  Gradient sensing requires at least two measurements at different points in
space. These measurements must then be communicated to a common location to be
compared, which is unavoidably noisy. While much is known about the limits of
measurement precision by cells, the limits placed by the communication are not
understood. Motivated by recent experiments, we derive the fundamental limits
to the precision of gradient sensing in a multicellular system, accounting for
communication and temporal integration. The gradient is estimated by comparing
a "local" and a "global" molecular reporter of the external concentration,
where the global reporter is exchanged between neighboring cells. Using the
fluctuation-dissipation framework, we find, in contrast to the case when
communication is ignored, that precision saturates with the number of cells
independently of the measurement time duration, since communication establishes
a maximum lengthscale over which sensory information can be reliably conveyed.
Surprisingly, we also find that precision is improved if the local reporter is
exchanged between cells as well, albeit more slowly than the global reporter.
The reason is that while exchange of the local reporter weakens the comparison,
it decreases the measurement noise. We term such a model "regional
excitation--global inhibition" (REGI). Our results demonstrate that fundamental
sensing limits are necessarily sharpened when the need to communicate
information is taken into account.
