Optimal Control of Collective Electrotaxis in Epithelial Monolayers.

Epithelial monolayers are some of the best-studied models for collective cell migration due to their abundance in multicellular systems and their tractability. Experimentally, the collective migration of epithelial monolayers can be robustly steered e.g. using electric fields, via a process termed electrotaxis. Theoretically, however, the question of how to design an electric field to achieve a desired spatiotemporal movement pattern is underexplored. In this work, we construct and calibrate an ordinary differential equation model to predict the average velocity of the centre of mass of a cellular monolayer in response to stimulation with an electric field. We use this model, in conjunction with optimal control theory, to derive physically realistic optimal electric field designs to achieve a variety of aims, including maximising the total distance travelled by the monolayer, maximising the monolayer velocity, and keeping the monolayer velocity constant during stimulation. Together, this work is the first to present a unified framework for optimal control of collective monolayer electrotaxis and provides a blueprint to optimally steer collective migration using other external cues.

Learning the rules of collective cell migration using deep attention networks.

Collective, coordinated cellular motions underpin key processes in all multicellular organisms, yet it has been difficult to simultaneously express the 'rules' behind these motions in clear, interpretable forms that effectively capture high-dimensional cell-cell interaction dynamics in a manner that is intuitive to the researcher. Here we apply deep attention networks to analyze several canonical living tissues systems and present the underlying collective migration rules for each tissue type using only cell migration trajectory data. We use these networks to learn the behaviors of key tissue types with distinct collective behaviors-epithelial, endothelial, and metastatic breast cancer cells-and show how the results complement traditional biophysical approaches. In particular, we present attention maps indicating the relative influence of neighboring cells to the learned turning decisions of a 'focal cell'-the primary cell of interest in a collective setting. Colloquially, we refer to this learned relative influence as 'attention', as it serves as a proxy for the physical parameters modifying the focal cell's future motion as a function of each neighbor cell. These attention networks reveal distinct patterns of influence and attention unique to each model tissue. Endothelial cells exhibit tightly focused attention on their immediate forward-most neighbors, while cells in more expansile epithelial tissues are more broadly influenced by neighbors in a relatively large forward sector. Attention maps of ensembles of more mesenchymal, metastatic cells reveal completely symmetric attention patterns, indicating the lack of any particular coordination or direction of interest. Moreover, we show how attention networks are capable of detecting and learning how these rules change based on biophysical context, such as location within the tissue and cellular crowding. That these results require only cellular trajectories and no modeling assumptions highlights the potential of attention networks for providing further biological insights into complex cellular systems.

Overriding native cell coordination enhances external programming of collective cell migration.

As collective cell migration is essential in biological processes spanning development, healing, and cancer progression, methods to externally program cell migration are of great value. However, problems can arise if the external commands compete with strong, preexisting collective behaviors in the tissue or system. We investigate this problem by applying a potent external migratory cue-electrical stimulation and electrotaxis-to primary mouse skin monolayers where we can tune cell-cell adhesion strength to modulate endogenous collectivity. Monolayers with high cell-cell adhesion showed strong natural coordination and resisted electrotactic control, with this conflict actively damaging the leading edge of the tissue. However, reducing preexisting coordination in the tissue by specifically inhibiting E-cadherin-dependent cell-cell adhesion, either by disrupting the formation of cell-cell junctions with E-cadherin-specific antibodies or rapidly dismantling E-cadherin junctions with calcium chelators, significantly improved controllability. Finally, we applied this paradigm of weakening existing coordination to improve control and demonstrate accelerated wound closure in vitro. These results are in keeping with those from diverse, noncellular systems and confirm that endogenous collectivity should be considered as a key quantitative design variable when optimizing external control of collective migration.

Size-dependent patterns of cell proliferation and migration in freely-expanding epithelia.

The coordination of cell proliferation and migration in growing tissues is crucial in development and regeneration but remains poorly understood. Here, we find that, while expanding with an edge speed independent of initial conditions, millimeter-scale epithelial monolayers exhibit internal patterns of proliferation and migration that depend not on the current but on the initial tissue size, indicating memory effects. Specifically, the core of large tissues becomes very dense, almost quiescent, and ceases cell-cycle progression. In contrast, initially-smaller tissues develop a local minimum of cell density and a tissue-spanning vortex. To explain vortex formation, we propose an active polar fluid model with a feedback between cell polarization and tissue flow. Taken together, our findings suggest that expanding epithelia decouple their internal and edge regions, which enables robust expansion dynamics despite the presence of size- and history-dependent patterns in the tissue interior.

Cells do not exist in isolation. Instead, they form tissues, where individual cells make contact with their neighbors and form microscopic 'architectures'. Epithelia are a type of tissue where cells are arranged in flat sheets, and are found in organs such as the lining of the kidney or the skin. Tissues need to grow, especially early in life. If tissues are damaged ­ for example, if the skin is cut or grazed ­ cells also need to divide (to create new healthy cells) and move as a group (to close the wound). Such coordinated motions result in cells exhibiting distinct group behaviors, similar to those observed within crowds of people or schools of fish. If coordination breaks down, problems can happen such as uncoordinated tissue growth seen in cancer. However, how cell movements are coordinated is still not fully understand. For example, researchers know that cells' positions within a group can determine how they behave, meaning that even the same type of cell could behave differently at the edge or center of a tissue. This suggests that the initial size and shape of a tissue should influence its subsequent growth and behavior; however, the nature of this influence is still largely unknown. Heinrich et al. therefore wanted to determine the differences in the way larger and smaller tissues grow. Microscope imaging was used to track the growth of circular, artificial tissues made from single-layered sheets of dog kidney cells grown in the laboratory. Comparing how quickly the tissues expanded revealed that the area of tissue circles that started out smaller increased at a much faster rate than that of tissue circles that were larger to begin with. This turned out to be because the edges of the tissues grew at a constant speed, independent of their initial size or shape, but circles with a smaller area have a larger proportion of cells on their edges. The motions of the cells at the center of the tissues had no effect on how the edges of the tissue grew. A final observation was that the way tissues of a given size behaved depended on whether they had grown to be that size, or they started off that big. These results shed light on how groups of cells interact in growing tissues. In the future, this information could be used to predict how different tissues grow over time, potentially helping scientists engineer better artificial tissues or organs for transplantation.

SCHEEPDOG: Programming Electric Cues to Dynamically Herd Large-Scale Cell Migration.

Directed cell migration is critical across biological processes spanning healing to cancer invasion, yet no existing tools allow real-time interactive guidance over such migration. We present a new bioreactor that harnesses electrotaxis-directed cell migration along electric field gradients-by integrating four independent electrodes under computer control to dynamically program electric field patterns, and hence steer cell migration. Using this platform, we programmed and characterized multiple precise, two-dimensional collective migration maneuvers in renal epithelia and primary skin keratinocyte ensembles. First, we demonstrated on-demand, 90-degree collective turning. Next, we developed a universal electrical stimulation scheme capable of programming arbitrary 2D migration maneuvers such as precise angular turns and migration in a complete circle. Our stimulation scheme proves that cells effectively time-average electric field cues, helping to elucidate the transduction timescales in electrotaxis. Together, this work represents an enabling platform for controlling cell migration with broad utility across many cell types.

Cell division orientation is coupled to cell-cell adhesion by the E-cadherin/LGN complex.

Both cell-cell adhesion and oriented cell division play prominent roles in establishing tissue architecture, but it is unclear how they might be coordinated. Here, we demonstrate that the cell-cell adhesion protein E-cadherin functions as an instructive cue for cell division orientation. This is mediated by the evolutionarily conserved LGN/NuMA complex, which regulates cortical attachments of astral spindle microtubules. We show that LGN, which adopts a three-dimensional structure similar to cadherin-bound catenins, binds directly to the E-cadherin cytosolic tail and thereby localizes at cell-cell adhesions. On mitotic entry, NuMA is released from the nucleus and competes LGN from E-cadherin to locally form the LGN/NuMA complex. This mediates the stabilization of cortical associations of astral microtubules at cell-cell adhesions to orient the mitotic spindle. Our results show how E-cadherin instructs the assembly of the LGN/NuMA complex at cell-cell contacts, and define a mechanism that couples cell division orientation to intercellular adhesion.

Galvanotactic control of collective cell migration in epithelial monolayers.

Many normal and pathological biological processes involve the migration of epithelial cell sheets. This arises from complex emergent behaviour resulting from the interplay between cellular signalling networks and the forces that physically couple the cells. Here, we demonstrate that collective migration of an epithelium can be interactively guided by applying electric fields that bias the underlying signalling networks. We show that complex, spatiotemporal cues are locally interpreted by the epithelium, resulting in rapid, coordinated responses such as a collective U-turn, divergent migration, and unchecked migration against an obstacle. We observed that the degree of external control depends on the size and shape of the cell population, and on the existence of physical coupling between cells. Together, our results offer design and engineering principles for the rational manipulation of the collective behaviour and material properties of a tissue.