  Molecular signalling in living cells occurs at low copy numbers and is
thereby inherently limited by the noise imposed by thermal diffusion. The
precision at which biochemical receptors can count signalling molecules is
intimately related to the noise correlation time. In addition to passive
thermal diffusion, messenger RNA and vesicle-engulfed signalling molecules can
transiently bind to molecular motors and are actively transported across
biological cells. Active transport is most beneficial when trafficking occurs
over large distances, for instance up to the order of 1 metre in neurons. Here
we explain how intermittent active transport allows for faster equilibration
upon a change in concentration triggered by biochemical stimuli. Moreover, we
show how intermittent active excursions induce qualitative changes in the noise
in effectively one-dimensional systems such as dendrites. Thereby they allow
for significantly improved signalling precision in the sense of a smaller
relative deviation in the concentration read-out by the receptor. On the basis
of linear response theory we derive the exact mean field precision limit for
counting actively transported molecules. We explain how intermittent active
excursions disrupt the recurrence in the molecular motion, thereby facilitating
improved signalling accuracy. Our results provide a deeper understanding of how
recurrence affects molecular signalling precision in biological cells and novel
diagnostic devices.
