  Biological cells are often found to sense their chemical environment near the
single-molecule detection limit. Surprisingly, this precision is higher than
simple estimates of the fundamental physical limit, hinting towards active
sensing strategies. In this work, we analyse the effect of cell memory, e.g.
from slow biochemical processes, on the precision of sensing by cell-surface
receptors. We derive analytical formulas, which show that memory significantly
improves sensing in weakly fluctuating environments. However, surprisingly when
memory is adjusted dynamically, the precision is always improved, even in
strongly fluctuating environments. In support of this prediction we quantify
the directional biases in chemotactic Dictyostelium discoideum cells in a flow
chamber with alternating chemical gradients. The strong similarities between
cell sensing and control engineering suggest universal problem-solving
strategies of living matter.
