Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Confinement plus myosin-II suppression maximizes heritable loss of chromosomes, as revealed by live-cell ChReporters

The mechanical environment of a cell can have many effects, but whether it impacts the DNA sequence of a cell has remained unexamined. To investigate this, we developed a live-cell method to measure changes in chromosome numbers. We edited constitutive genes with GFP or RFP tags on single alleles and discovered that cells that lose Chromosome reporters (ChReporters) become non-fluorescent. We applied our new tools to confined mitosis and to inhibition of the putative tumor suppressor myosin-II. We quantified compression of mitotic chromatin in vivo and demonstrated that similar compression in vitro resulted in cell death, but also rare and heritable ChReptorter loss. Myosin-II suppression rescued lethal multipolar divisions and maximized ChReporter loss during three-dimensional (3D) compression and two-dimensional (2D) lateral confinement, but not in standard 2D culture. ChReporter loss was associated with chromosome mis-segregation, rather than just the number of divisions, and loss in vitro and in mice was selected against in subsequent 2D cultures. Inhibition of the spindle assembly checkpoint (SAC) caused ChReporter loss in 2D culture, as expected, but not during 3D compression, suggesting a SAC perturbation. Thus, ChReporters enable diverse studies of viable genetic changes, and show that confinement and myosin-II affect DNA sequence and mechano-evolution.

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.

Delineating the 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 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.

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.

Deconstructing gastrulation at single-cell resolution

Gastrulation movements in all animal embryos start with regulated deformations of patterned epithelial sheets, which are driven by cell divisions, cell shape changes, and cell intercalations. Each of these behaviors has been associated with distinct aspects of gastrulation1-4 and has been a subject of intense research using genetic, cell biological, and more recently, biophysical approaches.5-14 Most of these studies, however, focus either on cellular processes driving gastrulation or on large-scale tissue deformations.15-23 Recent advances in microscopy and image processing create a unique opportunity for integrating these complementary viewpoints.24-28 Here, we take a step toward bridging these complementary strategies and deconstruct the early stages of gastrulation in the entire Drosophila embryo. Our approach relies on an integrated computational framework for cell segmentation and tracking and on efficient algorithms for event detection. The detected events are then mapped back onto the blastoderm shell, providing an intuitive visual means to examine complex cellular activity patterns within the context of their initial anatomic domains. By analyzing these maps, we identified that the loss of nearly half of surface cells to invaginations is compensated primarily by transient mitotic rounding. In addition, by analyzing mapped cell intercalation events, we derived direct quantitative relations between intercalation frequency and the rate of axis elongation. This work is setting the stage for systems-level dissection of a pivotal step in animal development.

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.

Viscoelasticity, Like Forces, Plays a Role in Mechanotransduction

Viscoelasticity and its alteration in time and space has turned out to act as a key element in fundamental biological processes in living systems, such as morphogenesis and motility. Based on experimental and theoretical findings it can be proposed that viscoelasticity of cells, spheroids and tissues seems to be a collective characteristic that demands macromolecular, intracellular component and intercellular interactions. A major challenge is to couple the alterations in the macroscopic structural or material characteristics of cells, spheroids and tissues, such as cell and tissue phase transitions, to the microscopic interferences of their elements. Therefore, the biophysical technologies need to be improved, advanced and connected to classical biological assays. In this review, the viscoelastic nature of cytoskeletal, extracellular and cellular networks is presented and discussed. Viscoelasticity is conceptualized as a major contributor to cell migration and invasion and it is discussed whether it can serve as a biomarker for the cells' migratory capacity in several biological contexts. It can be hypothesized that the statistical mechanics of intra- and extracellular networks may be applied in the future as a powerful tool to explore quantitatively the biomechanical foundation of viscoelasticity over a broad range of time and length scales. Finally, the importance of the cellular viscoelasticity is illustrated in identifying and characterizing multiple disorders, such as cancer, tissue injuries, acute or chronic inflammations or fibrotic diseases.

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.

Energetic rigidity. II. Applications in examples of biological and underconstrained materials

This is the second paper devoted to energetic rigidity, in which we apply our formalism to examples in two dimensions: Underconstrained random regular spring networks, vertex models, and jammed packings of soft particles. Spring networks and vertex models are both highly underconstrained, and first-order constraint counting does not predict their rigidity, but second-order rigidity does. In contrast, spherical jammed packings are overconstrained and thus first-order rigid, meaning that constraint counting is equivalent to energetic rigidity as long as prestresses in the system are sufficiently small. Aspherical jammed packings on the other hand have been shown to be jammed at hypostaticity, which we use to argue for a modified constraint counting for systems that are energetically rigid at quartic order.

Activation of Topological Defects Induces a Brittle-to-Ductile Transition in Epithelial Monolayers

Epithelial monolayers are subjected to various mechanical forces, such as stretching, shearing, and compression. Thus, its mechanical response to external loadings is essential for its biological functions. However, the mechanism of the fracture failure of the epithelial monolayer remains poorly understood. Here, by introducing a new type of topological transition, i.e., detach transition or T4 transition, we develop a modified cellular vertex model to investigate the rupture of the cell monolayer. Interestingly, we find a brittle-to-ductile transition in epithelial monolayers, which is controlled by the mechanical properties of single cells and cell-cell contacts. We reveal that the external loadings can activate cell rearrangement in ductile cell monolayers. The plastic deformation results from the nucleation and propagation of "pentagon-heptagon defects" in analogy with the topological defects commonly seen in 2D materials. By using a simplified four-cell model, we further demonstrate that the brittle-to-ductile transition is induced by the competition between cell rearrangement and cell detachment. Our work provides a new theoretical framework to study the rupture of living tissues and may have important implications for many other biological processes, such as wound healing and tissue morphogenesis.

Sculpting with stem cells: how models of embryo development take shape

During embryogenesis, organisms acquire their shape given boundary conditions that impose geometrical, mechanical and biochemical constraints. A detailed integrative understanding how these morphogenetic information modules pattern and shape the mammalian embryo is still lacking, mostly owing to the inaccessibility of the embryo in vivo for direct observation and manipulation. These impediments are circumvented by the developmental engineering of embryo-like structures (stembryos) from pluripotent stem cells that are easy to access, track, manipulate and scale. Here, we explain how unlocking distinct levels of embryo-like architecture through controlled modulations of the cellular environment enables the identification of minimal sets of mechanical and biochemical inputs necessary to pattern and shape the mammalian embryo. We detail how this can be complemented with precise measurements and manipulations of tissue biochemistry, mechanics and geometry across spatial and temporal scales to provide insights into the mechanochemical feedback loops governing embryo morphogenesis. Finally, we discuss how, even in the absence of active manipulations, stembryos display intrinsic phenotypic variability that can be leveraged to define the constraints that ensure reproducible morphogenesis in vivo.

Viscoelasticity Acts as a Marker for Tumor Extracellular Matrix Characteristics

Biological materials such as extracellular matrix scaffolds, cancer cells, and tissues are often assumed to respond elastically for simplicity; the viscoelastic response is quite commonly ignored. Extracellular matrix mechanics including the viscoelasticity has turned out to be a key feature of cellular behavior and the entire shape and function of healthy and diseased tissues, such as cancer. The interference of cells with their local microenvironment and the interaction among different cell types relies both on the mechanical phenotype of each involved element. However, there is still not yet clearly understood how viscoelasticity alters the functional phenotype of the tumor extracellular matrix environment. Especially the biophysical technologies are still under ongoing improvement and further development. In addition, the effect of matrix mechanics in the progression of cancer is the subject of discussion. Hence, the topic of this review is especially attractive to collect the existing endeavors to characterize the viscoelastic features of tumor extracellular matrices and to briefly highlight the present frontiers in cancer progression and escape of cancers from therapy. Finally, this review article illustrates the importance of the tumor extracellular matrix mechano-phenotype, including the phenomenon viscoelasticity in identifying, characterizing, and treating specific cancer types.

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.

Mitosis, a springboard for epithelial-mesenchymal transition?

Mitosis is a key process in development and remains critical to ensure homeostasis in adult tissues. Besides its primary role in generating two new cells, cell division involves deep structural and molecular changes that might have additional effects on cell and tissue fate and shape. Specific quantitative and qualitative regulation of mitosis has been observed in multiple morphogenetic events in different embryo models. For instance, during mouse embryo gastrulation, the portion of epithelium that undergoes epithelial to mesenchymal transition, where a static epithelial cell become mesenchymal and motile, has a higher mitotic index and a distinct localization of mitotic rounding, compared to the rest of the tissue. Here we explore the potential mechanisms through which mitosis may favor tissue reorganization in various models. Notably, we discuss the mechanical impact of cell rounding on the cell and its environment, and the modification of tissue physical parameters through changes in cell-cell and cell-matrix adhesion.

Phase transitions in biology: from bird flocks to population dynamics

Phase transitions are an important and extensively studied concept in physics. The insights derived from understanding phase transitions in physics have recently and successfully been applied to a number of different phenomena in biological systems. Here, we provide a brief review of phase transitions and their role in explaining biological processes ranging from collective behaviour in animal flocks to neuronal firing. We also highlight a new and exciting area where phase transition theory is particularly applicable: population collapse and extinction. We discuss how phase transition theory can give insight into a range of extinction events such as population decline due to climate change or microbial responses to stressors such as antibiotic treatment.

Cell state transitions: definitions and challenges

A fundamental challenge when studying biological systems is the description of cell state dynamics. During transitions between cell states, a multitude of parameters may change - from the promoters that are active, to the RNAs and proteins that are expressed and modified. Cells can also adopt different shapes, alter their motility and change their reliance on cell-cell junctions or adhesion. These parameters are integral to how a cell behaves and collectively define the state a cell is in. Yet, technical challenges prevent us from measuring all of these parameters simultaneously and dynamically. How, then, can we comprehend cell state transitions using finite descriptions? The recent virtual workshop organised by The Company of Biologists entitled 'Cell State Transitions: Approaches, Experimental Systems and Models' attempted to address this question. Here, we summarise some of the main points that emerged during the workshop's themed discussions. We also present examples of cell state transitions and describe models and systems that are pushing forward our understanding of how cells rewire their state.

A theoretical understanding of mammalian preimplantation development

The blastocyst has long been a hallmark system of study in developmental biology due to its importance in mammalian development and clinical relevance for assisted reproductive technologies. In recent years, the blastocyst is emerging as a system of study for mathematical modelling. In this review, we compile, to our knowledge, all models describing preimplantation development. Coupled with experiments, these models have provided insight regarding the morphogenesis and cell-fate specification throughout preimplantation development. In the case of cell-fate specification, theoretical models have provided mechanisms explaining how proportion of cell types are established and maintained when confronted to perturbations. For cell-shape based models, they have described quantitatively how mechanical forces sculpt the blastocyst and even predicted how morphogenesis could be manipulated. As theoretical biology develops, we believe the next critical stage in modelling involves an integration of cell fate and mechanics to provide integrative models of development at distinct spatiotemporal scales. We discuss how, building on a balanced base of mechanical and chemical models, the preimplantation embryo will play a key role in integrating these two faces of the same coin.

Holding it together: when cadherin meets cadherin

Intercellular adhesion is the key to multicellularity, and its malfunction plays an important role in various developmental and disease-related processes. Although it has been intensively studied by both biologists and physicists, a commonly accepted definition of cell-cell adhesion is still being debated. Cell-cell adhesion has been described at the molecular scale as a function of adhesion receptors controlling binding affinity, at the cellular scale as resistance to detachment forces or modulation of surface tension, and at the tissue scale as a regulator of cellular rearrangements and morphogenesis. In this review, we aim to summarize and discuss recent advances in the molecular, cellular, and theoretical description of cell-cell adhesion, ranging from biomimetic models to the complexity of cells and tissues in an organismal context. In particular, we will focus on cadherin-mediated cell-cell adhesion and the role of adhesion signaling and mechanosensation therein, two processes central for understanding the biological and physical basis of cell-cell adhesion.

Jamming and arrest of cell motion in biological tissues

Collective cell motility is crucial to many biological processes including morphogenesis, wound healing, and cancer invasion. Recently, the biology and biophysics communities have begun to use the term 'cell jamming' to describe the collective arrest of cell motion in tissues. Although this term is widely used, the underlying mechanisms are varied. In this review, we highlight three independent mechanisms that can potentially drive arrest of cell motion - crowding, tension-driven rigidity, and reduction of fluctuations - and propose a framework that connects all three. Because multiple mechanisms may be operating simultaneously, this emphasizes that experiments should strive to identify which mechanism dominates in a given situation. We also discuss how specific cell-scale and molecular-scale biological processes, such as cell-cell and cell-substrate interactions, control aspects of these underlying physical mechanisms.

Mechanical and genetic control of ascidian endoderm invagination during gastrulation

Gastrulation is a near universal developmental process of animal embryogenesis, during which dramatic morphogenetic events take place: the mesodermal and endodermal tissues are internalized, the ectoderm spreads to cover the embryo surface, and the animal body plan and germ layers are established. Morphogenesis during gastrulation has long been considered the result of spatio-temporally localised forces driven by the transcriptional programme of the embryo. Recent work has shown that tissue rheological properties, which define the mechanical response of tissues to internally-generated or external forces, are also important dynamic regulators of gastrulation. Here, we first introduce how embryonic mechanics can be represented, before outlining current knowledge of the mechanical and genetic control of gastrulation in ascidians, invertebrate marine chordates which develop with invariant cell lineages and a solid-like rheological behaviour until the neurula stages. We discuss the potential of these organisms for the experimental and computational whole-embryo characterisation of the mechanisms shaping gastrulation, and how they may inform the more complex tissue internalization strategies used by other model organisms.

Engineering life in synthetic systems

The second EMBO-EMBL Symposium 'Synthetic Morphogenesis: From Gene Circuits to Tissue Architecture' was held virtually in March 2021, with participants from all over the world joining from the comfort of their sofas to discuss synthetic morphogenesis at large. Leading scientists from a range of disciplines, including developmental biology, physics, chemistry and computer science, covered a gamut of topics from the principles of cell and tissue organization, patterning and gene regulatory networks, to synthetic approaches for exploring evolutionary and developmental biology principles. Here, we describe some of the high points.

The cell in the age of the genomic revolution: Cell Regulatory Networks

Over the last few years an intense activity in the areas of advanced microscopy and quantitative cell biology has put the focus on the morphogenetic events that shape embryos. The interest in these processes is taking place against the backdrop of genomic studies, particularly of global patterns of gene expression at the level of single cells, which cannot fully account for the way cells build tissues and organs. Here we discuss the need to integrate the activity of genes with that of cells and propose the need to develop a framework, based on cellular processes and cell interactions, that parallels that which has been created for gene activity in the form of Gene Regulatory Networks (GRNs). We begin to do this by suggesting elements for building Cell Regulatory Networks (CRNs). In the same manner that GRNs create schedules of gene expression that result in the emergence of cell fates over time, CRNs create tissues and organs i.e. space. We also suggest how GRNs and CRNs might interact in the building of embryos through feedback loops involving mechanics and tissue tectonics.