Self-assembly of tessellated tissue sheets by expansion and collision

A new paradigm considering multicellular adhesion, repulsion and attraction represent diverse cellular tile patterns

Cell sorting by differential adhesion is one of the basic mechanisms explaining spatial organization of neurons in early stage brain development of fruit flies. The columnar arrangements of neurons determine the large-scale patterns in the fly visual center. Experimental studies indicate that hexagonal configurations regularly appear in the fly compound eye, which is connected to the visual center by photoreceptor axons, while tetragonal configurations can be induced in mutants. We need a mathematical framework to study the mechanisms of such a transition between hexagonal and tetragonal arrangements. Here, we propose a new mathematical model based on macroscopic approximations of agent-based models that produces a similar behavior changing from hexagonal to tetragonal steady configurations when medium-range repulsion and longer-range attraction between individuals are incorporated in previous successful models for cell sorting based on adhesion and volume constraints. We analyze the angular configurations of these patterns based on angle summary statistics and compare between experimental data and parameter fitted ARA (Adhesion-Repulsion-Attraction) models showing that intermediate patterns between hexagonal and tetragonal configuration are common in experimental data as well as in our ARA mathematical model. Our studies indicate an overall qualitative agreement of ARA models in tile patterning and pave the way for their quantitative studies. Our study opens up a new avenue to explore tile pattern transitions, found not only in the column arrangement in the brain, but also in the other related biological processes.

Large-scale control over collective cell migration using light-activated epidermal growth factor receptors

Receptor tyrosine kinases (RTKs) play key roles in coordinating cell movement at both single-cell and tissue scales. The recent development of optogenetic tools for controlling RTKs and their downstream signaling pathways suggests that these responses may be amenable to engineering-based control for sculpting tissue shape and function. Here, we report that a light-controlled epidermal growth factor (EGF) receptor (OptoEGFR) can be deployed in epithelial cells for precise, programmable control of long-range tissue movements. We show that in OptoEGFR-expressing tissues, light can drive millimeter-scale cell rearrangements to densify interior regions or produce rapid outgrowth at tissue edges. Light-controlled tissue movements are driven primarily by phosphoinositide 3-kinase (PI3K) signaling, rather than diffusible ligands, tissue contractility, or ERK kinase signaling as seen in other RTK-driven migration contexts. Our study suggests that synthetic, light-controlled RTKs could serve as a powerful platform for controlling cell positions and densities for diverse applications, including wound healing and tissue morphogenesis.

Quantifying cell cycle regulation by tissue crowding

The spatiotemporal coordination and regulation of cell proliferation is fundamental in many aspects of development and tissue maintenance. Cells have the ability to adapt their division rates in response to mechanical constraints, yet we do not fully understand how cell proliferation regulation impacts cell migration phenomena. Here, we present a minimal continuum model of cell migration with cell cycle dynamics, which includes density-dependent effects and hence can account for cell proliferation regulation. By combining minimal mathematical modeling, Bayesian inference, and recent experimental data, we quantify the impact of tissue crowding across different cell cycle stages in epithelial tissue expansion experiments. Our model suggests that cells sense local density and adapt cell cycle progression in response, during G1 and the combined S/G2/M phases, providing an explicit relationship between each cell-cycle-stage duration and local tissue density, which is consistent with several experimental observations. Finally, we compare our mathematical model's predictions to different experiments studying cell cycle regulation and present a quantitative analysis on the impact of density-dependent regulation on cell migration patterns. Our work presents a systematic approach for investigating and analyzing cell cycle data, providing mechanistic insights into how individual cells regulate proliferation, based on population-based experimental measurements.

Gradients in cell density and shape transitions drive collective cell migration into confining environments

Epithelial cell collectives migrate through tissue interfaces and crevices to orchestrate development processes, tumor invasion, and wound healing. Naturally, the traversal of cell collective through confining environments involves crowding due to narrowing spaces, which seems tenuous given the conventional inverse relationship between cell density and migration. However, the physical transitions required to overcome such epithelial densification for migration across confinements remain unclear. Here, in a system of contiguous microchannels of varying confinements, we show that epithelial (MCF10A) monolayers accumulate higher cell density and undergo fluid-like shape transitions before entering narrower channels. However, overexpression of breast cancer oncogene ErbB2 did not require such accumulation of cell density to migrate across matrix confinement. While wild-type MCF10A cells migrated faster in narrow channels, this confinement sensitivity was reduced after +ErbB2 mutation or with constitutively active RhoA. This physical interpretation of collective cell migration as density and shape transitions in granular matter could advance our understanding of complex living systems.

A programmable, open-source robot that scratches cultured tissues to investigate cell migration, healing, and tissue sculpting

Despite the widespread popularity of the "scratch assay," where a pipette is dragged manually through cultured tissue to create a gap to study cell migration and healing, it carries significant drawbacks. Its heavy reliance on manual technique can complicate quantification, reduce throughput, and limit the versatility and reproducibility. We present an open-source, low-cost, accessible, robotic scratching platform that addresses all of the core issues. Compatible with nearly all standard cell culture dishes and usable directly in a sterile culture hood without specialized training, our robot makes highly reproducible scratches in a variety of complex cultured tissues with high throughput. Moreover, the robot demonstrates precise removal of tissues for sculpting arbitrary tissue and wound shapes, enabling complex co-culture experiments. This system significantly improves the usefulness of the conventional scratch assay and opens up new possibilities in complex tissue engineering for realistic wound healing and migration research.

Scale-dependent sharpening of interfacial fluctuations in shape-based models of dense cellular sheets

The properties of tissue interfaces - between separate populations of cells, or between a group of cells and its environment - has attracted intense theoretical, computational, and experimental study. Recent work on shape-based models inspired by dense epithelia have suggested a possible "topological sharpening" effect, by which four-fold vertices spatially coordinated along a cellular interface lead to a cusp-like restoring force acting on cells at the interface, which in turn greatly suppresses interfacial fluctuations. We revisit these interfacial fluctuations, focusing on the distinction between short length scale reduction of interfacial fluctuations and long length scale renormalized surface tension. To do this, we implement a spectrally resolved analysis of fluctuations over extremely long simulation times. This leads to more quantitative information on the topological sharpening effect, in which the degree of sharpening depends on the length scale over which it is measured. We compare our findings with a Brownian bridge model of the interface, and close by analyzing existing experimental data in support of the role of short-length-scale topological sharpening effects in real biological systems.

SCRATCH: A programmable, open-hardware, benchtop robot that automatically scratches cultured tissues to investigate cell migration, healing, and tissue sculpting

Despite the widespread popularity of the 'scratch assay', where a pipette is dragged through cultured tissue to create an injury gap to study cell migration and healing, the manual nature of the assay carries significant drawbacks. So much of the process depends on individual manual technique, which can complicate quantification, reduce throughput, and limit the versatility and reproducibility of the approach. Here, we present a truly open-source, low-cost, accessible, and robotic scratching platform that addresses all of the core issues. Compatible with nearly all standard cell culture dishes and usable directly in a sterile culture hood, our robot makes highly reproducible scratches in a variety of complex cultured tissues with high throughput. Moreover, we demonstrate how scratching can be programmed to precisely remove areas of tissue to sculpt arbitrary tissue and wound shapes, as well as enable truly complex co-culture experiments. This system significantly improves the usefulness of the conventional scratch assay, and opens up new possibilities in complex tissue engineering and cell biological assays for realistic wound healing and migration research.

Discovering dynamic laws from observations: The case of self-propelled, interacting colloids

Active matter spans a wide range of time and length scales, from groups of cells and synthetic self-propelled colloids to schools of fish and flocks of birds. The theoretical framework describing these systems has shown tremendous success in finding universal phenomenology. However, further progress is often burdened by the difficulty of determining forces controlling the dynamics of individual elements within each system. Accessing this local information is pivotal for the understanding of the physics governing an ensemble of active particles and for the creation of numerical models capable of explaining the observed collective phenomena. In this work, we present ActiveNet, a machine-learning tool consisting of a graph neural network that uses the collective motion of particles to learn active and two-body forces controlling their individual dynamics. We verify our approach using numerical simulations of active Brownian particles, active particles undergoing underdamped Langevin dynamics, and chiral active Brownian particles considering different interaction potentials and values of activity. Interestingly, ActiveNet can equally learn conservative or nonconservative forces as well as torques. Moreover, ActiveNet has proven to be a useful tool to learn the stochastic contribution to the forces, enabling the estimation of the diffusion coefficients. Therefore, all coefficients of the equation of motion of Active Brownian Particles are captured. Finally, we apply ActiveNet to experiments of electrophoretic Janus particles, extracting the active and two-body forces controlling colloids' dynamics. On the one side, we have learned that the active force depends on the electric field and area fraction. On the other side, we have also discovered a dependence of the two-body interaction with the electric field that leads us to propose that the dominant force between active colloids is a screened electrostatic interaction with a constant length scale. We believe that the proposed methodological tool, ActiveNet, might open a new avenue for the study and modeling of experimental suspensions of active particles.

Large-scale control over collective cell migration using light-controlled epidermal growth factor receptors

Receptor tyrosine kinases (RTKs) are thought to play key roles in coordinating cell movement at single-cell and tissue scales. The recent development of optogenetic tools for controlling RTKs and their downstream signaling pathways suggested these responses may be amenable to engineering-based control for sculpting tissue shape and function. Here, we report that a light-controlled EGF receptor (OptoEGFR) can be deployed in epithelial cell lines for precise, programmable control of long-range tissue movements. We show that in OptoEGFR-expressing tissues, light can drive millimeter-scale cell rearrangements to densify interior regions or produce rapid outgrowth at tissue edges. Light-controlled tissue movements are driven primarily by PI 3-kinase signaling, rather than diffusible signals, tissue contractility, or ERK kinase signaling as seen in other RTK-driven migration contexts. Our study suggests that synthetic, light-controlled RTKs could serve as a powerful platform for controlling cell positions and densities for diverse applications including wound healing and tissue morphogenesis.

E-cadherin biomaterials reprogram collective cell migration and cell cycling by forcing homeostatic conditions

Cells attach to the world through either cell-extracellular matrix adhesion or cell-cell adhesion, and traditional biomaterials imitate the matrix for integrin-based adhesion. However, materials incorporating cadherin proteins that mimic cell-cell adhesion offer an alternative to program cell behavior and integrate into living tissues. We investigated how cadherin substrates affect collective cell migration and cell cycling in epithelia. Our approach involved biomaterials with matrix proteins on one-half and E-cadherin proteins on the other, forming a "Janus" interface across which we grew a single sheet of cells. Tissue regions over the matrix side exhibited normal collective dynamics, but an abrupt behavior shift occurred across the Janus boundary onto the E-cadherin side, where cells attached to the substrate via E-cadherin adhesions, resulting in stalled migration and slowing of the cell cycle. E-cadherin surfaces disrupted long-range mechanical coordination and nearly doubled the length of the G0/G1 phase of the cell cycle, linked to the lack of integrin focal adhesions on the E-cadherin surface.

Free and Interfacial Boundaries in Individual-Based Models of Multicellular Biological systems

Coordination of cell behaviour is key to a myriad of biological processes including tissue morphogenesis, wound healing, and tumour growth. As such, individual-based computational models, which explicitly describe inter-cellular interactions, are commonly used to model collective cell dynamics. However, when using individual-based models, it is unclear how descriptions of cell boundaries affect overall population dynamics. In order to investigate this we define three cell boundary descriptions of varying complexities for each of three widely used off-lattice individual-based models: overlapping spheres, Voronoi tessellation, and vertex models. We apply our models to multiple biological scenarios to investigate how cell boundary description can influence tissue-scale behaviour. We find that the Voronoi tessellation model is most sensitive to changes in the cell boundary description with basic models being inappropriate in many cases. The timescale of tissue evolution when using an overlapping spheres model is coupled to the boundary description. The vertex model is demonstrated to be the most stable to changes in boundary description, though still exhibits timescale sensitivity. When using individual-based computational models one should carefully consider how cell boundaries are defined. To inform future work, we provide an exploration of common individual-based models and cell boundary descriptions in frequently studied biological scenarios and discuss their benefits and disadvantages.

Topological packing statistics of living and nonliving matter

Complex disordered matter is of central importance to a wide range of disciplines, from bacterial colonies and embryonic tissues in biology to foams and granular media in materials science to stellar configurations in astrophysics. Because of the vast differences in composition and scale, comparing structural features across such disparate systems remains challenging. Here, by using the statistical properties of Delaunay tessellations, we introduce a mathematical framework for measuring topological distances between general three-dimensional point clouds. The resulting system-agnostic metric reveals subtle structural differences between bacterial biofilms as well as between zebrafish brain regions, and it recovers temporal ordering of embryonic development. We apply the metric to construct a universal topological atlas encompassing bacterial biofilms, snowflake yeast, plant shoots, zebrafish brain matter, organoids, and embryonic tissues as well as foams, colloidal packings, glassy materials, and stellar configurations. Living systems localize within a bounded island-like region of the atlas, reflecting that biological growth mechanisms result in characteristic topological properties.

Programing Cell Assembly via Ink-Free, Label-Free Magneto-Archimedes Based Strategy

Tissue engineering raised a high requirement to control cell distribution in defined materials and structures. In "ink"-based bioprintings, such as 3D printing and photolithography, cells were associated with inks for spatial orientation; the conditions suitable for one ink are hard to apply on other inks, which increases the obstacle in their universalization. The Magneto-Archimedes effect based (Mag-Arch) strategy can modulate cell locomotion directly without impelling inks. In a paramagnetic medium, cells were repelled from high magnetic strength zones due to their innate diamagnetism, which is independent of substrate properties. However, Mag-Arch has not been developed into a powerful bioprinting strategy as its precision, complexity, and throughput are limited by magnetic field distribution. By controlling the paramagnetic reagent concentration in the medium and the gaps between magnets, which decide the cell repelling scope of magnets, we created simultaneously more than a hundred micrometer scale identical assemblies into designed patterns (such as alphabets) with single/multiple cell types. Cell patterning models for cell migration and immune cell adhesion studies were conveniently created by Mag-Arch. As a proof of concept, we patterned a tumor/endothelial coculture model within a covered microfluidic channel to mimic epithelial-mesenchymal transition (EMT) under shear stress in a cancer pathological environment, which gave a potential solution to pattern multiple cell types in a confined space without any premodification. Overall, our Mag-Arch patterning presents an alternative strategy for the biofabrication and biohybrid assembly of cells with biomaterials featured in controlled distribution and organization, which can be broadly employed in tissue engineering, regenerative medicine, and cell biology research.

Quantifying tissue growth, shape and collision via continuum models and Bayesian inference

Although tissues are usually studied in isolation, this situation rarely occurs in biology, as cells, tissues and organs coexist and interact across scales to determine both shape and function. Here, we take a quantitative approach combining data from recent experiments, mathematical modelling and Bayesian parameter inference, to describe the self-assembly of multiple epithelial sheets by growth and collision. We use two simple and well-studied continuum models, where cells move either randomly or following population pressure gradients. After suitable calibration, both models prove to be practically identifiable, and can reproduce the main features of single tissue expansions. However, our findings reveal that whenever tissue-tissue interactions become relevant, the random motion assumption can lead to unrealistic behaviour. Under this setting, a model accounting for population pressure from different cell populations is more appropriate and shows a better agreement with experimental measurements. Finally, we discuss how tissue shape and pressure affect multi-tissue collisions. Our work thus provides a systematic approach to quantify and predict complex tissue configurations with applications in the design of tissue composites and more generally in tissue engineering.

Independent control over cell patterning and adhesion on hydrogel substrates for tissue interface mechanobiology

Tissue boundaries and interfaces are engines of morphogenesis in vivo. However, despite a wealth of micropatterning approaches available to control tissue size, shape, and mechanical environment in vitro, fine-scale spatial control of cell positioning within tissue constructs remains an engineering challenge. To address this, we augment DNA "velcro" technology for selective patterning of ssDNA-labeled cells on mechanically defined photoactive polyacrylamide hydrogels. Hydrogels bearing photopatterned single-stranded DNA (ssDNA) features for cell capture are then co-functionalized with extracellular matrix (ECM) proteins to support subsequent adhesion of patterned tissues. ECM protein co-functionalization does not alter ssDNA pattern fidelity, cell capture, or hydrogel elastic stiffness. This approach enables mechanobiology studies and measurements of signaling activity at dynamic cell interfaces with precise initial patterning. Combining DNA velcro patterning and ECM functionalization provides independent control of initial cell placement, adhesion, and mechanics, constituting a new tool for studying biological interfaces and for programming multicellular interactions in engineered tissues.

Transitions in density, pressure, and effective temperature drive collective cell migration into confining environments

Epithelial cell collectives migrate through tissue interfaces and crevices to orchestrate processes of development, tumor invasion, and wound healing. Naturally, traversal of cell collective through confining environments involves crowding due to the narrowing space, which seems tenuous given the conventional inverse relationship between cell density and migration. However, physical transitions required to overcome such epithelial densification for migration across confinements remain unclear. Here, in contiguous microchannels, we show that epithelial (MCF10A) monolayers accumulate higher cell density before entering narrower channels; however, overexpression of breast cancer oncogene +ErbB2 reduced this need for density accumulation across confinement. While wildtype MCF10A cells migrated faster in narrow channels, this confinement sensitivity reduced after +ErbB2 mutation or with constitutively-active RhoA. The migrating collective developed pressure differentials upon encountering microchannels, like fluid flow into narrowing spaces, and this pressure dropped with their continued migration. These transitions of pressure and density altered cell shapes and increased effective temperature, estimated by treating cells as granular thermodynamic system. While +RhoA cells and those in confined regions were effectively warmer, cancer-like +ErbB2 cells remained cooler. Epithelial reinforcement by metformin treatment increased density and temperature differentials across confinement, indicating that higher cell cohesion could reduce unjamming. Our results provide experimental evidence for previously proposed theories of inverse relationship between density and motility-related effective temperature. Indeed, we show across cell lines that confinement increases pressure and effective temperature, which enable migration by reducing density. This physical interpretation of collective cell migration as granular matter could advance our understanding of complex living systems.

Fluid-Mediated Fabrication of Complex Assemblies

This Perspective accounts for recent progress in the directed control of interfacial fluid flows harnessed to assemble architected soft materials. We are focusing on the paradigmatic problem of free-surface flows in curable elastomers. These elastomers are initially liquid and cure into elastic solids whose shape is imparted by concomitant and competing phenomena: flow-induced deformations and curing. Particular attention is given to the role of capillary forces in these systems. Originating from the cohesive nature of liquids and thus favoring smooth interfaces, capillary forces can also promote the destabilization of interfaces, e.g., into droplets. In turn, such mechanical instabilities tend to grow into regular patterns, e.g., forming hexagonal lattices. We discuss how the universality, robustness, and ultimate regularity of these out-of-equilibrium processes could serve as a basis for new fabrication paradigms, where instabilities are directed to generate target architected solids obtained without each element laid in place by direct mechanized intervention.

4-bit adhesion logic enables universal multicellular interface patterning

Multicellular systems, from bacterial biofilms to human organs, form interfaces (or boundaries) between different cell collectives to spatially organize versatile functions1,2. The evolution of sufficiently descriptive genetic toolkits probably triggered the explosion of complex multicellular life and patterning3,4. Synthetic biology aims to engineer multicellular systems for practical applications and to serve as a build-to-understand methodology for natural systems5-8. However, our ability to engineer multicellular interface patterns2,9 is still very limited, as synthetic cell-cell adhesion toolkits and suitable patterning algorithms are underdeveloped5,7,10-13. Here we introduce a synthetic cell-cell adhesin logic with swarming bacteria and establish the precise engineering, predictive modelling and algorithmic programming of multicellular interface patterns. We demonstrate interface generation through a swarming adhesion mechanism, quantitative control over interface geometry and adhesion-mediated analogues of developmental organizers and morphogen fields. Using tiling and four-colour-mapping concepts, we identify algorithms for creating universal target patterns. This synthetic 4-bit adhesion logic advances practical applications such as human-readable molecular diagnostics, spatial fluid control on biological surfaces and programmable self-growing materials5-8,14. Notably, a minimal set of just four adhesins represents 4 bits of information that suffice to program universal tessellation patterns, implying a low critical threshold for the evolution and engineering of complex multicellular systems3,5.