Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes, adopting a shape named 'scutoid' that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here, we use live imaging of the sea star embryo coupled with deep learning-based segmentation to dissect the relative contributions of cell density, tissue compaction and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing immediately after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Short-range correlation of stress chains near solid-to-liquid transition in active monolayers

Using a three-dimensional model of cell monolayers, we study the spatial organization of active stress chains as the monolayer transitions from a solid to a liquid state. The critical exponents that characterize this transition map the isotropic stress percolation onto the two-dimensional random percolation universality class, suggesting short-range stress correlations near this transition. This mapping is achieved via two distinct, independent pathways: (i) cell-cell adhesion and (ii) active traction forces. We unify our findings by linking the nature of this transition to high-stress fluctuations, distinctly linked to each pathway. The results elevate the importance of the transmission of mechanical information in dense active matter and provide a new context for understanding the non-equilibrium statistical physics of phase transition in active systems.

Penetrating the ultra-tough yeast cell wall with finite element analysis model-aided design of microtools

Microinjecting yeast cells has been challenging for decades with no significant breakthrough due to the ultra-tough cell wall and low stiffness of the traditional injector tip at the micro-scale. Penetrating this protection wall is the key step for artificially bringing foreign substance into the yeast. In this paper, a yeast cell model was built by using finite element analysis (FEA) method to analyze the penetrating process. The key parameters of the yeast cell wall in the model (the Young's modulus, the shear modulus, and the Lame constant) were calibrated according to a general nanoindentation experiment. Then by employing the calibrated model, the injection parameters were optimized to minimize the cell damage (the maximum cell deformation at the critical stress of the cell wall). Key guidelines were suggested for penetrating the cell wall during microinjection.

Mechanical state transitions in the regulation of tissue form and function

From embryonic development, postnatal growth and adult homeostasis to reparative and disease states, cells and tissues undergo constant changes in genome activity, cell fate, proliferation, movement, metabolism and growth. Importantly, these biological state transitions are coupled to changes in the mechanical and material properties of cells and tissues, termed mechanical state transitions. These mechanical states share features with physical states of matter, liquids and solids. Tissues can switch between mechanical states by changing behavioural dynamics or connectivity between cells. Conversely, these changes in tissue mechanical properties are known to control cell and tissue function, most importantly the ability of cells to move or tissues to deform. Thus, tissue mechanical state transitions are implicated in transmitting information across biological length and time scales, especially during processes of early development, wound healing and diseases such as cancer. This Review will focus on the biological basis of tissue-scale mechanical state transitions, how they emerge from molecular and cellular interactions, and their roles in organismal development, homeostasis, regeneration and disease.

Adherens junctions as molecular regulators of emergent tissue mechanics

Tissue and organ development during embryogenesis relies on the collective and coordinated action of many cells. Recent studies have revealed that tissue material properties, including transitions between fluid and solid tissue states, are controlled in space and time to shape embryonic structures and regulate cell behaviours. Although the collective cellular flows that sculpt tissues are guided by tissue-level physical changes, these ultimately emerge from cellular-level and subcellular-level molecular mechanisms. Adherens junctions are key subcellular structures, built from clusters of classical cadherin receptors. They mediate physical interactions between cells and connect biochemical signalling to the physical characteristics of cell contacts, hence playing a fundamental role in tissue morphogenesis. In this Review, we take advantage of the results of recent, quantitative measurements of tissue mechanics to relate the molecular and cellular characteristics of adherens junctions, including adhesion strength, tension and dynamics, to the emergent physical state of embryonic tissues. We focus on systems in which cell-cell interactions are the primary contributor to morphogenesis, without significant contribution from cell-matrix interactions. We suggest that emergent tissue mechanics is an important direction for future research, bridging cell biology, developmental biology and mechanobiology to provide a holistic understanding of morphogenesis in health and disease.

Collective effects of cell cleavage dynamics

A conserved process of early embryonic development in metazoans is the reductive cell divisions following oocyte fertilization, termed cell cleavages. Cell cleavage cycles usually start synchronously, lengthen differentially between the embryonic cells becoming asynchronous, and cease before major morphogenetic events, such as germ layer formation and gastrulation. Despite exhibiting species-specific characteristics, the regulation of cell cleavage dynamics comes down to common controllers acting mostly at the single cell/nucleus level, such as nucleus-to-cytoplasmic ratio and zygotic genome activation. Remarkably, recent work has linked cell cleavage dynamics to the emergence of collective behavior during embryogenesis, including pattern formation and changes in embryo-scale mechanics, raising the question how single-cell controllers coordinate embryo-scale processes. In this review, we summarize studies across species where an association between cell cleavages and collective behavior was made, discuss the underlying mechanisms, and propose that cell-to-cell variability in cell cleavage dynamics can serve as a mechanism of long-range coordination in developing embryos.

Demixing in Binary Mixtures with Differential Diffusivity at High Density

Spontaneous phase separation, or demixing, is important in biological phenomena such as cell sorting. In particle-based models, an open question is whether differences in diffusivity can drive such demixing. While differential-diffusivity-induced phase separation occurs in mixtures with a packing fraction up to 0.7 [S. N. Weber et al. Binary mixtures of particles with different diffusivities demix, Phys. Rev. Lett. 116, 058301 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.058301], here we investigate whether demixing persists at even higher densities relevant for cells. For particle packing fractions between 0.7 and 1.0 the system demixes, but at packing fractions above unity the system remains mixed, exposing re-entrant behavior in the phase diagram that occurs when phase separation can no longer drive a change in entropy production at high densities. We also find that a confluent Voronoi model for tissues does not phase separate, consistent with particle-based simulations.

A Hierarchical Mechanotransduction System: From Macro to Micro

Mechanotransduction is a strictly regulated process whereby mechanical stimuli, including mechanical forces and properties, are sensed and translated into biochemical signals. Increasing data demonstrate that mechanotransduction is crucial for regulating macroscopic and microscopic dynamics and functionalities. However, the actions and mechanisms of mechanotransduction across multiple hierarchies, from molecules, subcellular structures, cells, tissues/organs, to the whole-body level, have not been yet comprehensively documented. Herein, the biological roles and operational mechanisms of mechanotransduction from macro to micro are revisited, with a focus on the orchestrations across diverse hierarchies. The implications, applications, and challenges of mechanotransduction in human diseases are also summarized and discussed. Together, this knowledge from a hierarchical perspective has the potential to refresh insights into mechanotransduction regulation and disease pathogenesis and therapy, and ultimately revolutionize the prevention, diagnosis, and treatment of human diseases.

Signatures of structural disorder in developing epithelial tissues

Epithelial cells generate functional tissues in developing embryos through collective movements and shape changes. In some morphogenetic events, a tissue dramatically reorganizes its internal structure - often generating high degrees of structural disorder - to accomplish changes in tissue shape. However, the origins of structural disorder in epithelia and what roles it might play in morphogenesis are poorly understood. We study this question in the Drosophila germband epithelium, which undergoes dramatic changes in internal structure as cell rearrangements drive elongation of the embryo body axis. Using two order parameters that quantify volumetric and shear disorder, we show that structural disorder increases during body axis elongation and is strongly linked with specific developmental processes. Both disorder metrics begin to increase around the onset of axis elongation, but then plateau at values that are maintained throughout the process. Notably, the disorder plateau values for volumetric disorder are similar to those for random cell packings, suggesting this may reflect a limit on tissue behavior. In mutant embryos with disrupted external stresses from the ventral furrow, both disorder metrics reach wild-type maximum disorder values with a delay, correlating with delays in cell rearrangements. In contrast, in mutants with disrupted internal stresses and cell rearrangements, volumetric disorder is reduced compared to wild type, whereas shear disorder depends on specific external stress patterns. Together, these findings demonstrate that internal and external stresses both contribute to epithelial tissue disorder and suggest that the maximum values of disorder in a developing tissue reflect physical or biological limits on morphogenesis.

Local and global changes in cell density induce reorganisation of 3D packing in a proliferating epithelium

Tissue morphogenesis is intimately linked to the changes in shape and organisation of individual cells. In curved epithelia, cells can intercalate along their own apicobasal axes adopting a shape named "scutoid" that allows energy minimization in the tissue. Although several geometric and biophysical factors have been associated with this 3D reorganisation, the dynamic changes underlying scutoid formation in 3D epithelial packing remain poorly understood. Here we use live-imaging of the sea star embryo coupled with deep learning-based segmentation, to dissect the relative contributions of cell density, tissue compaction, and cell proliferation on epithelial architecture. We find that tissue compaction, which naturally occurs in the embryo, is necessary for the appearance of scutoids. Physical compression experiments identify cell density as the factor promoting scutoid formation at a global level. Finally, the comparison of the developing embryo with computational models indicates that the increase in the proportion of scutoids is directly associated with cell divisions. Our results suggest that apico-basal intercalations appearing just after mitosis may help accommodate the new cells within the tissue. We propose that proliferation in a compact epithelium induces 3D cell rearrangements during development.

Creative processes during vertebrate organ morphogenesis: Biophysical self-organization at the supracellular scale

Here, we review recent developments in the literature that provide insight into self-organization at supracellular scales in vertebrate organ morphogenesis. We briefly present a historical and conceptual analysis of the term "self-organization." Based on this analysis, we suggest that self-organizing processes, at their root, possess a form of causal relationship, reciprocal causality, that is markedly distinct from linear causal chains. We survey the extent to which reciprocal causality can be used to interpret or clarify supracellular studies in development and disease. Finally, we explore how reciprocal causality can exist across length-scales, identifying situations where multiple scales require simultaneous analysis.

Pulling the strings on solid-to-liquid phase transitions in cell collectives

Cell collectives must dynamically adapt to different biological contexts. For instance, in homeostatic conditions, epithelia must establish a barrier between body compartments and resist external stresses, while during development, wound healing or cancer invasion, these tissues undergo extensive remodeling. Using analogies from inert, passive materials, changes in cellular density, shape, rearrangements and/or migration were shown to result in collective transitions between solid and fluid states. However, what biological mechanisms govern these transitions remains an open question. In particular, the upstream signaling pathways and molecular effectors controlling the key physical axes determining tissue rheology and dynamics remain poorly understood. In this perspective, we focus on emerging evidence identifying the first biological signals determining the collective state of living tissues, with an emphasis on how these mechanisms are exploited for functionality across biological contexts.

Free volume theory explains the unusual behavior of viscosity in a non-confluent tissue during morphogenesis

A recent experiment on zebrafish blastoderm morphogenesis showed that the viscosity (η) of a non-confluent embryonic tissue grows sharply until a critical cell packing fraction (ϕS). The increase in η up to ϕS is similar to the behavior observed in several glass-forming materials, which suggests that the cell dynamics is sluggish or glass-like. Surprisingly, η is a constant above ϕS. To determine the mechanism of this unusual dependence of η on ϕ, we performed extensive simulations using an agent-based model of a dense non-confluent two-dimensional tissue. We show that polydispersity in the cell size, and the propensity of the cells to deform, results in the saturation of the available free area per cell beyond a critical packing fraction. Saturation in the free space not only explains the viscosity plateau above ϕS but also provides a relationship between equilibrium geometrical packing to the dramatic increase in the relaxation dynamics.

Schramm-Loewner Evolution in 2D Rigidity Percolation

Amorphous solids may resist external deformation such as shear or compression, while they do not present any long-range translational order or symmetry at the microscopic scale. Yet, it was recently discovered that, when they become rigid, such materials acquire a high degree of symmetry hidden in the disorder fluctuations: their microstructure becomes statistically conformally invariant. In this Letter, we exploit this finding to characterize the universality class of central-force rigidity percolation (RP), using Schramm-Loewner evolution (SLE) theory. We provide numerical evidence that the interfaces of the mechanically stable structures (rigid clusters), at the rigidification transition, are consistently described by SLE_{κ}, showing that this powerful framework can be applied to a mechanical percolation transition. Using well-known relations between different SLE observables and the universal diffusion constant κ, we obtain the estimation κ∼2.9 for central-force RP. This value is consistent, through relations coming from conformal field theory, with previously measured values for the clusters' fractal dimension D_{f} and correlation length exponent ν, providing new, nontrivial relations between critical exponents for RP. These findings open the way to a fine understanding of the microstructure in other important classes of rigidity and jamming transitions.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster . During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrinkage of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Significance Statement

During embryogenesis, cells in tissues can undergo significant shape changes. Many epithelial tissues fluidize, i.e. cells exchange neighbors, when the average cell aspect ratio increases above a threshold value, consistent with the standard vertex model. During dorsal closure in Drosophila melanogaster , however, the amnioserosa tissue remains solid even as the average cell aspect ratio increases well above threshold. We introduce perimeter polydispersity and allow the preferred cell perimeters, usually held fixed in vertex models, to decrease linearly with time as seen experimentally. With these extensions to the standard vertex model, we capture experimental observations quantitatively. Our results demonstrate that vertex models can describe the behavior of the amnioserosa in dorsal closure by allowing normally fixed parameters to vary with time.

Minimal vertex model explains how the amnioserosa avoids fluidization during Drosophila dorsal closure

Dorsal closure is a process that occurs during embryogenesis of Drosophila melanogaster. During dorsal closure, the amnioserosa (AS), a one-cell thick epithelial tissue that fills the dorsal opening, shrinks as the lateral epidermis sheets converge and eventually merge. During this process, the aspect ratio of amnioserosa cells increases markedly. The standard 2-dimensional vertex model, which successfully describes tissue sheet mechanics in multiple contexts, would in this case predict that the tissue should fluidize via cell neighbor changes. Surprisingly, however, the amnioserosa remains an elastic solid with no such events. We here present a minimal extension to the vertex model that explains how the amnioserosa can achieve this unexpected behavior. We show that continuous shrink-age of the preferred cell perimeter and cell perimeter polydispersity lead to the retention of the solid state of the amnioserosa. Our model accurately captures measured cell shape and orientation changes and predicts non-monotonic junction tension that we confirm with laser ablation experiments.

Connecting theory and experiment in cell and tissue mechanics

Understanding complex living systems, which are fundamentally constrained by physical phenomena, requires combining experimental data with theoretical physical and mathematical models. To develop such models, collaborations between experimental cell biologists and theoreticians are increasingly important but these two groups often face challenges achieving mutual understanding. To help navigate these challenges, this Perspective discusses different modelling approaches, including bottom-up hypothesis-driven and top-down data-driven models, and highlights their strengths and applications. Using cell mechanics as an example, we explore the integration of specific physical models with experimental data from the molecular, cellular and tissue level up to multiscale input. We also emphasize the importance of constraining model complexity and outline strategies for crosstalk between experimental design and model development. Furthermore, we highlight how physical models can provide conceptual insights and produce unifying and generalizable frameworks for biological phenomena. Overall, this Perspective aims to promote fruitful collaborations that advance our understanding of complex biological systems.

Bridging the gap between collective motility and epithelial-mesenchymal transitions through the active finite voronoi model

We introduce an active version of the recently proposed finite Voronoi model of epithelial tissue. The resultant Active Finite Voronoi (AFV) model enables the study of both confluent and non-confluent geometries and transitions between them, in the presence of active cells. Our study identifies six distinct phases, characterized by aggregation-segregation, dynamical jamming-unjamming, and epithelial-mesenchymal transitions (EMT), thereby extending the behavior beyond that observed in previously studied vertex-based models. The AFV model with rich phase diagram provides a cohesive framework that unifies the well-observed progression to collective motility via unjamming with the intricate dynamics enabled by EMT. This approach should prove useful for challenges in developmental biology systems as well as the complex context of cancer metastasis. The simulation code is also provided.

Optimal mechanical interactions direct multicellular network formation on elastic substrates

Cells self-organize into functional, ordered structures during tissue morphogenesis, a process that is evocative of colloidal self-assembly into engineered soft materials. Understanding how intercellular mechanical interactions may drive the formation of ordered and functional multicellular structures is important in developmental biology and tissue engineering. Here, by combining an agent-based model for contractile cells on elastic substrates with endothelial cell culture experiments, we show that substrate deformation-mediated mechanical interactions between cells can cluster and align them into branched networks. Motivated by the structure and function of vasculogenic networks, we predict how measures of network connectivity like percolation probability and fractal dimension as well as local morphological features including junctions, branches, and rings depend on cell contractility and density and on substrate elastic properties including stiffness and compressibility. We predict and confirm with experiments that cell network formation is substrate stiffness dependent, being optimal at intermediate stiffness. We also show the agreement between experimental data and predicted cell cluster types by mapping a combined phase diagram in cell density substrate stiffness. Overall, we show that long-range, mechanical interactions provide an optimal and general strategy for multicellular self-organization, leading to more robust and efficient realizations of space-spanning networks than through just local intercellular interactions.

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.

Patterning and folding of intestinal villi by active mesenchymal dewetting

Tissue folding generates structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, the numerous finger-like protrusions that are essential for nutrient absorption. However, the molecular and mechanical mechanisms driving the initiation and morphogenesis of villi remain a matter of debate. Here, we identify an active mechanical mechanism that simultaneously patterns and folds intestinal villi. We find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. At the cell-level, this occurs through a process dependent upon matrix metalloproteinase-mediated tissue fluidization and altered cell-ECM adhesion. By combining computational models with in vivo experiments, we reveal these cellular features manifest at the tissue-level as differences in interfacial tensions that promote mesenchymal aggregation and interface bending through a process analogous to the active de-wetting of a thin liquid film.

Effective mechanical potential of cell-cell interaction explains three-dimensional morphologies during early embryogenesis

Mechanical forces are critical for the emergence of diverse three-dimensional morphologies of multicellular systems. However, it remains unclear what kind of mechanical parameters at cellular level substantially contribute to tissue morphologies. This is largely due to technical limitations of live measurements of cellular forces. Here we developed a framework for inferring and modeling mechanical forces of cell-cell interactions. First, by analogy to coarse-grained models in molecular and colloidal sciences, we approximated cells as particles, where mean forces (i.e. effective forces) of pairwise cell-cell interactions are considered. Then, the forces were statistically inferred by fitting the mathematical model to cell tracking data. This method was validated by using synthetic cell tracking data resembling various in vivo situations. Application of our method to the cells in the early embryos of mice and the nematode Caenorhabditis elegans revealed that cell-cell interaction forces can be written as a pairwise potential energy in a manner dependent on cell-cell distances. Importantly, the profiles of the pairwise potentials were quantitatively different among species and embryonic stages, and the quantitative differences correctly described the differences of their morphological features such as spherical vs. distorted cell aggregates, and tightly vs. non-tightly assembled aggregates. We conclude that the effective pairwise potential of cell-cell interactions is a live measurable parameter whose quantitative differences can be a parameter describing three-dimensional tissue morphologies.

Jamming and unusual charge density fluctuations of strange metals

The strange metallic regime across a number of high-temperature superconducting materials presents numerous challenges to the classic theory of Fermi liquid metals. Recent measurements of the dynamical charge response of strange metals, including optimally doped cuprates, have revealed a broad, featureless continuum of excitations, extending over much of the Brillouin zone. The collective density oscillations of this strange metal decay into the continuum in a manner that is at odds with the expectations of Fermi liquid theory. Inspired by these observations, we investigate the phenomenology of bosonic collective modes and the particle-hole excitations in a class of strange metals by making an analogy to the phonons of classical lattices falling apart across an unconventional jamming-like transition associated with the onset of rigidity. By making comparisons to the experimentally measured dynamical response functions, we reproduce many of the qualitative features using the above framework. We conjecture that the dynamics of electronic charge density over an intermediate range of energy scales in a class of strongly correlated metals can be at the brink of a jamming-like transition.

Evidences of Conformal Invariance in 2D Rigidity Percolation

The rigidity transition occurs when, as the density of microscopic components is increased, a disordered medium becomes able to transmit and ensure macroscopic mechanical stability, owing to the appearance of a space-spanning rigid connected component, or cluster. As a second-order phase transition it exhibits a scale invariant critical point, at which the rigid clusters are random fractals. We show, using numerical analysis, that these clusters are also conformally invariant, and we use conformal field theory to predict the form of universal finite-size effects. Furthermore, although connectivity and rigidity percolation are usually thought to be of fundamentally different natures, we provide evidence of unexpected similarities between the statistical properties of their random clusters at criticality. Our work opens a new research avenue through the application of the powerful 2D conformal field theory tools to understand the critical behavior of a wide range of physical and biological materials exhibiting such a mechanical transition.

Sculpting with stiffness: rigidity as a regulator of morphogenesis

From a physical perspective, morphogenesis of tissues results from interplay between their material properties and the mechanical forces exerted on them. The importance of mechanical forces in influencing cell behaviour is widely recognised, whereas the importance of tissue material properties in vivo, like stiffness, has only begun to receive attention in recent years. In this mini-review, we highlight key themes and concepts that have emerged related to how tissue stiffness, a fundamental material property, guides various morphogenetic processes in living organisms.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Self-organized collective cell behaviors as design principles for synthetic developmental biology

Over the past two decades, molecular cell biology has graduated from a mostly analytic science to one with substantial synthetic capability. This success is built on a deep understanding of the structure and function of biomolecules and molecular mechanisms. For synthetic biology to achieve similar success at the scale of tissues and organs, an equally deep understanding of the principles of development is required. Here, we review some of the central concepts and recent progress in tissue patterning, morphogenesis and collective cell migration and discuss their value for synthetic developmental biology, emphasizing in particular the power of (guided) self-organization and the role of theoretical advances in making developmental insights applicable in synthesis.

Cell state transitions: catch them if you can

The Company of Biologists' 2022 workshop on 'Cell State Transitions: Approaches, Experimental Systems and Models' brought together an international and interdisciplinary team of investigators spanning the fields of cell and developmental biology, stem cell biology, physics, mathematics and engineering to tackle the question of how cells precisely navigate between distinct identities and do so in a dynamic manner. This second edition of the workshop was organized after a successful virtual workshop on the same topic that took place in 2021.

A hydraulic feedback loop between mesendoderm cell migration and interstitial fluid relocalization promotes embryonic axis formation in zebrafish

Interstitial fluid (IF) accumulation between embryonic cells is thought to be important for embryo patterning and morphogenesis. Here, we identify a positive mechanical feedback loop between cell migration and IF relocalization and find that it promotes embryonic axis formation during zebrafish gastrulation. We show that anterior axial mesendoderm (prechordal plate [ppl]) cells, moving in between the yolk cell and deep cell tissue to extend the embryonic axis, compress the overlying deep cell layer, thereby causing IF to flow from the deep cell layer to the boundary between the yolk cell and the deep cell layer, directly ahead of the advancing ppl. This IF relocalization, in turn, facilitates ppl cell protrusion formation and migration by opening up the space into which the ppl moves and, thereby, the ability of the ppl to trigger IF relocalization by pushing against the overlying deep cell layer. Thus, embryonic axis formation relies on a hydraulic feedback loop between cell migration and IF relocalization.

Collective chemotaxis in a Voronoi model for confluent clusters

Collective chemotaxis, where single cells cannot climb a biochemical signaling gradient but clusters of cells can, has been observed in different biological contexts, including confluent tissues where there are no gaps or overlaps between cells. Although particle-based models have been developed that predict important features of collective chemotaxis, the mechanisms in those models depend on particle overlaps, and so it remains unclear if they can explain behavior in confluent systems. Here, we develop an open-source code that couples a two-dimensional Voronoi simulation for confluent cell mechanics to a dynamic chemical signal that can diffuse, advect, and/or degrade and use the code to study potential mechanisms for collective chemotaxis in cellular monolayers. We first study the impact of advection on collective chemotaxis and delineate a regime where advective terms are important. Next, we investigate two possible chemotactic mechanisms, contact inhibition of locomotion and heterotypic interfacial tension, and demonstrate that both can drive collective chemotaxis in certain parameter regimes. We further demonstrate that the scaling behavior of cluster motion is well captured by simple analytic theories.

aPKC regulates apical constriction to prevent tissue rupture in the Drosophila follicular epithelium

Apical-basal polarity is an essential epithelial trait controlled by the evolutionarily conserved PAR-aPKC polarity network. Dysregulation of polarity proteins disrupts tissue organization during development and in disease, but the underlying mechanisms are unclear due to the broad implications of polarity loss. Here, we uncover how Drosophila aPKC maintains epithelial architecture by directly observing tissue disorganization after fast optogenetic inactivation in living adult flies and ovaries cultured ex vivo. We show that fast aPKC perturbation in the proliferative follicular epithelium produces large epithelial gaps that result from increased apical constriction, rather than loss of apical-basal polarity. Accordingly, we can modulate the incidence of epithelial gaps by increasing and decreasing actomyosin-driven contractility. We traced the origin of these large epithelial gaps to tissue rupture next to dividing cells. Live imaging shows that aPKC perturbation induces apical constriction in non-mitotic cells within minutes, producing pulling forces that ultimately detach dividing and neighboring cells. We further demonstrate that epithelial rupture requires a global increase of apical constriction, as it is prevented by the presence of non-constricting cells. Conversely, a global induction of apical tension through light-induced recruitment of RhoGEF2 to the apical side is sufficient to produce tissue rupture. Hence, our work reveals that the roles of aPKC in polarity and actomyosin regulation are separable and provides the first in vivo evidence that excessive tissue stress can break the epithelial barrier during proliferation.

Single-molecule tracking of Nodal and Lefty in live zebrafish embryos supports hindered diffusion model

The hindered diffusion model postulates that the movement of a signaling molecule through an embryo is affected by tissue geometry and binding-mediated hindrance, but these effects have not been directly demonstrated in vivo. Here, we visualize extracellular movement and binding of individual molecules of the activator-inhibitor signaling pair Nodal and Lefty in live developing zebrafish embryos using reflected light-sheet microscopy. We observe that diffusion coefficients of molecules are high in extracellular cavities, whereas mobility is reduced and bound fractions are high within cell-cell interfaces. Counterintuitively, molecules nevertheless accumulate in cavities, which we attribute to the geometry of the extracellular space by agent-based simulations. We further find that Nodal has a larger bound fraction than Lefty and shows a binding time of tens of seconds. Together, our measurements and simulations provide direct support for the hindered diffusion model and yield insights into the nanometer-to-micrometer-scale mechanisms that lead to macroscopic signal dispersal.

Adhesion-Based Self-Organization in Tissue Patterning

Since the proposal of the differential adhesion hypothesis, scientists have been fascinated by how cell adhesion mediates cellular self-organization to form spatial patterns during development. The search for molecular tool kits with homophilic binding specificity resulted in a diverse repertoire of adhesion molecules. Recent understanding of the dominant role of cortical tension over adhesion binding redirects the focus of differential adhesion studies to the signaling function of adhesion proteins to regulate actomyosin contractility. The broader framework of differential interfacial tension encompasses both adhesion and nonadhesion molecules, sharing the common function of modulating interfacial tension during cell sorting to generate diverse tissue patterns. Robust adhesion-based patterning requires close coordination between morphogen signaling, cell fate decisions, and changes in adhesion. Current advances in bridging theoretical and experimental approaches present exciting opportunities to understand molecular, cellular, and tissue dynamics during adhesion-based tissue patterning across multiple time and length scales.

Adhesion strength between cells regulate nonmonotonic growth by a biomechanical feedback mechanism

We determine how intercellular interactions and mechanical pressure experienced by single cells regulate cell proliferation using a minimal computational model for three-dimensional multicellular spheroid (MCS) growth. We discover that emergent spatial variations in the cell division rate, depending on the location of the cells either at the core or periphery within the MCS, is regulated by intercellular adhesion strength (fad). Varying fad results in nonmonotonic proliferation of cells in the MCS. A biomechanical feedback mechanism coupling the fad and microenvironment-dependent pressure fluctuations relative to a threshold value (pc) determines the onset of a dormant phase, and explains the nonmonotonic proliferation response. Increasing fad from low values enhances cell proliferation because pressure on individual cells is smaller compared with pc. However, at high fad, cells readily become dormant and cannot rearrange effectively in spacetime, leading to arrested cell proliferation. Utilizing our theoretical predictions, we explain experimental data on the impact of adhesion strength on cell proliferation and find good agreement. Our work, which shows that proliferation is regulated by pressure-adhesion feedback mechanism, may be a general feature of multicellular growth.

Stem cell-derived synthetic embryos self-assemble by exploiting cadherin codes and cortical tension

Mammalian embryos sequentially differentiate into trophectoderm and an inner cell mass, the latter of which differentiates into primitive endoderm and epiblast. Trophoblast stem (TS), extraembryonic endoderm (XEN) and embryonic stem (ES) cells derived from these three lineages can self-assemble into synthetic embryos, but the mechanisms remain unknown. Here, we show that a stem cell-specific cadherin code drives synthetic embryogenesis. The XEN cell cadherin code enables XEN cell sorting into a layer below ES cells, recapitulating the sorting of epiblast and primitive endoderm before implantation. The TS cell cadherin code enables TS cell sorting above ES cells, resembling extraembryonic ectoderm clustering above epiblast following implantation. Whereas differential cadherin expression drives initial cell sorting, cortical tension consolidates tissue organization. By optimizing cadherin code expression in different stem cell lines, we tripled the frequency of correctly formed synthetic embryos. Thus, by exploiting cadherin codes from different stages of development, lineage-specific stem cells bypass the preimplantation structure to directly assemble a postimplantation embryo.

A quantitative biophysical principle to explain the 3D cellular connectivity in curved epithelia

Epithelial cell organization and the mechanical stability of tissues are closely related. In this context, it has been recently shown that packing optimization in bended or folded epithelia is achieved by an energy minimization mechanism that leads to a complex cellular shape: the "scutoid". Here, we focus on the relationship between this shape and the connectivity between cells. We use a combination of computational, experimental, and biophysical approaches to examine how energy drivers affect the three-dimensional (3D) packing of tubular epithelia. We propose an energy-based stochastic model that explains the 3D cellular connectivity. Then, we challenge it by experimentally reducing the cell adhesion. As a result, we observed an increment in the appearance of scutoids that correlated with a decrease in the energy barrier necessary to connect with new cells. We conclude that tubular epithelia satisfy a quantitative biophysical principle that links tissue geometry and energetics with the average cellular connectivity.

Delineating mechanisms and design principles of Caenorhabditis elegans embryogenesis using in toto high-resolution imaging data and computational modeling

The nematode (roundworm) Caenorhabditis elegans is one of the most popular animal models for the study of developmental biology, as its invariant development and transparent body enable in toto cellular-resolution fluorescence microscopy imaging of developmental processes at 1-min intervals. This has led to the development of various computational tools for the systematic and automated analysis of imaging data to delineate the molecular and cellular processes throughout the embryogenesis of C. elegans, such as those associated with cell lineage, cell migration, cell morphology, and gene activity. In this review, we first introduce C. elegans embryogenesis and the development of techniques for tracking cell lineage and reconstructing cell morphology during this process. We then contrast the developmental modes of C. elegans and the customized technologies used for studying them with the ones of other animal models, highlighting its advantage for studying embryogenesis with exceptional spatial and temporal resolution. This is followed by an examination of the physical models that have been devised—based on accurate determinations of developmental processes afforded by analyses of imaging data—to interpret the early embryonic development of C. elegans from subcellular to intercellular levels of multiple cells, which focus on two key processes: cell polarization and morphogenesis. We subsequently discuss how quantitative data-based theoretical modeling has improved our understanding of the mechanisms of C. elegans embryogenesis. We conclude by summarizing the challenges associated with the acquisition of C. elegans embryogenesis data, the construction of algorithms to analyze them, and the theoretical interpretation.

A discrete fiber network finite element model of arterial elastin network considering inter-fiber crosslinking property and density

Inter-fiber crosslinks within the extracellular matrix (ECM) play important roles in determining the mechanical properties of the fibrous network. Discrete fiber network (DFN) models have been used to study fibrous biological material, however the contribution of inter-fiber crosslinks to the mechanics of the ECM network is not well understood. In this study, a DFN model of arterial elastin network was developed based on measured structural features to study the contribution of inter-fiber crosslinking properties and density to the mechanics and fiber kinematics of the network. The DFN was generated by randomly placing line segments into a given domain following a fiber orientation distribution function obtained from multiphoton microscopy until a desired fiber areal fraction was reached. Intersections between the line segments were treated as crosslinks. The generated DFN model was then incorporated into an ABAQUS finite element model to simulate the network under equi- and nonequi-biaxial deformation. The inter-fiber crosslinks were modeled using connector elements with either zero (pin joint) or infinite (weld joint) rotational stiffness. Furthermore, inter-fiber crosslinking density was systematically reduced and its effect on both network- and fiber-level mechanics was studied. The DFN model showed good fitting and predicting capabilities of the stress-strain behavior of the elastin network. While the pin and weld joints do not seem to have noticeable effect on the network stress-strain behavior, the crosslinking properties can affect the local fiber mechanics and kinematics. Overall, our study suggests that inter-fiber crosslinking properties are important to the multiscale mechanics and fiber kinematics of the ECM network.

Powering morphogenesis: multiscale challenges at the interface of cell adhesion and the cytoskeleton

Among the defining features of the animal kingdom is the ability of cells to change shape and move. This underlies embryonic and postembryonic development, tissue homeostasis, regeneration, and wound healing. Cell shape change and motility require linkage of the cell's force-generating machinery to the plasma membrane at cell-cell and cell-extracellular matrix junctions. Connections of the actomyosin cytoskeleton to cell-cell adherens junctions need to be both resilient and dynamic, preventing tissue disruption during the dramatic events of embryonic morphogenesis. In the past decade, new insights radically altered the earlier simple paradigm that suggested simple linear linkage via the cadherin-catenin complex as the molecular mechanism of junction-cytoskeleton interaction. In this Perspective we provide a brief overview of our current state of knowledge and then focus on selected examples highlighting what we view as the major unanswered questions in our field and the approaches that offer exciting new insights at multiple scales from atomic structure to tissue mechanics.

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.

Shear-Driven Solidification and Nonlinear Elasticity in Epithelial Tissues

Biological processes, from morphogenesis to tumor invasion, spontaneously generate shear stresses inside living tissue. The mechanisms that govern the transmission of mechanical forces in epithelia and the collective response of the tissue to bulk shear deformations remain, however, poorly understood. Using a minimal cell-based computational model, we investigate the constitutive relation of confluent tissues under simple shear deformation. We show that an initially undeformed fluidlike tissue acquires finite rigidity above a critical applied strain. This is akin to the shear-driven rigidity observed in other soft matter systems. Interestingly, shear-driven rigidity can be understood by a critical scaling analysis in the vicinity of the second order critical point that governs the liquid-solid transition of the undeformed system. We further show that a solidlike tissue responds linearly only to small strains and but then switches to a nonlinear response at larger stains, with substantial stiffening. Finally, we propose a mean-field formulation for cells under shear that offers a simple physical explanation of shear-driven rigidity and nonlinear response in a tissue.

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.

Mechanical control of tissue shape: Cell-extrinsic and -intrinsic mechanisms join forces to regulate morphogenesis

During vertebrate development, cells must proliferate, move, and differentiate to form complex shapes. Elucidating the mechanisms underlying the molecular and cellular processes involved in tissue morphogenesis is essential to understanding developmental programmes. Mechanical stimuli act as a major contributor of morphogenetic processes and impact on cell behaviours to regulate tissue shape and size. Specifically, cell extrinsic physical forces are translated into biochemical signals within cells, through the process of mechanotransduction, activating multiple mechanosensitive pathways and defining cell behaviours. Physical forces generated by tissue mechanics and the extracellular matrix are crucial to orchestrate tissue patterning and cell fate specification. At the cell scale, the actomyosin network generates the cellular tension behind the tissue mechanics involved in building tissue. Thus, understanding the role of physical forces during morphogenetic processes requires the consideration of the contribution of cell intrinsic and cell extrinsic influences. The recent development of multidisciplinary approaches, as well as major advances in genetics, microscopy, and force-probing tools, have been key to push this field forward. With this review, we aim to discuss recent work on how tissue shape can be controlled by mechanical forces by focusing specifically on vertebrate organogenesis. We consider the influences of mechanical forces by discussing the cell-intrinsic forces (such as cell tension and proliferation) and cell-extrinsic forces (such as substrate stiffness and flow forces). We review recently described processes supporting the role of intratissue force generation and propagation in the context of shape emergence. Lastly, we discuss the emerging role of tissue-scale changes in tissue material properties, extrinsic forces, and shear stress on shape establishment.

On the origins of order

A cardinal feature common to embryonic development and tissue reorganization, as well as to wound healing and cancer cell invasion, is collective cellular migration. During collective migratory events the phenomena of cell jamming and unjamming are increasingly recognized, and underlying mechanical, genomic, transcriptional, and signaling events are increasingly coming to light. In this brief perspective I propose a synthesis that brings together in a new way two key concepts. On the one hand, it has been suggested that the unjammed phase of the cellular collective evolved under a selective pressure favoring fluid-like migratory dynamics as would be required so as to accommodate episodes of tissue evolution, development, plasticity, and repair. Being dynamic, such an unjammed migratory phase is expected to be energetically expensive compared with the jammed non-migratory phase, which is presumed to have evolved under a selective pressure favoring a solid-like homeostatic regime that, by comparison, is energetically economical and mechanically stable. On the other hand, well before the discovery of cell jamming and unjamming Kauffman proposed the general biological principle that living systems exist in a solid regime near the edge of chaos, and that natural selection achieves and sustains such a poised state. Here I propose that, in certain systems at least, this poised solid-like state as predicted in the abstract by Kauffman is realized in the particular by the jammed regime just at the brink of unjamming.

Mechanical regulation of early vertebrate embryogenesis

Embryonic cells grow in environments that provide a plethora of physical cues, including mechanical forces that shape the development of the entire embryo. Despite their prevalence, the role of these forces in embryonic development and their integration with chemical signals have been mostly neglected, and scrutiny in modern molecular embryology tilted, instead, towards the dissection of molecular pathways involved in cell fate determination and patterning. It is now possible to investigate how mechanical signals induce downstream genetic regulatory networks to regulate key developmental processes in the embryo. Here, we review the insights into mechanical control of early vertebrate development, including the role of forces in tissue patterning and embryonic axis formation. We also highlight recent in vitro approaches using individual embryonic stem cells and self-organizing multicellular models of human embryos, which have been instrumental in expanding our understanding of how mechanics tune cell fate and cellular rearrangements during human embryonic development.