Diffusion vs. direct transport in the precision of morphogen readout.

Morphogen profiles allow cells to determine their position within a developing organism, but not all morphogen profiles form by the same mechanism. Here, we derive fundamental limits to the precision of morphogen concentration sensing for two canonical mechanisms: the diffusion of morphogen through extracellular space and the direct transport of morphogen from source cell to target cell, for example, via cytonemes. We find that direct transport establishes a morphogen profile without adding noise in the process. Despite this advantage, we find that for sufficiently large values of profile length, the diffusion mechanism is many times more precise due to a higher refresh rate of morphogen molecules. We predict a profile lengthscale below which direct transport is more precise, and above which diffusion is more precise. This prediction is supported by data from a wide variety of morphogens in developing Drosophila and zebrafish.

Temporal precision of molecular events with regulation and feedback.

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.

Precision of Flow Sensing by Self-Communicating Cells.

Metastatic cancer cells detect the direction of lymphatic flow by self-communication: they secrete and detect a chemical which, due to the flow, returns to the cell surface anisotropically. The secretion rate is low, meaning detection noise may play an important role, but the sensory precision of this mechanism has not been explored. Here we derive the precision of flow sensing for two ubiquitous detection methods: absorption vs reversible binding to surface receptors. We find that binding is more precise due to the fact that absorption distorts the signal that the cell aims to detect. Comparing to experiments, our results suggest that the cancer cells operate remarkably close to the physical detection limit. Our prediction that cells should bind the chemical reversibly, not absorb it, is supported by endocytosis data for this ligand-receptor pair.

Emergent versus Individual-Based Multicellular Chemotaxis.

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.

Fundamental Limits to Collective Concentration Sensing in Cell Populations.

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 trade-off 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.

Role of spatial averaging in multicellular gradient sensing.

Gradient sensing underlies important biological processes including morphogenesis, polarization, and cell migration. The precision of gradient sensing increases with the length of a detector (a cell or group of cells) in the gradient direction, since a longer detector spans a larger range of concentration values. Intuition from studies of concentration sensing suggests that precision should also increase with detector length in the direction transverse to the gradient, since then spatial averaging should reduce the noise. However, here we show that, unlike for concentration sensing, the precision of gradient sensing decreases with transverse length for the simplest gradient sensing model, local excitation-global inhibition. The reason is that gradient sensing ultimately relies on a subtraction of measured concentration values. While spatial averaging indeed reduces the noise in these measurements, which increases precision, it also reduces the covariance between the measurements, which results in the net decrease in precision. We demonstrate how a recently introduced gradient sensing mechanism, regional excitation-global inhibition (REGI), overcomes this effect and recovers the benefit of transverse averaging. Using a REGI-based model, we compute the optimal two- and three-dimensional detector shapes, and argue that they are consistent with the shapes of naturally occurring gradient-sensing cell populations.