Limits to the precision of gradient sensing with spatial communication and temporal integration

Abstract

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. Although 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, because communication establishes a maximum length scale 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 whereas exchange of the local reporter weakens the comparison, it decreases the measurement noise. We term such a model "regional excitation-global inhibition." Our results demonstrate that fundamental sensing limits are necessarily sharpened when the need to communicate information is taken into account.