Directed cell motion in response to an external chemical gradient occurs in many biological phenomena such as wound healing, angiogenesis, and cancer metastasis. Chemotaxis is often characterized by the accuracy, persistence, and speed of cell motion, but whether any of these quantities is physically constrained by the others is poorly understood. Using a combination of theory, simulations, and 3D chemotaxis assays on single metastatic breast cancer cells, we investigate the links among these different aspects of chemotactic performance. In particular, we observe in both experiments and simulations that the chemotactic accuracy, but not the persistence or speed, increases with the gradient strength. We use a random walk model to explain this result and to propose that cells’ chemotactic accuracy and persistence are mutually constrained. Our results suggest that key aspects of chemotactic performance are inherently limited regardless of how favorable the environmental conditions are.

Collective cell migration in response to a chemical cue occurs in many biological processes such as morphogenesis and cancer metastasis. Clusters of migratory cells in these systems are capable of responding to gradients of <1% difference in chemical concentration across a cell length. Multicellular systems are extremely sensitive to their environment, and although the limits to multicellular sensing are becoming known, how this information leads to coherent migration remains poorly understood. We develop a computational model of multicellular sensing and migration in which groups of cells collectively measure noisy chemical gradients. The output of the sensing process is coupled to the polarization of individual cells to model migratory behavior. Through the use of numerical simulations, we find that larger clusters of cells detect the gradient direction with higher precision and thus achieve stronger polarization bias, but larger clusters also induce more drag on collective motion. The trade-off between these two effects leads to an optimal cluster size for most efficient migration. We discuss how our model could be validated using simple, phenomenological experiments.

Important cellular processes such as migration, differentiation, and development often rely on precise timing. Yet, the molecular machinery that regulates timing is inherently noisy. How do cells achieve precise timing with noisy components? We investigate this question using a first-passage-time approach, for an event triggered by a molecule that crosses an abundance threshold and that is regulated by either an accumulating activator or a diminishing repressor. We find that either activation or repression outperforms an unregulated strategy. The optimal regulation corresponds to a nonlinear increase in the amount of the target molecule over time, arises from a tradeoff between minimizing the timing noise of the regulator and that of the target molecule itself, and is robust to additional effects such as bursts and cell division. Our results are in quantitative agreement with the nonlinear increase and low noise of mig-1 gene expression in migrating neuroblast cells during Caenorhabditis elegans development. These findings suggest that dynamic regulation may be a simple and powerful strategy for precise cellular timing.

Metastasis is a process of cell migration that can be collective and guided by chemical cues. Viewing metastasis in this way, as a physical phenomenon, allows one to draw upon insights from other studies of collective sensing and migration in cell biology. Here we review recent progress in the study of cell sensing and migration as collective phenomena, including in the context of metastatic cells. We describe simple physical models that yield the limits to the precision of cell sensing, and we review experimental evidence that cells operate near these limits. Models of collective migration are surveyed in order understand how collective metastatic invasion can occur. We conclude by contrasting cells' sensory abilities with their sensitivity to drugs, and suggesting potential alternatives to cell-death-based cancer therapies.Keywords: metastasis, collective behavior, gradient sensing, cell migration Metastasis is one of the most intensely studied stages of cancer progression because it is the most deadly stage of cancer. The first step of metastasis is invasion, wherein cells break away from the tumor and invade the surrounding tissue. Our understanding of metastatic invasion has benefited tremendously from genetic and biochemical approaches [25,26,36]. However, the physical aspects of metastatic invasion are still unclear [26]. We know that at a fundamental level, metastatic invasion is a physical process. Tumor cells sense and respond to chemical gradients provided by surrounding cells [4,14,51,55] or other features of the tumor environment [49,54,55] (Fig. 1A). Indeed, tumor cells are highly sensitive, able to detect a 1% difference in concentration across the cell length [55]. Sensing is ultimately a physical phenomenon. Therefore, can we build a simple physical theory to understand the sensory behavior of tumor cells, and can this physical theory inform treatment options?Metastatic invasion involves coordinated migration of tumor cells away from the tumor site. In many types of cancer, migration is collective and highly organized, involving the coherent motion of connected groups of cells [1,11,21,51] (Fig. 1B). Collective migration is ultimately a physical phenomenon, since it relies on mechanical coupling and can often be understood as emerging from simple physical interactions at the cell-to-cell level. Can we understand the collective migration of tumor cells with simple physical models?Here we review recent progress on modeling sensing and migration in cells and cell collectives. We discuss metastatic cells explicitly, and emphasize that physical insights gained from other cellular systems can inform our understanding of metastatic invasion. We focus on simple physical models and order-of-magnitude numerical estimates in order to quantitatively probe the extent of, and the limits to, cell sensory and migratory behavior. Our hope is that a more quantitative understanding of * Electronic address: amugler@purdue.edu metastatic invasion will inform treatment protocols, and to that end we conclude by discus...

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.