Rigidity percolation uncovers a structural basis for embryonic tissue phase transitions

Cell position-based evaluation of mechanical features of cells in multicellular systems

Measurement of mechanical forces of cell-cell interactions is important for studying the emergence of diverse three-dimensional morphologies of multicellular organisms. We previously reported an image-based statistical method for inferring effective pairwise forces of cell-cell interactions (i.e., attractive/repulsive forces), where a cell particle model was fitted to cell tracking data acquired by live imaging. However, because the particle model is a coarse-grained model, it remains unclear how the pairwise forces relates to sub-cellular mechanical components including cell-cell adhesive forces. Here we applied our inference method to cell tracking data generated by vertex models that assumed sub-cellular components. Through this approach, we investigated the relationship between the effective pairwise forces and various sub-cellular components: cell-cell adhesion forces, cell surface tensions, cell-extracellular matrix (ECM) adhesion, traction forces between cells and ECM, cell growth, etc. We found that the cell-cell adhesion forces were attractive, and both the cell surface tensions and cell-ECM adhesive forces were repulsive, etc. These results indicate that sub-cellular mechanical components can contribute to the effective attractive/repulsive forces of cell-cell interactions. This comprehensive analysis provides theoretical bases for linking the pairwise forces to the sub-cellular mechanical components: this showcase is useful for speculating the sub-cellular mechanical components from the information of cell positions, and for interpreting simulation results based on particle models.

The role of extracellular matrix viscoelasticity in development and disease

For several decades, research has studied the influence of the extracellular matrix (ECM) mechanical properties in cell response, primarily emphasising its elasticity as the main determinant of cell and tissue behaviour. However, the ECM is not purely elastic; it is viscoelastic. ECM viscoelasticity has now emerged as a major regulator of collective cell dynamics. This review highlights recent findings on the role of ECM viscoelasticity in development and pathology.

BMP-dependent patterning of ectoderm tissue material properties modulates lateral mesendoderm cell migration during early zebrafish gastrulation

Cell migration is a fundamental process during embryonic development. Most studies in vivo have focused on the migration of cells using the extracellular matrix (ECM) as their substrate for migration. In contrast, much less is known about how cells migrate on other cells, as found in early embryos when the ECM has not yet formed. Here, we show that lateral mesendoderm (LME) cells in the early zebrafish gastrula use the ectoderm as their substrate for migration. We show that the lateral ectoderm is permissive for the animal-pole-directed migration of LME cells, while the ectoderm at the animal pole halts it. These differences in permissiveness depend on the lateral ectoderm being more cohesive than the animal ectoderm, a property controlled by bone morphogenetic protein (BMP) signaling within the ectoderm. Collectively, these findings identify ectoderm tissue cohesion as one critical factor in regulating LME migration during zebrafish gastrulation.

Unsupervised spatiotemporal classification of deformation patterns of embryonic tissues matches their fate map

During morphogenesis, embryonic tissues display fluid-like behavior with fluctuating strain rates. Digital cell lineages reconstructed from 4D images of developing zebrafish embryos are used to infer representative tissue deformation patterns and their association with developmental events. Finite deformation analysis along cell trajectories and unsupervised machine learning are applied to obtain reduced-order models condensing the collective cell motions, delineating tissue domains with distinct 4D biomechanical behavior. This reduced-order kinematic description is reproducible across specimens and matches fate maps of the zebrafish brain in wild-type and nodal pathway mutants (zoeptz57/tz57 ), shedding light into the morphogenetic defects causing these mutants' cyclopia. Furthermore, the inferred kinematic maps also match expression maps of the gene transcription factor goosecoid (gsc). In summary, this work introduces an objective analytical framework to systematically unravel the complex spatiotemporal patterns of embryonic tissue deformations and couple them with cell fate and gene expression maps.

CM, Martínez Fernández R, Betterelli Giuliano C, Zhang R, Valeriani C, Wilson LG. The carnivorous plant Genlisea harnesses active particle dynamics to prey on microfauna

Carnivory in plants is an unusual trait that has arisen multiple times, independently, throughout evolutionary history. Plants in the genus Genlisea are carnivorous and feed on microorganisms that live in soil using modified subterranean leaf structures (rhizophylls). A surprisingly broad array of microfauna has been observed in the plants' digestive chambers, including ciliates, amoebae, and soil mites. Here, we show, through experiments and simulations, that Genlisea exploit active matter physics to "rectify" bacterial swimming and establish a local flux of bacteria through the structured environment of the rhizophyll toward the plant's digestion vesicle. In contrast, macromolecular digestion products are free to diffuse away from the digestion vesicle and establish a concentration gradient of carbon sources to draw larger microorganisms further inside the plant. Our experiments and simulations show that this mechanism is likely to be a localized one and that no large-scale efflux of digested matter is present.

A 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, both shape index and aspect ratio of amnioserosa cells increase 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 nonmonotonic junction tension that we confirm with laser ablation experiments.

Planar polarized force propagation integrates cell behavior with tissue shaping during convergent extension

Convergent extension (CE) is an evolutionarily conserved developmental process that elongates tissues and organs via collective cell movements known as cell intercalation. Here, we sought to understand the mechanisms connecting cell behaviors and tissue shaping. We focus on an often-overlooked aspect of cell intercalation, the resolution of 4-cell vertices. Our data reveal that imbalanced cellular forces are involved in a timely vertex resolution, which, in turn, enables the propagation of such cellular forces, facilitating the propagation of tissue-scale CE. Conversely, delayed vertex resolution leads to a subtle but significant change in tissue-wide cell packing and exerts a profound impact by blocking force propagation, resulting in CE propagation defects. Our findings propose a collaborative nature of local cell intercalations in propagating tissue-wide CE. It unveils a multiscale biomechanical synergy underpinning the cellular mechanisms that orchestrate tissue morphogenesis during CE.

Open problems in synthetic multicellularity

Multicellularity is one of the major evolutionary transitions, and its rise provided the ingredients for the emergence of a biosphere inhabited by complex organisms. Over the last decades, the potential for bioengineering multicellular systems has been instrumental in interrogating nature and exploring novel paths to regeneration, disease, cognition, and behaviour. Here, we provide a list of open problems that encapsulate many of the ongoing and future challenges in the field and suggest conceptual approaches that may facilitate progress.

An actin bracket-induced elastoplastic transition determines epithelial folding irreversibility

During morphogenesis, epithelial sheets undergo sequential folding to form three-dimensional organ structures. The resulting folds are often irreversible, ensuring that morphogenesis progresses in one direction. However, the mechanism establishing folding irreversibility remains unclear. Here, we report a mechanical property of epithelia that determines folding irreversibility. Using a mechanical assay, we demonstrate that long-term, high-curvature folding induces plastic, irreversible deformations, while short-term or low-curvature folding results in an elastic, shape-restoring response. This elastic-plastic transition occurs in a switch-like manner, with critical thresholds in folding curvature and duration. The transition is induced by F-actin accumulating into a bracket-like structure across the fold, triggered by cells sensing deformations via mechanosensitive signaling pathways, including TRPC 3/6-mediated calcium influx and ligand-independent EGFR activation. These results demonstrate that cells control epithelial folding irreversibility by detecting folding characteristics and adaptively switching between elastic and plastic responses, providing mechanical insight into the directionality of morphogenesis.

Programming the elongation of mammalian cell aggregates with synthetic gene circuits

A key goal of synthetic morphogenesis is the identification and implementation of methods to control morphogenesis. One line of research is the use of synthetic genetic circuits guiding the self-organization of cell ensembles. This approach has led to several recent successes, including control of cellular rearrangements in 3D via control of cell-cell adhesion by user-designed artificial genetic circuits. However, the methods employed to reach such achievements can still be optimized along three lines: identification of circuits happens by hand, 3D structures are spherical, and effectors are limited to cell-cell adhesion. Here we show the identification, in a computational framework, of genetic circuits for volumetric axial elongation via control of proliferation, tissue fluidity, and cell-cell signaling. We then seek to implement this design in mammalian cell aggregates in vitro. We start by identifying effectors to control tissue growth and fluidity in vitro. We then combine these new modules to construct complete circuits that control cell behaviors of interest in space and time, resulting in measurable tissue deformation along an axis that depends on the engineered signaling modules. Finally, we contextualize in vitro and in silico implementations within a unified morphospace to suggest further elaboration of this initial family of circuits towards more robust programmed axial elongation. These results and integrated in vitro/in silico pipeline demonstrate a promising method for designing, screening, and implementing synthetic genetic circuits of morphogenesis, opening the way to the programming of various user-defined tissue shapes.

Regulation of epithelial cell jamming transition by cytoskeleton and cell-cell interactions

Multicellular systems, such as epithelial cell collectives, undergo transitions similar to those in inert physical systems like sand piles and foams. To remodel or maintain tissue organization during development or disease, these collectives transition between fluid-like and solid-like states, undergoing jamming or unjamming transitions. While these transitions share principles with physical systems, understanding their regulation and implications in cell biology is challenging. Although cell jamming and unjamming follow physics principles described by the jamming diagram, they are fundamentally biological processes. In this review, we explore how cellular processes and interactions regulate jamming and unjamming transitions. We begin with an overview of how these transitions control tissue remodeling in epithelial model systems and describe recent findings of the physical principles governing tissue solidification and fluidization. We then explore the mechanistic pathways that modulate the jamming phase diagram axes, focusing on the regulation of cell fluctuations and geometric compatibility. Drawing upon seminal works in cell biology, we discuss the roles of cytoskeleton and cell-cell adhesion in controlling cell motility and geometry. This comprehensive view illustrates the molecular control of cell jamming and unjamming, crucial for tissue remodeling in various biological contexts.

The cellular Potts model on disordered lattices

The cellular Potts model, also known as the Glazier-Graner-Hogeweg model, is a lattice-based approach by which biological tissues at the level of individual cells can be numerically studied. Traditionally, a square or hexagonal underlying lattice structure is assumed for two-dimensional systems, and this is known to introduce artifacts in the structure and dynamics of the model tissues. That is, on regular lattices, cells can assume shapes that are dictated by the symmetries of the underlying lattice. Here, we developed a variant of this method that can be applied to a broad class of (ir)regular lattices. We show that on an irregular lattice deriving from a fluid-like configuration, two types of artifacts can be removed. We further report on the transition between a fluid-like disordered and a solid-like hexagonally ordered phase present for monodisperse confluent cells as a function of their surface tension. This transition shows the hallmarks of a first-order phase transition and is different from the glass/jamming transitions commonly reported for the vertex and active Voronoi models. We emphasize this by analyzing the distribution of shape parameters found in our state space. Our analysis provides a useful reference for the future study of epithelia using the (ir)regular cellular Potts model.

Intercellular fluid dynamics in tissue morphogenesis

During embryonic development, cells shape our body, which is mostly made up of water. It is often forgotten that some of this water is found in intercellular fluid, which, for example, immerses the cells of developing embryos. Intercellular fluid contributes to the properties of tissues and influences cell behaviour, thereby participating in tissue morphogenesis. While our understanding of the role of cells in shaping tissues advances, the exploration of the contribution of intercellular fluid dynamics is just beginning. In this review, we delve into the intricate mechanisms employed by cells to control fluid movements both across and within sealed tissue compartments. These mechanisms encompass sealing by tight junctions and controlled leakage, osmotic pumping, hydraulic fracturing of cell adhesion, cell and tissue contractions, as well as beating cilia. We illustrate key concepts by drawing extensively from the early mouse embryo, which successively forms multiple lumens that play essential roles in its development. Finally, we detail experimental approaches and emerging techniques that allow for the quantitative characterization and the manipulation of intercellular fluids in vivo, as well as theoretical frameworks that are crucial for comprehending their dynamics.

Rigidity in mechanical biological networks

Multicellular organisms generate complex morphologies required for their function. Organisms control these morphologies by tuning active forces and by altering the emergent 'material properties' of a tissue, i.e. the rheology of the tissue. In many cases, organisms take advantage of dramatic changes in the rheology that occur when the material undergoes a rigidity transition from a fluid-like or floppy state to a solid-like or rigid state. This transition in turn depends on internal parameters at the scale of cells and molecules. This review highlights recent theoretical work identifying the mechanisms that drive such transitions, so that biologists can look for these mechanisms in in vivo or in vitro systems. We discuss two main types of transition: a first-order rigidity transition that depends on the connectivity of small-scale structures, such as the number of contacts between cells or the number of branch points in a biopolymer network; and a second-order rigidity transition that depends on the geometry of small-scale structures, such as the shape of cells or the distance between crosslinks in a polymer network. We provide examples of each type of transition in model organisms and discuss methods for distinguishing between the mechanisms in future experiments.

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, both shape index and aspect ratio of amnioserosa cells increase 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 shape index 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 shape index 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.

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.

Fundamental constraints to the logic of living systems

It has been argued that the historical nature of evolution makes it a highly path-dependent process. Under this view, the outcome of evolutionary dynamics could have resulted in organisms with different forms and functions. At the same time, there is ample evidence that convergence and constraints strongly limit the domain of the potential design principles that evolution can achieve. Are these limitations relevant in shaping the fabric of the possible? Here, we argue that fundamental constraints are associated with the logic of living matter. We illustrate this idea by considering the thermodynamic properties of living systems, the linear nature of molecular information, the cellular nature of the building blocks of life, multicellularity and development, the threshold nature of computations in cognitive systems and the discrete nature of the architecture of ecosystems. In all these examples, we present available evidence and suggest potential avenues towards a well-defined theoretical formulation.

Temporal variability and cell mechanics control robustness in mammalian embryogenesis

How living systems achieve precision in form and function despite their intrinsic stochasticity is a fundamental yet ongoing question in biology. We generated morphomaps of preimplantation embryogenesis in mouse, rabbit, and monkey embryos, and these morphomaps revealed that although blastomere divisions desynchronized passively, 8-cell embryos converged toward robust three-dimensional shapes. Using topological analysis and genetic perturbations, we found that embryos progressively changed their cellular connectivity to a preferred topology, which could be predicted by a physical model in which actomyosin contractility and noise facilitate topological transitions, lowering surface energy. This mechanism favored regular embryo packing and promoted a higher number of inner cells in the 16-cell embryo. Synchronized division reduced embryo packing and generated substantially more misallocated cells and fewer inner-cell-mass cells. These findings suggest that stochasticity in division timing contributes to robust patterning.

Inverse blebs operate as hydraulic pumps during mouse blastocyst formation

During preimplantation development, mouse embryos form a fluid-filled lumen. Pressurized fluid fractures cell-cell contacts and accumulates into pockets, which coarsen into a single lumen. How the embryo controls intercellular fluid movement during coarsening is unknown. Here we report inverse blebs growing into cells at adhesive contacts. Throughout the embryo we observed hundreds of inverse blebs, each filling with intercellular fluid and retracting within a minute. Inverse blebs grow due to pressure build-up resulting from fluid accumulation and cell-cell adhesion, which locally confines fluid. Inverse blebs retract due to actomyosin contraction, practically pushing fluid within the intercellular space. Importantly, inverse blebs occur infrequently at contacts formed by multiple cells, which effectively serve as fluid sinks. Manipulation of the embryo topology reveals that without sinks inverse blebs pump fluid into one another in futile cycles. We propose that inverse blebs operate as hydraulic pumps to promote luminal coarsening, thereby constituting an instrument used by cells to control fluid movement.

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.

A fibronectin gradient remodels mixed-phase mesoderm

Physical processes ultimately shape tissue during development. Two emerging proposals are that cells migrate toward stiffer tissue (durotaxis) and that the extent of cell rearrangements reflects tissue phase, but it is unclear whether and how these concepts are related. Here, we identify fibronectin-dependent tissue stiffness as a control variable that underlies and unifies these phenomena in vivo. In murine limb bud mesoderm, cells are either caged, move directionally, or intercalate as a function of their location along a stiffness gradient. A modified Landau phase equation that incorporates tissue stiffness accurately predicts cell diffusivity upon loss or gain of fibronectin. Fibronectin is regulated by WNT5A-YAP feedback that controls cell movements, tissue shape, and skeletal pattern. The results identify a key determinant of phase transition and show how fibronectin-dependent directional cell movement emerges in a mixed-phase environment in vivo.

How a reaction-diffusion signal can control spinal cord regeneration in axolotls: A modeling study

Axolotls are uniquely able to completely regenerate the spinal cord after amputation. The underlying governing mechanisms of this regenerative response have not yet been fully elucidated. We previously found that spinal cord regeneration is mainly driven by cell-cycle acceleration of ependymal cells, recruited by a hypothetical signal propagating from the injury. However, the nature of the signal and its propagation remain unknown. In this theoretical study, we investigated whether the regeneration-inducing signal can follow a reaction-diffusion process. We developed a computational model, validated it with experimental data, and showed that the signal dynamics can be understood in terms of reaction-diffusion mechanism. By developing a theory of the regenerating outgrowth in the limit of fast reaction-diffusion, we demonstrate that control of regenerative response solely relies on cell-to-signal sensitivity and the signal reaction-diffusion characteristic length. This study lays foundations for further identification of the signal controlling regeneration of the spinal cord.

Dynamical forces drive organ morphology changes during embryonic development

Organs and tissues must change shape in precise ways during embryonic development to execute their functions. Multiple mechanisms including biochemical signaling pathways and biophysical forces help drive these morphology changes, but it has been difficult to tease apart their contributions, especially from tissue-scale dynamic forces that are typically ignored. We use a combination of mathematical models and in vivo experiments to study a simple organ in the zebrafish embryo called Kupffer's vesicle. Modeling indicates that dynamic forces generated by tissue movements in the embryo produce shape changes in Kupffer's vesicle that are observed during development. Laser ablations in the zebrafish embryo that alter these forces result in altered organ shapes matching model predictions. These results demonstrate that dynamic forces sculpt organ shape during embryo development.

Capillarity in Interfacial Liquids and Marbles: Mechanisms, Properties, and Applications

The mechanics of capillary force in biological systems have critical roles in the formation of the intra- and inter-cellular structures, which may mediate the organization, morphogenesis, and homeostasis of biomolecular condensates. Current techniques may not allow direct and precise measurements of the capillary forces at the intra- and inter-cellular scales. By preserving liquid droplets at the liquid-liquid interface, we have discovered and studied ideal models, i.e., interfacial liquids and marbles, for understanding general capillary mechanics that existed in liquid-in-liquid systems, e.g., biomolecular condensates. The unexpectedly long coalescence time of the interfacial liquids revealed that the Stokes equation does not hold as the radius of the liquid bridge approaches zero, evidencing the existence of a third inertially limited viscous regime. Moreover, liquid transport from a liquid droplet to a liquid reservoir can be prohibited by coating the droplet surface with hydrophobic or amphiphilic particles, forming interfacial liquid marbles. Unique characteristics, including high stability, transparency, gas permeability, and self-assembly, are observed for the interfacial liquid marbles. Phase transition and separation induced by the formation of nanostructured materials can be directly observed within the interfacial liquid marbles without the need for surfactants and agitation, making them useful tools to research the interfacial mechanics.

Patterning and folding of intestinal villi by active mesenchymal dewetting

Tissue folds are structural motifs critical to organ function. In the intestine, bending of a flat epithelium into a periodic pattern of folds gives rise to villi, finger-like protrusions that enable nutrient absorption. However, the molecular and mechanical processes driving villus morphogenesis remain unclear. Here, we identify an active mechanical mechanism that simultaneously patterns and folds the intestinal epithelium to initiate villus formation. At the cellular level, we find that PDGFRA+ subepithelial mesenchymal cells generate myosin II-dependent forces sufficient to produce patterned curvature in neighboring tissue interfaces. This symmetry-breaking process requires altered cell and extracellular matrix interactions that are enabled by matrix metalloproteinase-mediated tissue fluidization. Computational models, together with in vitro and in vivo experiments, revealed that 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 dewetting of a thin liquid film.

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.

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.

Discontinuous Shear Thickening in Biological Tissue Rheology

During embryonic morphogenesis, tissues undergo dramatic deformations in order to form functional organs. Similarly, in adult animals, living cells and tissues are continually subjected to forces and deformations. Therefore, the success of embryonic development and the proper maintenance of physiological functions rely on the ability of cells to withstand mechanical stresses as well as their ability to flow in a collective manner. During these events, mechanical perturbations can originate from active processes at the single-cell level, competing with external stresses exerted by surrounding tissues and organs. However, the study of tissue mechanics has been somewhat limited to either the response to external forces or to intrinsic ones. In this work, we use an active vertex model of a 2D confluent tissue to study the interplay of external deformations that are applied globally to a tissue with internal active stresses that arise locally at the cellular level due to cell motility. We elucidate, in particular, the way in which this interplay between globally external and locally internal active driving determines the emergent mechanical properties of the tissue as a whole. For a tissue in the vicinity of a solid-fluid jamming or unjamming transition, we uncover a host of fascinating rheological phenomena, including yielding, shear thinning, continuous shear thickening, and discontinuous shear thickening. These model predictions provide a framework for understanding the recently observed nonlinear rheological behaviors in vivo.

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.

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.