Glassy dynamics in three-dimensional embryonic tissues

Motility driven glassy dynamics in confluent epithelial monolayers

As wounds heal, embryos develop, cancer spreads, or asthma progresses, the cellular monolayer undergoes a glass transition between solid-like jammed and fluid-like flowing states. During some of these processes, the cells undergo an epithelial-to-mesenchymal transition (EMT): they acquire in-plane polarity and become motile. Thus, how motility drives the glassy dynamics in epithelial systems is critical for the EMT process. However, no analytical framework that is indispensable for deeper insights exists. Here, we develop such a theory inspired by a well-known glass theory. One crucial result of this work is that the confluency affects the effective persistence time-scale of active force, described by its rotational diffusivity, Deffr. Deffr differs from the bare rotational diffusivity, Dr, of the motile force due to cell shape dynamics, which acts to rectify the force dynamics: Deffr is equal to Dr when Dr is small and saturates when Dr is large. We test the theoretical prediction of Deffr and how it affects the relaxation dynamics in our simulations of the active Vertex model. This novel effect of Deffr is crucial to understanding the new and previously published simulation data of active glassy dynamics in epithelial monolayers.

A shape-driven reentrant jamming transition in confluent monolayers of synthetic cell-mimics

Many critical biological processes, like wound healing, require densely packed cell monolayers/tissues to transition from a jammed solid-like to a fluid-like state. Although numerical studies anticipate changes in the cell shape alone can lead to unjamming, experimental support for this prediction is not definitive because, in living systems, fluidization due to density changes cannot be ruled out. Additionally, a cell's ability to modulate its motility only compounds difficulties since even in assemblies of rigid active particles, changing the nature of self-propulsion has non-trivial effects on the dynamics. Here, we design and assemble a monolayer of synthetic cell-mimics and examine their collective behaviour. By systematically increasing the persistence time of self-propulsion, we discovered a cell shape-driven, density-independent, re-entrant jamming transition. Notably, we observed cell shape and shape variability were mutually constrained in the confluent limit and followed the same universal scaling as that observed in confluent epithelia. Dynamical heterogeneities, however, did not conform to this scaling, with the fast cells showing suppressed shape variability, which our simulations revealed is due to a transient confinement effect of these cells by their slower neighbors. Our experiments unequivocally establish a morphodynamic link, demonstrating that geometric constraints alone can dictate epithelial jamming/unjamming.

Entropic timescales of dynamic heterogeneity in supercooled liquid

Non-Gaussian displacement distributions are universal predictors of dynamic heterogeneity in slowly varying environments. Here, we explore heterogeneous dynamics in supercooled liquid using molecular dynamics simulations and show the efficiency of the relative-entropy based measure, negentropy, in quantifying dynamic heterogeneity over the widely used non-Gaussian parameter. Our analysis shows that the heterogeneity quantified by the negentropy is significantly different from the one obtained using the conventional moment-based definition that considers deviation from Gaussianity up to lower-order moments. We extract the timescales of dynamic heterogeneity using the two methods and show that the differential changes diverge as the system experiences strong intermittency near the glass transition. Further, we interpret the entropic timescales and discuss the general implications of our work.

Shape-driven confluent rigidity transition in curved biological tissues

Collective cell motions underlie structure formation during embryonic development. Tissues exhibit emergent multicellular characteristics such as jamming, rigidity transitions, and glassy dynamics, but there remain questions about how those tissue-scale dynamics derive from local cell-level properties. Specifically, there has been little consideration of the interplay between local tissue geometry and cellular properties influencing larger-scale tissue behaviors. Here, we consider a simple two-dimensional computational vertex model for confluent tissue monolayers, which exhibits a rigidity phase transition controlled by the shape index (ratio of perimeter to square root area) of cells, on surfaces of constant curvature. We show that the critical point for the rigidity transition is a function of curvature such that positively curved systems are likely to be in a less rigid, more fluid, phase. Likewise, negatively curved systems (saddles) are likely to be in a more rigid, less fluid, phase. A phase diagram we generate for the curvature and shape index constitutes a testable prediction from the model. The curvature dependence is interesting because it suggests a natural explanation for more dynamic tissue remodeling and facile growth in regions of higher surface curvature. Conversely, we would predict stability at the base of saddle-shaped budding structures without invoking the need for biochemical or other physical differences. This concept has potential ramifications for our understanding of morphogenesis of budding and branching structures.

Random Traction Yielding Transition in Epithelial Tissues

We investigate how randomly oriented cell traction forces lead to fluidization in a vertex model of epithelial tissues. We find that the fluidization occurs at a critical value of the traction force magnitude F_{c}. We show that this transition exhibits critical behavior, similar to the yielding transition of sheared amorphous solids. However, we find that it belongs to a different universality class, even though it satisfies the same scaling relations between critical exponents established in the yielding transition of sheared amorphous solids. Our work provides a fluidization mechanism through active force generation that could be relevant in biological tissues.

Fluid-Glass-Jamming Rheology of Soft Active Brownian Particles

We numerically study the shear rheology of a binary mixture of soft active Brownian particles, from the fluid to the disordered solid regime. At low shear rates, we find a Newtonian regime, where a Green-Kubo relation with an effective temperature provides the linear viscosity. It is followed by a shear-thinning regime at high shear rates. At high densities, solidification is signaled by the emergence of a finite yield stress. We construct a "fluid-glass-jamming" phase diagram with activity replacing temperature. While both parameters gauge fluctuations, activity also changes the exponent characterizing the decay of the diffusivity close to the glass transition and the shape of the yield stress surface. The dense disordered active solid appears to be mostly dominated by athermal jamming rather than glass rheology.

Soft pinning: Experimental validation of static correlations in supercooled molecular glass-forming liquids

Enormous enhancement in the viscosity of a liquid near its glass transition is a hallmark of glass transition. Within a class of theoretical frameworks, it is connected to growing many-body static correlations near the transition, often called "amorphous ordering." At the same time, some theories do not invoke the existence of such a static length scale in the problem. Thus, proving the existence and possible estimation of the static length scales of amorphous order in different glass-forming liquids is very important to validate or falsify the predictions of these theories and unravel the true physics of glass formation. Experiments on molecular glass-forming liquids become pivotal in this scenario as the viscosity grows several folds (∼ 10 14 ), and simulations or colloidal glass experiments fail to access these required long-time scales. Here we design an experiment to extract the static length scales in molecular liquids using dilute amounts of another large molecule as a pinning site. Results from dielectric relaxation experiments on supercooled Glycerol with different pinning concentrations of Sorbitol and Glucose, as well as the simulations on a few model glass-forming liquids with pinning sites, indicate the versatility of the proposed method, opening possible new avenues to study the physics of glass transition in other molecular liquids.

How dynamic prestress governs the shape of living systems, from the subcellular to tissue scale

Cells and tissues change shape both to carry out their function and during pathology. In most cases, these deformations are driven from within the systems themselves. This is permitted by a range of molecular actors, such as active crosslinkers and ion pumps, whose activity is biologically controlled in space and time. The resulting stresses are propagated within complex and dynamical architectures like networks or cell aggregates. From a mechanical point of view, these effects can be seen as the generation of prestress or prestrain, resulting from either a contractile or growth activity. In this review, we present this concept of prestress and the theoretical tools available to conceptualize the statics and dynamics of living systems. We then describe a range of phenomena where prestress controls shape changes in biopolymer networks (especially the actomyosin cytoskeleton and fibrous tissues) and cellularized tissues. Despite the diversity of scale and organization, we demonstrate that these phenomena stem from a limited number of spatial distributions of prestress, which can be categorized as heterogeneous, anisotropic or differential. We suggest that in addition to growth and contraction, a third type of prestress-topological prestress-can result from active processes altering the microstructure of tissue.

Meis2 controls skeletal formation in the hyoid region

A vertebrate skull is composed of many skeletal elements which display enormous diversity of shapes. Cranial bone formation embodies a multitude of processes, i.e., epithelial-mesenchymal induction, mesenchymal condensation, and endochondral or intramembranous ossification. Molecular pathways determining complex architecture and growth of the cranial skeleton during embryogenesis are poorly understood. Here, we present a model of the hyoid apparatus development in Wnt1-Cre2-induced Meis2 conditional knock-out (cKO) mice. Meis2 cKO embryos develop an aberrant hyoid apparatus—a complete skeletal chain from the base of the neurocranium to lesser horns of the hyoid, resembling extreme human pathologies of the hyoid-larynx region. We examined key stages of hyoid skeletogenesis to obtain a complex image of the hyoid apparatus formation. Lack of Meis2 resulted in ectopic loci of mesenchymal condensations, ectopic cartilage and bone formation, disinhibition of skeletogenesis, and elevated proliferation of cartilage precursors. We presume that all these mechanisms contribute to formation of the aberrant skeletal chain in the hyoid region. Moreover, Meis2 cKO embryos exhibit severely reduced expression of PBX1 and HAND2 in the hyoid region. Altogether, MEIS2 in conjunction with PBX1 and HAND2 affects mesenchymal condensation, specification and proliferation of cartilage precursors to ensure development of the anatomically correct hyoid apparatus.

A platform for automated and label-free monitoring of morphological features and kinetics of spheroid fusion

Spheroids are widely applied as building blocks for biofabrication of living tissues, where they exhibit spontaneous fusion toward an integrated structure upon contact. Tissue fusion is a fundamental biological process, but due to a lack of automated monitoring systems, the in-depth characterization of this process is still limited. Therefore, a quantitative high-throughput platform was developed to semi-automatically select doublet candidates and automatically monitor their fusion kinetics. Spheroids with varying degrees of chondrogenic maturation (days 1, 7, 14, and 21) were produced from two different cell pools, and their fusion kinetics were analyzed via the following steps: (1) by applying a novel spheroid seeding approach, the background noise was decreased due to the removal of cell debris while a sufficient number of doublets were still generated. (2) The doublet candidates were semi-automatically selected, thereby reducing the time and effort spent on manual selection. This was achieved by automatic detection of the microwells and building a random forest classifier, obtaining average accuracies, sensitivities, and precisions ranging from 95.0% to 97.4%, from 51.5% to 92.0%, and from 66.7% to 83.9%, respectively. (3) A software tool was developed to automatically extract morphological features such as the doublet area, roundness, contact length, and intersphere angle. For all data sets, the segmentation procedure obtained average sensitivities and precisions ranging from 96.8% to 98.1% and from 97.7% to 98.8%, respectively. Moreover, the average relative errors for the doublet area and contact length ranged from 1.23% to 2.26% and from 2.30% to 4.66%, respectively, while the average absolute errors for the doublet roundness and intersphere angle ranged from 0.0083 to 0.0135 and from 10.70 to 13.44°, respectively. (4) The data of both cell pools were analyzed, and an exponential model was used to extract kinetic parameters from the time-series data of the doublet roundness. For both cell pools, the technology was able to characterize the fusion rate and quality in an automated manner and allowed us to demonstrate that an increased chondrogenic maturity was linked with a decreased fusion rate. The platform is also applicable to other spheroid types, enabling an increased understanding of tissue fusion. Finally, our approach to study spheroid fusion over time will aid in the design of controlled fabrication of “assembloids” and bottom-up biofabrication of living tissues using spheroids.

Varied solutions to multicellularity: The biophysical and evolutionary consequences of diverse intercellular bonds

The diversity of multicellular organisms is, in large part, due to the fact that multicellularity has independently evolved many times. Nonetheless, multicellular organisms all share a universal biophysical trait: cells are attached to each other. All mechanisms of cellular attachment belong to one of two broad classes; intercellular bonds are either reformable or they are not. Both classes of multicellular assembly are common in nature, having independently evolved dozens of times. In this review, we detail these varied mechanisms as they exist in multicellular organisms. We also discuss the evolutionary implications of different intercellular attachment mechanisms on nascent multicellular organisms. The type of intercellular bond present during early steps in the transition to multicellularity constrains future evolutionary and biophysical dynamics for the lineage, affecting the origin of multicellular life cycles, cell-cell communication, cellular differentiation, and multicellular morphogenesis. The types of intercellular bonds used by multicellular organisms may thus result in some of the most impactful historical constraints on the evolution of multicellularity.

Arrested coalescence of multicellular aggregates

Multicellular aggregates are known to exhibit liquid-like properties. The fusion process of two cell aggregates is commonly studied as the coalescence of two viscous drops. However, tissues are complex materials and can exhibit viscoelastic behaviour. It is known that elastic effects can prevent the complete fusion of two drops, a phenomenon known as arrested coalescence. Here we study this phenomenon in stem cell aggregates and provide a theoretical framework which agrees with the experiments. In addition, agent-based simulations show that active cell fluctuations can control a solid-to-fluid phase transition, revealing that arrested coalescence can be found in the vicinity of an unjamming transition. By analysing the dynamics of the fusion process and combining it with nanoindentation measurements, we obtain the effective viscosity, shear modulus and surface tension of the aggregates. More generally, our work provides a simple, fast and inexpensive method to characterize the mechanical properties of viscoelastic materials.

Mechanical Control of Cell Differentiation: Insights from the Early Embryo

Differentiation is the process by which a cell activates the expression of tissue-specific genes, downregulates the expression of potency markers, and acquires the phenotypic characteristics of its mature fate. The signals that regulate differentiation include biochemical and mechanical factors within the surrounding microenvironment. We describe recent breakthroughs in our understanding of the mechanical control mechanisms that regulate differentiation, with a specific emphasis on the differentiation events that build the early mouse embryo. Engineering approaches to reproducibly mimic the mechanical regulation of differentiation will permit new insights into early development and applications in regenerative medicine. Expected final online publication date for the Annual Review of Biomedical Engineering, Volume 24 is June 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Avalanches during epithelial tissue growth; Uniform Growth and a drosophila eye disc model

Epithelial tissues constitute an exotic type of active matter with non-linear properties reminiscent of amorphous materials. In the context of a proliferating epithelium, modeled by the quasistatic vertex model, we identify novel discrete tissue scale rearrangements, i.e. cellular rearrangement avalanches, which are a form of collective cell movement. During the avalanches, the vast majority of cells retain their neighbors, and the resulting cellular trajectories are radial in the periphery, a vortex in the core. After the onset of these avalanches, the epithelial area grows discontinuously. The avalanches are found to be stochastic, and their strength is correlated with the density of cells in the tissue. Overall, avalanches redistribute accumulated local spatial pressure along the tissue. Furthermore, the distribution of avalanche magnitudes is found to obey a power law, with an exponent consistent with sheer induced avalanches in amorphous materials. To understand the role of avalanches in organ development, we simulate epithelial growth of the Drosophila eye disc during the third instar using a computational model, which includes both chemical and mechanistic signaling. During the third instar, the morphogenetic furrow (MF), a ~10 cell wide wave of apical area constriction propagates through the epithelium. These simulations are used to understand the details of the growth process, the effect of the MF on the growth dynamics on the tissue scale, and to make predictions for experimental observations. The avalanches are found to depend on the strength of the apical constriction of cells in the MF, with a stronger apical constriction leading to less frequent and more pronounced avalanches. The results herein highlight the dependence of simulated tissue growth dynamics on relaxation timescales, and serve as a guide for in vitro experiments.

Searching for structural predictors of plasticity in dense active packings

In amorphous solids subject to shear or thermal excitation, so-called structural indicators have been developed that predict locations of future plasticity or particle rearrangements. An open question is whether similar tools can be used in dense active materials, but a challenge is that under most circumstances, active systems do not possess well-defined solid reference configurations. We develop a computational model for a dense active crowd attracted to a point of interest, which does permit a mechanically stable reference state in the limit of infinitely persistent motion. Previous work on a similar system suggested that the collective motion of crowds could be predicted by inverting a matrix of time-averaged two-particle correlation functions. Seeking a first-principles understanding of this result, we demonstrate that this active matter system maps directly onto a granular packing in the presence of an external potential, and extend an existing structural indicator based on linear response to predict plasticity in the presence of noisy dynamics. We find that the strong pressure gradient necessitated by the directed activity, as well as a self-generated free boundary, strongly impact the linear response of the system. In low-pressure regions the linear-response-based indicator is predictive, but it does not work well in the high-pressure interior of our active packings. Our findings motivate and inform future work that could better formulate structure-dynamics predictions in systems with strong pressure gradients.

Sculpting tissues by phase transitions

Biological systems display a rich phenomenology of states that resemble the physical states of matter - solid, liquid and gas. These phases result from the interactions between the microscopic constituent components - the cells - that manifest in macroscopic properties such as fluidity, rigidity and resistance to changes in shape and volume. Looked at from such a perspective, phase transitions from a rigid to a flowing state or vice versa define much of what happens in many biological processes especially during early development and diseases such as cancer. Additionally, collectively moving confluent cells can also lead to kinematic phase transitions in biological systems similar to multi-particle systems where the particles can interact and show sub-populations characterised by specific velocities. In this Perspective we discuss the similarities and limitations of the analogy between biological and inert physical systems both from theoretical perspective as well as experimental evidence in biological systems. In understanding such transitions, it is crucial to acknowledge that the macroscopic properties of biological materials and their modifications result from the complex interplay between the microscopic properties of cells including growth or death, neighbour interactions and secretion of matrix, phenomena unique to biological systems. Detecting phase transitions in vivo is technically difficult. We present emerging approaches that address this challenge and may guide our understanding of the organization and macroscopic behaviour of biological tissues.

Are cell jamming and unjamming essential in tissue development?

The last decade has seen a surge of evidence supporting the existence of the transition of the multicellular tissue from a collective material phase that is regarded as being jammed to a collective material phase that is regarded as being unjammed. The jammed phase is solid-like and effectively 'frozen', and therefore is associated with tissue homeostasis, rigidity, and mechanical stability. The unjammed phase, by contrast, is fluid-like and effectively 'melted', and therefore is associated with mechanical fluidity, plasticity and malleability that are required in dynamic multicellular processes that sculpt organ microstructure. Such multicellular sculpturing, for example, occurs during embryogenesis, growth and remodeling. Although unjamming and jamming events in the multicellular collective are reminiscent of those that occur in the inert granular collective, such as grain in a hopper that can flow or clog, the analogy is instructive but limited, and the implications for cell biology remain unclear. Here we ask, are the cellular jamming transition and its inverse --the unjamming transition-- mere epiphenomena? That is, are they dispensable downstream events that accompany but neither cause nor quench these core multicellular processes? Drawing from selected examples in developmental biology, here we suggest the hypothesis that, to the contrary, the graded departure from a jammed phase enables controlled degrees of malleability as might be required in developmental dynamics. We further suggest that the coordinated approach to a jammed phase progressively slows those dynamics and ultimately enables long-term mechanical stability as might be required in the mature homeostatic multicellular tissue.

Collective dynamics of gastric cancer cells in fluid

Gastric cancer (GC) is the most common digestive system malignant cancer, and gastric cancer cells (GCC) can migrate in normal solid tissue and lymphatic fluid. Previously, much research has focused on the migration process when the cells are in the solid condition, such as migration through tissue, adhesion, and invasion processes, while little is known about the migration process of GCC in lymphatic fluid. In the current study, we investigate the migration of GCC in a fluid condition in an in vitro environment. We find that the cells diffuse mainly because of their cell viability. Therefore, despite the fact that lymph fluid is almost quiescent, GCCs can migrate around easily. The dynamics of cells also demonstrate a collective glassy dynamic similar to ordinary inactive glassy materials. As density of the cells increases, the movement of the cells becomes slower, and the collective dynamic becomes heterogeneous, which is similar to the dynamically heterogeneous behavior in glassy materials. The results will help us gain a better knowledge of the characteristics of GCC dynamics in the liquid phase which is crucial for the understanding of the mechanism for lymphatic metastasis. This can also potentially help early diagnosis of lymph node metastasis in GC and provide new insights for future clinical treatment.

Paxillin Promotes Breast Tumor Collective Cell Invasion through Maintenance of Adherens Junction Integrity

Distant organ metastasis is linked to poor prognosis during cancer progression. The expression level of the focal adhesion adapter protein paxillin varies among different human cancers, but its role in tumor progression is unclear. Herein, we utilize a newly generated PyMT mammary tumor mouse model with conditional paxillin ablation in breast tumor epithelial cells, combined with in vitro 3D tumor organoids invasion analysis and 2D calcium switch assays, to assess the roles for paxillin in breast tumor cell invasion. Paxillin had little effect on primary tumor initiation and growth but is critical for the formation of distant lung metastasis. In paxillin-depleted 3D tumor organoids, collective cell invasion was substantially perturbed. Two-dimensional cell culture revealed paxillin-dependent stabilization of adherens junctions (AJ). Mechanistically, paxillin is required for AJ assembly through facilitating E-cadherin endocytosis and recycling and HDAC6-mediated microtubule acetylation. Furthermore, Rho GTPase activity analysis and rescue experiments with a RhoA activator or Rac1 inhibitor suggest paxillin is potentially regulating the E-cadherin-dependent junction integrity and contractility through control of the balance of RhoA and Rac1 activities. Together, these data highlight new roles for paxillin in the regulation of cell-cell adhesion and collective tumor cell migration to promote the formation of distance organ metastases. [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text] [Media: see text].

Distribution and propagation of mechanical stress in simulated structurally heterogeneous tissue spheroids

The mechanical microenvironment of cells has been associated with phenotypic changes that cells undergo in three-dimensional spheroid culture formats. Radial asymmetry in mechanical stress - with compression in the core and tension at the periphery - has been analyzed by representing tissue spheroids as homogeneous visco-elastic droplets under surface tension. However, the influence of the granular microstructure of tissue spheroids in the distribution of mechanical stress in tissue spheroids has not been accounted for in a generic manner. Here, we quantify the distribution and propagation of mechanical forces in structurally heterogeneous multicellular assemblies. For this, we perform numerical simulations of a deformable cell model, which represents cells as elastic, contractile shells surrounding a liquid incompressible cytoplasm, interacting by means of non-specific adhesion. Using this model, we show how cell-scale properties such as cortical stiffness, active tension and cell-cell adhesive tension influence the distribution of mechanical stress in simulated tissue spheroids. Next, we characterize the transition at the tissue-scale from a homogeneous liquid droplet to a heterogeneous packed granular assembly.

Mechanics of developmental migration

The ability to migrate is a fundamental property of animal cells which is essential for development, homeostasis and disease progression. Migrating cells sense and respond to biochemical and mechanical cues by rapidly modifying their intrinsic repertoire of signalling molecules and by altering their force generating and transducing machinery. We have a wealth of information about the chemical cues and signalling responses that cells use during migration. Our understanding of the role of forces in cell migration is rapidly evolving but is still best understood in the context of cells migrating in 2D and 3D environments in vitro. Advances in live imaging of developing embryos combined with the use of experimental and theoretical tools to quantify and analyse forces in vivo, has begun to shed light on the role of mechanics in driving embryonic cell migration. In this review, we focus on the recent studies uncovering the physical basis of embryonic cell migration in vivo. We look at the physical basis of the classical steps of cell migration such as protrusion formation and cell body translocation and review the recent research on how these processes work in the complex 3D microenvironment of a developing organism.

Embryonic Tissues as Active Foams

The physical state of embryonic tissues emerges from non-equilibrium, collective interactions among constituent cells. Cellular jamming, rigidity transitions and characteristics of glassy dynamics have all been observed in multicellular systems, but it is unclear how cells control these emergent tissue states and transitions, including tissue fluidization. Combining computational and experimental methods, here we show that tissue fluidization in posterior zebrafish tissues is controlled by the stochastic dynamics of tensions at cell-cell contacts. We develop a computational framework that connects cell behavior to embryonic tissue dynamics, accounting for the presence of extracellular spaces, complex cell shapes and cortical tension dynamics. We predict that tissues are maximally rigid at the structural transition between confluent and non-confluent states, with actively-generated tension fluctuations controlling stress relaxation and tissue fluidization. By directly measuring strain and stress relaxation, as well as the dynamics of cell rearrangements, in elongating posterior zebrafish tissues, we show that tension fluctuations drive active cell rearrangements that fluidize the tissue. These results highlight a key role of non-equilibrium tension dynamics in developmental processes.

Mechanical control of tissue shape and morphogenetic flows during vertebrate body axis elongation

Shaping embryonic tissues into their functional morphologies requires cells to control the physical state of the tissue in space and time. While regional variations in cellular forces or cell proliferation have been typically assumed to be the main physical factors controlling tissue morphogenesis, recent experiments have revealed that spatial variations in the tissue physical (fluid/solid) state play a key role in shaping embryonic tissues. Here we theoretically study how the regional control of fluid and solid tissue states guides morphogenetic flows to shape the extending vertebrate body axis. Our results show that both the existence of a fluid-to-solid tissue transition along the anteroposterior axis and the tissue surface tension determine the shape of the tissue and its ability to elongate unidirectionally, with large tissue tensions preventing unidirectional elongation and promoting blob-like tissue expansions. We predict both the tissue morphogenetic flows and stresses that enable unidirectional axis elongation. Our results show the existence of a sharp transition in the structure of morphogenetic flows, from a flow with no vortices to a flow with two counter-rotating vortices, caused by a transition in the number and location of topological defects in the flow field. Finally, comparing the theoretical predictions to quantitative measurements of both tissue flows and shape during zebrafish body axis elongation, we show that the observed morphogenetic events can be explained by the existence of a fluid-to-solid tissue transition along the anteroposterior axis. These results highlight the role of spatiotemporally-controlled fluid-to-solid transitions in the tissue state as a physical mechanism of embryonic morphogenesis.

Softness, anomalous dynamics, and fractal-like energy landscape in model cell tissues

Epithelial cell tissues have a slow relaxation dynamics resembling that of supercooled liquids. Yet, they also have distinguishing features. These include an extended short-time subdiffusive transient, as observed in some experiments and recent studies of model systems, and a sub-Arrhenius dependence of the relaxation time on temperature, as reported in numerical studies. Here we demonstrate that the anomalous glassy dynamics of epithelial tissues originates from the emergence of a fractal-like energy landscape, particles becoming virtually free to diffuse in specific phase space directions up to a small distance. Furthermore, we clarify that the stiffness of the cells tunes this anomalous behavior, tissues of stiff cells having conventional glassy relaxation dynamics.

Connecting relaxation time to a dynamical length scale in athermal active glass formers

Supercooled liquids display dynamics that are inherently heterogeneous in space. This essentially means that at temperatures below the melting point, particle dynamics in certain regions of the liquid can be orders of magnitude faster than other regions. Often dubbed dynamical heterogeneity, this behavior has fascinated researchers involved in the study of glass transition for over two decades. A fundamentally important question in all glass transition studies is whether one can connect the growing relaxation time to a concomitantly growing length scale. In this paper, we go beyond the realm of ordinary glass forming liquids and study the origin of a growing dynamical length scale ξ in a self-propelled "active" glass former. This length scale, which is constructed using structural correlations, agrees well with the average size of the clusters of slow-moving particles that are formed as the liquid becomes spatially heterogeneous. We further report that the concomitantly growing α-relaxation time exhibits a simple scaling law, τ_{α}∼exp(μξ/T_{eff}), with μ as an effective chemical potential, T_{eff} as the effective temperature, and μξ as the growing free energy barrier for cluster rearrangements. The findings of our study are valid over four decades of persistence times, and hence they could be very useful in understanding the slow dynamics of a generic active liquid such as an active colloidal suspension, or a self-propelled granular medium.

Mechanics of Development

Mechanical forces are integral to development-from the earliest stages of embryogenesis to the construction and differentiation of complex organs. Advances in imaging and biophysical tools have allowed us to delve into the developmental mechanobiology of increasingly complex organs and organisms. Here, we focus on recent work that highlights the diversity and importance of mechanical influences during morphogenesis. Developing tissues experience intrinsic mechanical signals from active forces and changes to tissue mechanical properties as well as extrinsic mechanical signals, including constraint and compression, pressure, and shear forces. Finally, we suggest promising avenues for future work in this rapidly expanding field.

Cell-cell adhesion and 3D matrix confinement determine jamming transitions in breast cancer invasion

Plasticity of cancer invasion and metastasis depends on the ability of cancer cells to switch between collective and single-cell dissemination, controlled by cadherin-mediated cell-cell junctions. In clinical samples, E-cadherin-expressing and -deficient tumours both invade collectively and metastasize equally, implicating additional mechanisms controlling cell-cell cooperation and individualization. Here, using spatially defined organotypic culture, intravital microscopy of mammary tumours in mice and in silico modelling, we identify cell density regulation by three-dimensional tissue boundaries to physically control collective movement irrespective of the composition and stability of cell-cell junctions. Deregulation of adherens junctions by downregulation of E-cadherin and p120-catenin resulted in a transition from coordinated to uncoordinated collective movement along extracellular boundaries, whereas single-cell escape depended on locally free tissue space. These results indicate that cadherins and extracellular matrix confinement cooperate to determine unjamming transitions and stepwise epithelial fluidization towards, ultimately, cell individualization.

Solid-fluid transition and cell sorting in epithelia with junctional tension fluctuations

Tissues transition between solid-like and fluid-like behavior, which has major implications for morphogenesis and disease. These transitions can occur due to changes in the intrinsic shape of constituent cells and cell motility. We consider an alternative mechanism by studying tissues that explore the energy landscape through stochastic dynamics, driven by turnover of junctional molecular motors. To identify the solid-fluid transition, we start with single-component tissues and show that the mean cell-shape index uniquely describes the effective diffusion coefficient of cell movements, which becomes finite at the transition. We generalize our approach to two-component tissues, and explore cell-sorting dynamics both due to differential adhesion and due to differential degree of junctional fluctuations. We recover some known characteristic scaling relations describing the sorting kinetics, and discover some discrepancies from these relations in the case of differential-fluctuations-driven sorting. Finally, we show that differential fluctuations efficiently sort two solid-like tissues with a fluid intercompartmental boundary.

Active glasses

Active glassy matter has recently emerged as a novel class of non-equilibrium soft matter, combining energy-driven, active particle movement with dense and disordered glass-like behavior. Here we review the state-of-the-art in this field from an experimental, numerical, and theoretical perspective. We consider both non-living and living active glassy systems, and discuss how several hallmarks of glassy dynamics (dynamical slowdown, fragility, dynamical heterogeneity, violation of the Stokes-Einstein relation, and aging) are manifested in such materials. We start by reviewing the recent experimental evidence in this area of research, followed by an overview of the main numerical simulation studies and physical theories of active glassy matter. We conclude by outlining several open questions and possible directions for future work.

Glassy dynamics in models of confluent tissue with mitosis and apoptosis

Recent work on particle-based models of tissues has suggested that any finite rate of cell division and cell death is sufficient to fluidize an epithelial tissue. At the same time, experimental evidence has indicated the existence of glassy dynamics in some epithelial layers despite continued cell cycling. To address this discrepancy, we quantify the role of cell birth and death on glassy states in confluent tissues using simulations of an active vertex model that includes cell motility, cell division, and cell death. Our simulation data is consistent with a simple ansatz in which the rate of cell-life cycling and the rate of relaxation of the tissue in the absence of cell cycling contribute independently and additively to the overall rate of cell motion. Specifically, we find that a glass-like regime with caging behavior indicated by subdiffusive cell displacements can be achieved in systems with sufficiently low rates of cell cycling.

Force and Collective Epithelial Activities

Cells apply forces to their surroundings to perform basic biological activities, including division, adhesion, and migration. Similarly, cell populations in epithelial tissues coordinate forces in physiological processes of morphogenesis and repair. These activities are highly regulated to yield the correct development and function of the body. The modification of this order is at the onset of pathological events and malfunctions. Mechanical forces and their translation into biological signals are the focus of an emerging field of research, shaping as a central discipline in the study of life and gathering knowledge at the interface of engineering, physics, biology and medicine. Novel engineering methods are needed to complement the classic instruments developed by molecular biology, physics and medicine. These should enable the measurement of forces at the cellular and multicellular level, and at a temporal and spatial resolution which is fully compatible with the ranges experienced by cells in vivo.

Tissue rheology in embryonic organization

Tissue morphogenesis in multicellular organisms is brought about by spatiotemporal coordination of mechanical and chemical signals. Extensive work on how mechanical forces together with the well-established morphogen signalling pathways can actively shape living tissues has revealed evolutionary conserved mechanochemical features of embryonic development. More recently, attention has been drawn to the description of tissue material properties and how they can influence certain morphogenetic processes. Interestingly, besides the role of tissue material properties in determining how much tissues deform in response to force application, there is increasing theoretical and experimental evidence, suggesting that tissue material properties can abruptly and drastically change in development. These changes resemble phase transitions, pointing at the intriguing possibility that important morphogenetic processes in development, such as symmetry breaking and self-organization, might be mediated by tissue phase transitions. In this review, we summarize recent findings on the regulation and role of tissue material properties in the context of the developing embryo. We posit that abrupt changes of tissue rheological properties may have important implications in maintaining the balance between robustness and adaptability during embryonic development.

Jamming state transition and collective cell migration

Jamming state transition has been used in literature to describe migrating-to-resting cell state transition during collective cell migration without proper rheological confirmation. Yield stress often has been used as an indicator of a jamming state. Yield stress points to the liquid-to-solid state transition, but not a priori to jamming state transition. Various solid states such as elastic solid and viscoelastic solids can be considered in the context of their ability to relax. The relaxation time for (1) an elastic solid tends to zero, (2) Kelvin-Voigt viscoelastic solid is finite, and (3) jamming state tends to infinity.

In order to clarify the meaning of jamming state from the rheological standpoint we formulated the constitutive model of this state based on following conditions (1) migration of the system constituents is much damped such that the diffusion coefficient tends to zero, (2) relaxation time tends to infinity, (3) storage and loss moduli satisfy the condition G^′(ω)/G^"(ω) = const > 1. Jamming state represents the non-linear viscoelastic solid state. The main characteristic of this state is that the system cannot relax.

Jamming state transition of multicellular systems caused by collective cell migration is discussed on a model system such as cell aggregate rounding after uni-axial compression between parallel plates based on the data from the literature. Cell aggregate rounding occurs via successive relaxation cycles. Every cycle corresponds to a different scenario of cell migration. Three scenarios were established depending on the magnitude of mechanical and biochemical perturbations (1) ordered scenario with reduced perturbations corresponds to the case that most of the cells migrate, (2) disordered scenario corresponds to the case that some cell groups migrate while the others (at the same time) stay in resting state (corresponds to medium perturbations), and (3) highly suppressed cell migration under large perturbations corresponds to the viscoelastic solid under jamming state. If cells reach the jamming state in one cycle, they are able to overcome this undesirable state and start migrating again in the next cycle by achieving the first or second scenarios again.

Surface tension determines tissue shape and growth kinetics

The collective self-organization of cells into three-dimensional structures can give rise to emergent physical properties such as fluid behavior. Here, we demonstrate that tissues growing on curved surfaces develop shapes with outer boundaries of constant mean curvature, similar to the energy minimizing forms of liquids wetting a surface. The amount of tissue formed depends on the shape of the substrate, with more tissue being deposited on highly concave surfaces, indicating a mechano-biological feedback mechanism. Inhibiting cell-contractility further revealed that active cellular forces are essential for generating sufficient surface stresses for the liquid-like behavior and growth of the tissue. This suggests that the mechanical signaling between cells and their physical environment, along with the continuous reorganization of cells and matrix is a key principle for the emergence of tissue shape.

Emergence of tissue-like mechanics from fibrous networks confined by close-packed cells

The viscoelasticity of the crosslinked semiflexible polymer networks-such as the internal cytoskeleton and the extracellular matrix-that provide shape and mechanical resistance against deformation is assumed to dominate tissue mechanics. However, the mechanical responses of soft tissues and semiflexible polymer gels differ in many respects. Tissues stiffen in compression but not in extension^1-5, whereas semiflexible polymer networks soften in compression and stiffen in extension^6,7. In shear deformation, semiflexible polymer gels stiffen with increasing strain, but tissues do not^1-8. Here we use multiple experimental systems and a theoretical model to show that a combination of nonlinear polymer network elasticity and particle (cell) inclusions is essential to mimic tissue mechanics that cannot be reproduced by either biopolymer networks or colloidal particle systems alone. Tissue rheology emerges from an interplay between strain-stiffening polymer networks and volume-conserving cells within them. Polymer networks that soften in compression but stiffen in extension can be converted to materials that stiffen in compression but not in extension by including within the network either cells or inert particles to restrict the relaxation modes of the fibrous networks that surround them. Particle inclusions also suppress stiffening in shear deformation; when the particle volume fraction is low, they have little effect on the elasticity of the polymer networks. However, as the particles become more closely packed, the material switches from compression softening to compression stiffening. The emergence of an elastic response in these composite materials has implications for how tissue stiffness is altered in disease and can lead to cellular dysfunction^9-11. Additionally, the findings could be used in the design of biomaterials with physiologically relevant mechanical properties.

Planar AFM macro-probes to study the biomechanical properties of large cells and 3D cell spheroids

The ability to measure mechanical response of cells under applied load is essential for developing more accurate models of cell mechanics and mechanotransduction. Living cells have been mechanically investigated by several approaches. Among them, atomic force microscopy (AFM) is widely used thanks to its high versatility and sensitivity. In the case of large cells or 3D multicellular aggregates, standard AFM probes may not be appropriate to investigate the mechanical properties of the whole biological system. Owing to their size, standard AFM probes can compress only a single somatic cell or part of it. To fill this gap, we have designed and fabricated planar AFM macro-probes compatible with commercial AFM instruments. The probes are constituted of a large flat compression plate, connected to the chip by two flexible arms, whose mechanical characteristics are tuned for specific biological applications. As proof of concept, we have used the macro-probes to measure the viscoelasticity of large spherical biological systems, which have a diameter above 100 μm: human oocytes and 3D cell spheroids. Compression experiments are combined with visual inspection, using a side-view configuration imaging, which allows us to monitor the sample morphology during the compression and to correlate it with the viscoelastic parameters. Our measurements provide a quantitative estimate of the relaxation times of such biological systems, which are discussed in relation to data present in literature. The broad applicability of the AFM macro-probes can be relevant to study the biomechanical features in any biological process involving large soft materials. STATEMENT OF SIGNIFICANCE: The understanding of the role of physical factors in defining cell and tissue functions requires to develop new methods or improve the existing ones to accurately measure the biomechanical properties. AFM is a sensitive and versatile tool to measure the mechanical features from single proteins to single cells. When cells or cell aggregates exceed few tens of microns, AFM suffers from limitations. On these biological systems the control of the contact area and the application of a precise uniform compression becomes crucial. A modification of the standard cantilevers fabrication allowed us obtaining AFM macro-probes, having large planar contact area and spring constant suitable for biological investigations. They were demonstrated valuable to characterize the mechanical properties of large hierarchical biological systems.

Coherent Timescales and Mechanical Structure of Multicellular Aggregates

Multicellular aggregates are an excellent model system to explore the role of tissue biomechanics in specifying multicellular reorganization during embryonic developments and malignant invasion. Tissue-like spheroids, when subjected to a compressive force, are known to exhibit liquid-like behaviors at long timescales (hours), largely because of cell rearrangements that serve to effectively dissipate the applied stress. At short timescales (seconds to minutes), before cell rearrangement, the mechanical behavior is strikingly different. The current work uses shape relaxation to investigate the structural characteristics of aggregates and discovers two coherent timescales: one on the order of seconds, the other tens of seconds. These timescales are universal, conserved across a variety of tested species, and persist despite great differences in other properties such as tissue surface tension and adhesion. A precise mathematical theory is used to correlate the timescales with mechanical properties and reveals that aggregates have a relatively strong envelope and an unusually "soft" interior (weak bulk elastic modulus). This characteristic is peculiar, considering that both layers consist of identical units (cells), but is consistent with the fact that this structure can engender both structural integrity and the flexibility required for remodeling. In addition, tissue surface tension, elastic modulus, and viscosity are proportional to each other. Considering that these tissue-level properties intrinsically derive from cellular-level properties, the proportionalities imply precise coregulation of the latter and in particular of the tension on the cell-medium and cell-cell interfaces.

Effect of liquid flow by pipetting during medium change on deformation of hiPSC aggregates

Introduction

Maintaining the pluripotency and homogeneity of human induced pluripotent stem cells (hiPSCs) requires stable culture conditions with consistent medium change. In this study, we evaluated the performance of medium change by machine vs. medium change performed manually in terms of their impact on the aggregate shape of hiPSCs.

Methods

Aggregates of two hiPSC lines (1383D2 and Tic) were cultured, and the medium change was conducted either manually or with a machine. The populational homogeneity in aggregate shape was determined based on the projected aggregate area for size expansion as well as the circularity for spherical morphology.

Results

In the case of manually performed medium changes, the size of 1383D2 aggregates expanded homogeneously, maintaining its spherical morphology as culture duration increased, while spherical morphology was deformed in Tic aggregates, which had a heterogeneous population in terms of shape. In the case of medium change performed by a machine under a low flux of liquid flow, cultures of both aggregates showed homogeneous populations without deformation, although a high flux led to a heterogeneous population. The heterogeneous population observed in manually performed medium change was caused by the low stability of motion. In addition, time-lapse observation revealed that the Tic aggregates underwent tardive deformation with cellular protrusions from the aggregate surface after medium change with high flux. Histological analysis revealed a spatial heterogeneity of collagen type I inside 1383D2 aggregates, which had a shell structure with strong formation of collagen type I at the periphery of the aggregates, while Tic aggregates did not have a shell structure, suggesting that the shell structure prevented aggregate deformation.

Conclusion

Medium change by a machine led to a homogeneous population of aggregate shapes. Liquid flow caused tardive deformation of aggregates, but the shell structure of collagen type I in aggregates maintained its spherical shape.

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Mechanization of medium change leads to homogeneous shape of iPSC aggregates.

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Tardive change of aggregates was observed.

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Collagen type I distribution in aggregates induces shell structure formation.

Origin of superdiffusive behavior in a class of nonequilibrium systems

Experiments and simulations have established that dynamics in a class of living and abiotic systems that are far from equilibrium exhibit superdiffusive behavior at long times, which in some cases (for example, an evolving tumor) is preceded by slow glass-like dynamics. By using the evolution of a collection of tumor cells, driven by mechanical forces and subject to cell birth and apoptosis, as a case study we show theoretically that on short timescales the mean-square displacement is subdiffusive due to jamming, whereas at long times it is superdiffusive. The results obtained by using a stochastic quantization method, which is needed because of the absence of the fluctuation-dissipation theorem, show that the superdiffusive behavior is universal and impervious to the nature of cell-cell interactions. Surprisingly, the theory also quantitatively accounts for the nontrivial dynamics observed in simulations of a model soap foam characterized by creation and destruction of spherical bubbles, which suggests that the two nonequilibrium systems belong to the same universality class. The theoretical prediction for the superdiffusion exponent is in excellent agreement with simulations for collective motion of tumor cells and dynamics associated with soap bubbles.

Dynamic and static analyses of glass-like properties of three-dimensional tissues

The mechanical properties of tissues are influenced by those of constituent cells in various ways. For instance, it has been theoretically demonstrated that two-dimensional confluent tissues comprising mechanically uniform cells can undergo density-independent rigidity transitions, and analysis of the dynamical behavior of tissues near the critical point revealed that the transitions are geometrically controlled by the so-called cell shape parameter. To investigate whether three-dimensional tissues behave similarly to two-dimensional ones, we herein extend the previously developed model to three dimensions both dynamically and statically, demonstrating that two mechanical states similar to those of glassy materials exist in the three-dimensional case. Scaling analysis is applied to the static model focused from the rearrangement viewpoint. The obtained results suggest that the upper critical dimension of tissues equals two and is therefore the same as that of the jamming transition.

Fluidization-mediated tissue spreading by mitotic cell rounding and non-canonical Wnt signalling

Tissue morphogenesis is driven by mechanical forces that elicit changes in cell size, shape and motion. The extent by which forces deform tissues critically depends on the rheological properties of the recipient tissue. Yet, whether and how dynamic changes in tissue rheology affect tissue morphogenesis and how they are regulated within the developing organism remain unclear. Here, we show that blastoderm spreading at the onset of zebrafish morphogenesis relies on a rapid, pronounced and spatially patterned tissue fluidization. Blastoderm fluidization is temporally controlled by mitotic cell rounding-dependent cell-cell contact disassembly during the last rounds of cell cleavages. Moreover, fluidization is spatially restricted to the central blastoderm by local activation of non-canonical Wnt signalling within the blastoderm margin, increasing cell cohesion and thereby counteracting the effect of mitotic rounding on contact disassembly. Overall, our results identify a fluidity transition mediated by loss of cell cohesion as a critical regulator of embryo morphogenesis.

Dispersible hydrogel force sensors reveal patterns of solid mechanical stress in multicellular spheroid cultures

Understanding how forces orchestrate tissue formation requires technologies to map internal tissue stress at cellular length scales. Here, we develop ultrasoft mechanosensors that visibly deform under less than 10 Pascals of cell-generated stress. By incorporating these mechanosensors into multicellular spheroids, we capture the patterns of internal stress that arise during spheroid formation. We experimentally demonstrate the spontaneous generation of a tensional 'skin', only a few cell layers thick, at the spheroid surface, which correlates with activation of mechanobiological signalling pathways, and balances a compressive stress profile within the tissue. These stresses develop through cell-driven mechanical compaction at the tissue periphery, and suggest that the tissue formation process plays a critically important role in specifying mechanobiological function. The broad applicability of this technique should ultimately provide a quantitative basis to design tissues that leverage the mechanical activity of constituent cells to evolve towards a desired form and function.

Pili mediated intercellular forces shape heterogeneous bacterial microcolonies prior to multicellular differentiation

Microcolonies are aggregates of a few dozen to a few thousand cells exhibited by many bacteria. The formation of microcolonies is a crucial step towards the formation of more mature bacterial communities known as biofilms, but also marks a significant change in bacterial physiology. Within a microcolony, bacteria forgo a single cell lifestyle for a communal lifestyle hallmarked by high cell density and physical interactions between cells potentially altering their behaviour. It is thus crucial to understand how initially identical single cells start to behave differently while assembling in these tight communities. Here we show that cells in the microcolonies formed by the human pathogen Neisseria gonorrhoeae (Ng) present differential motility behaviors within an hour upon colony formation. Observation of merging microcolonies and tracking of single cells within microcolonies reveal a heterogeneous motility behavior: cells close to the surface of the microcolony exhibit a much higher motility compared to cells towards the center. Numerical simulations of a biophysical model for the microcolonies at the single cell level suggest that the emergence of differential behavior within a multicellular microcolony of otherwise identical cells is of mechanical origin. It could suggest a route toward further bacterial differentiation and ultimately mature biofilms.

A fluid-to-solid jamming transition underlies vertebrate body axis elongation

Just as in clay molding or glass blowing, sculpting biological structures requires the constituent material to locally flow like a fluid while maintaining overall mechanical integrity like a solid. Disordered soft materials, such as foams, emulsions and colloidal suspensions, switch from fluid-like to solid-like behaviors at a jamming transition^1–4. Similarly, cell collectives have been shown to display glassy dynamics in 2D and 3D^5,6 and jamming in cultured epithelial monolayers^7,8, behaviors recently predicted theoretically^9–11 and proposed to influence asthma pathobiology⁸ and tumor progression¹². However, it is unknown if these seemingly universal behaviors occur in vivo and, specifically, if they play any functional role during embryonic morphogenesis. By combining direct in vivo measurements of tissue mechanics with analysis of cellular dynamics, we show that during vertebrate body axis elongation, posterior tissues undergo a jamming transition from a fluid-like behavior at the extending end, the mesodermal progenitor zone (MPZ), to a solid-like behavior in the presomitic mesoderm (PSM). We uncover an anteroposterior, N-cadherin-dependent gradient in yield stress that provides increasing mechanical integrity to the PSM, consistent with the tissue transiting from a wetter to a dryer foam-like architecture. Our results show that cell-scale stresses fluctuate rapidly (~1 min), enabling cell rearrangements and effectively ‘melting’ the tissue at the growing end. Persistent (>0.5 h) stresses at supracellular scales, rather than cell-scale stresses, guide morphogenetic flows in fluid-like tissue regions. Unidirectional axis extension is sustained by the reported PSM rigidification, which mechanically supports posterior, fluid-like tissues during remodeling prior to their maturation. The spatiotemporal control of fluid-like and solid-like tissue states may represent a generic physical mechanism of embryonic morphogenesis.

Fluidization of epithelial sheets by active cell rearrangements

We theoretically explore fluidization of epithelial tissues by active T1 neighbor exchanges. We show that the geometry of cell-cell junctions encodes important information about the local features of the energy landscape, which we support by an elastic theory of T1 transformations. Using a 3D vertex model, we show that the degree of active noise driving forced cell rearrangements governs the stress-relaxation timescale of the tissue. We study tissue response to in-plane shear at different timescales. At short time, the tissue behaves as a solid, whereas its long-time fluid behavior can be associated with an effective viscosity which scales with the rate of active T1 transformations. Furthermore, we develop a coarse-grained theory, where we treat the tissue as an active fluid and confirm the results of the vertex model. The impact of cell rearrangements on tissue shape is illustrated by studying axial compression of an epithelial tube.

Hydrodynamics of shape-driven rigidity transitions in motile tissues

In biological tissues, it is now well-understood that mechanical cues are a powerful mechanism for pattern regulation. While much work has focused on interactions between cells and external substrates, recent experiments suggest that cell polarization and motility might be governed by the internal shear stiffness of nearby tissue, deemed "plithotaxis". Meanwhile, other work has demonstrated that there is a direct relationship between cell shapes and tissue shear modulus in confluent tissues. Joining these two ideas, we develop a hydrodynamic model that couples cell shape, and therefore tissue stiffness, to cell motility and polarization. Using linear stability analysis and numerical simulations, we find that tissue behavior can be tuned between largely homogeneous states and patterned states such as asters, controlled by a composite "morphotaxis" parameter that encapsulates the nature of the coupling between shape and polarization. The control parameter is in principle experimentally accessible, and depends both on whether a cell tends to move in the direction of lower or higher shear modulus, and whether sinks or sources of polarization tend to fluidize the system.

Tracer Transport Probes Relaxation and Structure of Attractive and Repulsive Glassy Liquids

Dynamic coupling of small penetrants to slow, cooperative relaxations within crowded cells, supercooled liquids, and polymer matrices has broad consequences for applications ranging from drug delivery to nanocomposite processing. Interactions between the constituents of these and other disordered media alter the cooperative relaxations, but their effect on penetrant dynamics remains incompletely understood. We use molecular dynamics simulations to show that the motions of hard-sphere tracer particles probe differences in local structure and cooperative relaxation processes in attractive and repulsive glassy liquid matrices with equal bulk packing fractions and long-time diffusivities. Coupling of the tracer dynamics to collective relaxations in each matrix affects the shape of tracer trajectories, which are fractal within the repulsive matrix and more compact in the attractive. These results reveal that the structure of relaxations controls penetrant transport and dispersion in cooperatively relaxing systems and provide insight into dynamical heterogeneity within glassy liquids.

No unjamming transition in a Voronoi model of biological tissue

Vertex models are a popular approach to simulating the mechanical and dynamical properties of dense biological tissues, describing the tissue as a network of polygons. Recently a class of two-dimensional vertex models was shown to exhibit a disordered rigidity transition controlled by the preferred cellular geometry, which was subsequently echoed by experimental findings. An attractive variant of these models uses a Voronoi tessellation to describe the cells, which reduces the number of degrees of freedom as compared the original vertex model. The Voronoi model was also endowed with a non-equilibrium model of cellular motility, leading to rich, glassy behavior. This glassy behavior was suggested to be inextricably linked to an underlying jamming transition. We test this conjecture, exploring the low-effective-temperature limit of the 2D Voronoi model by studying cell trajectories from detailed dynamical simulations in combination with rigidity measurements of energy-minimized disordered cell configurations. We find that the zero-temperature limit of this model has no unjamming transition. We show that this absence of an unjamming transition is intimately linked to the marginality of the model, i.e. the fact that the constraints imposed on cell areas and perimeters precisely balance the number of degrees of freedom in the model. Our work suggests that constraint counting arguments are useful to understand rigidity in a broad class of models of dense biological tissues.

Why we need mechanics to understand animal regeneration

Mechanical forces are an important contributor to cell fate specification and cell migration during embryonic development in animals. Similarities between embryogenesis and regeneration, particularly with regards to pattern formation and large-scale tissue movements, suggest similarly important roles for physical forces during regeneration. While the influence of the mechanical environment on stem cell differentiation in vitro is being actively exploited in the fields of tissue engineering and regenerative medicine, comparatively little is known about the role of stresses and strains acting during animal regeneration. In this review, we summarize published work on the role of physical principles and mechanical forces in animal regeneration. Novel experimental techniques aimed at addressing the role of mechanics in embryogenesis have greatly enhanced our understanding at scales from the subcellular to the macroscopic - we believe the time is ripe for the field of regeneration to similarly leverage the tools of the mechanobiological research community.