The precision of concentration sensing is improved when cells communicate. Here we derive the physical limits to concentration sensing for cells that communicate over short distances by directly exchanging small molecules (juxtacrine signaling), or over longer distances by secreting and sensing a diffusive messenger molecule (autocrine signaling). In the latter case, we find that the optimal cell spacing can be large, due to a tradeoff between maintaining communication strength and reducing signal cross-correlations. This leads to the surprising result that sparsely packed communicating cells sense concentrations more precisely than densely packed communicating cells. We compare our results to data from a wide variety of communicating cell types.Single cells sense chemical concentrations with extraordinary precision. In some cases this precision approaches the physical limits set by molecular diffusion [1,2]. Yet, no cell performs this sensory task in isolation. Cells exist in communities, such as colonies, biofilms, and tissues. Within these communities, cells communicate in diverse ways. Communication mechanisms include the exchange of molecules between cells in contact (juxtacrine signaling), and secretion and detection of diffusible molecules over distances comparable to the cell size or longer (autocrine signaling [3]) [4][5][6][7]. This raises the question of whether cell-cell communication improves a cell's sensory precision, beyond what the cell achieves alone.Experiments have shown that cells are more sensitive in groups than they are alone. Groups of neurons [8], lymphocytes [9], and epithelial cells [10] exhibit biased morphological or motile responses to chemical gradients that are too shallow for cells to detect individually. Groups of cell nuclei in fruit fly embryos detect morphogen concentrations with a higher precision than is expected for a single nucleus [11][12][13]. In some cases, such as with epithelial cells [10], cell-cell communication has been shown to be directly responsible for the enhanced sensitivity. Yet, from a theoretical perspective, the fundamental limits to concentration sensing [1,2,[14][15][16][17][18][19][20] or gradient sensing [21][22][23] have been largely limited to single receptors or single cells. Analogous limits for groups of communicating cells have been derived only for specific geometries [24], and are otherwise poorly understood. In particular, it remains unknown whether the limits depend on the communication mechanism (juxtacrine vs. autocrine), and how they scale with collective properties like communication strength and population size.Here we derive the fundamental limits to the precision of collective sensing by one-, two-, and three-dimensional (3D) populations of cells. We focus on the basic task of sensing a uniform chemical concentration. We compare two ubiquitous communication mechanisms, juxtacrine signaling and autocrine signaling. Intuitively one expects that sensory precision is enhanced by communication, that communication is strongest when cells ...

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Multicellular chemotaxis can occur via individually chemotaxing cells that are mechanically coupled. Alternatively, it can emerge collectively, from cells chemotaxing differently in a group than they would individually. Here we consider collective movement that emerges from cells on the exterior of the collective responding to chemotactic signals, whereas bulk cells remain uninvolved in sensing and directing the collective. We find that the precision of this type of emergent chemotaxis is higher than that of individual-based chemotaxis for one-dimensional cell chains and two-dimensional cell sheets, but not three-dimensional cell clusters. We describe the physical origins of these results, discuss their biological implications, and show how they can be tested using common experimental measures such as the chemotactic index.

Cellular behaviors such as migration, division, and differentiation rely on precise timing, and yet the molecular events that govern these behaviors are highly stochastic. We investigate regulatory strategies that decrease the timing noise of molecular events. Autoregulatory feedback increases noise. Yet, we find that in the presence of regulation by a second species, autoregulatory feedback decreases noise. To explain this finding, we develop a method to calculate the optimal regulation function that minimizes the timing noise. The method reveals that the combination of feedback and regulation minimizes noise by maximizing the number of molecular events that must happen in sequence before a threshold is crossed. We compute the optimal timing precision for all two-node networks with regulation and feedback, derive a generic lower bound on timing noise, and discuss our results in the context of neuroblast migration during Caenorhabditis elegans development.