
