Topological defects in epithelia govern cell death and extrusion

Topological defects induced intra-tissue heterogeneity of mesenchymal stem cell via regulatory self-organization and differentiation

Currently, in vitro fabrication of intra-tissue heterogeneity remains a critical challenge in development of adult stem cell based tissue engineering. Interestingly, as a typical structure in symmetry-breaking phase transitions, topological defects are extensively presented in biological substances. These topological defects are commonly observed within cell monolayer in vitro and demonstrated to be effective in induction of intra-tissue heterogeneity by regulating cell migration. Nevertheless, their impacts on the behavior of mesenchymal stem cells (MSCs) remain elusive. In this study, micro-grooved substrates were utilized to explore the role of topological defects in regulation of MSCs' self-organization and osteogenic differentiation. The results indicated that topological defects could induce the central aggregates of MSCs at central region of +1 and +1/2 topological defects by modulating centripetal migration. On the contrast, negatively charged topological were able to induce centrifugal migration and further inducing heterogeneous distribution of MSCs. Subsequently, these heterogeneously distributed MSCs were capable of inducing intra-tissue heterogeneity in terms of proliferation, stemness maintenance and osteogenic differentiation via regulatory morphogenesis.

Bacillus subtilisbiofilm expansion mediated by the interaction between matrix-producing cells formed "Van Gogh bundles" and other phenotypic cells

During the expansion of Bacillus subtilis biofilm on a solid MSgg substrate, cells within the biofilm form highly organized structures through interactions, growth and differentiation. This organized structure evolves from an initial single chain to bundles known as "Van Gogh bundles," which guild the biofilm' expansion. In this paper, we present a model for biofilm growth based on cell interaction forces. In this model, cell interactions within Van Gogh bundles are represented by spring connections, and the interactions between Van Gogh bundles and other phenotypic cells are confined to a specific region (repulsive inside the region, attractive outside it). In a single-biofilm system, as nutrients are depleted, increasing numbers of motile cells transform into matrix-producing cells, forming Van Gogh bundles that guide the biofilm expansion towards areas with higher nutrient concentrations, thereby enhancing its expansion ability. In a muti-biofilm system, extreme nutrient depletion leads to the transformation of matrix-producing cells into spores, which affects the number and folding characteristics of Van Gogh bundles, thereby influencing the biofilm expansion. Our study illustrates how the simple organization of cells within a community can provide a significant ecological advantage.

Cell competition as an emerging mechanism and therapeutic target in cancer

Cell competition, as an internal quality control mechanism that constantly monitor cell fitness and eliminate unfit cells, maintains proper embryogenesis and tissue integrity during early development and adult homeostasis. Recent studies have revealed that cell competition functions as a tumor-suppressive mechanism to defend against cancer by removing neoplastic cell, which however, is hijacked by tumor cells and drive cell competition in favor of mutant cells, thereby promoting cancer initiation and progression. In this review, with a special focus on mammalian systems, we discuss the latest insights into the mechanisms regulating cell competition and its dual role in tumor development. We also provide current strategies to modulate the direction of cell competition for the prevention and treatment of cancers.

From Mechanoelectric Conversion to Tissue Regeneration: Translational Progress in Piezoelectric Materials

Piezoelectric materials, capable of converting mechanical stimuli into electrical signals, have emerged as promising tools in regenerative medicine due to their potential to stimulate tissue repair. Despite a surge in research on piezoelectric biomaterials, systematic insights to direct their translational optimization remain limited. This review addresses the current landscape by bridging fundamental principles with clinical potential. The biomimetic basis of piezoelectricity, key molecular pathways involved in the synergy between mechanical and electrical stimulation for enhanced tissue regeneration, and critical considerations for material optimization, structural design, and biosafety is discussed. More importantly, the current status and translational quagmire of mechanisms and applications in recent years are explored. A mechanism-driven strategy is proposed for the therapeutic application of piezoelectric biomaterials for tissue repair and identify future directions for accelerated clinical applications.

Interface morphodynamics in living tissues

Interfaces between distinct tissues or between tissues and environments are common in multicellular organisms. The evolution and stability of these interfaces are essential for tissue development, and their dysfunction can lead to diseases such as cancer. Mounting efforts, either theoretical or experimental, have been devoted to uncovering the morphodynamics of tissue interfaces. Here, we review the recent progress of studies on interface morphodynamics. The regulatory mechanisms governing interface evolution are dissected, with a focus on adhesion, cortical tension, cell activity, extracellular matrix, and microenvironment. We examine the methodologies used to study morphodynamics, emphasizing the characteristics of experimental techniques and theoretical models. Finally, we explore the broader implications of interface morphodynamics in tissue morphogenesis and diseases, offering a comprehensive perspective on this rapidly developing field.

Cell-Sheet Shape Transformation by Internally-Driven, Oriented Forces

During morphogenesis, cells collectively execute directional forces that drive the programmed folding and growth of the layers, forming tissues and organs. The ability to recapitulate aspects of these processes in  vitro will constitute a significant leap forward in the field of tissue engineering. Free-standing, self-organizing, cell-laden matrices are fabricated using a sequential deposition approach that uses liquid crystal-templated hydrogel fibers to direct cell arrangements. The orientation of hydrogel fibers is controlled using flow or boundary cues, while their microstructures are controlled by depletion interaction and probed by scattering and microscopy. These fibers effectively direct cells embedded in a collagen matrix, creating multilayer structures through contact guidance and by leveraging steric interactions amongst the cells. In uniformly aligned cell matrices, oriented cells exert traction forces that can induce preferential contraction of the matrix. Simultaneously, the matrix densifies and develops anisotropy through cell remodeling. Such an approach can be extended to create cell arrangements with arbitrary in-plane patterns, allowing for coordinated cell forces and pre-programmed, macroscopic shape changes. This work reveals a fundamentally new path for controlled force generation, emphasizing the role of a carefully designed initial orientational field for manipulating shape transformations of reconstituted matrices.

Entropy Production in Epithelial Monolayers Due to Collective Cell Migration

The intricate multi-scale phenomenon of entropy generation, resulting from the inhomogeneous and anisotropic rearrangement of cells during their collective migration, is examined across three distinct regimes: (i) convective, (ii) conductive (diffusion), and (iii) sub-diffusion. The collective movement of epithelial monolayers on substrate matrices induces the accumulation of mechanical stress within the cells, which subsequently influences cell packing density, velocity, and alignment. Variations in these physical parameters affect cell-cell interactions, which play a crucial role in the storage and dissipation of energy within multicellular systems. The internal dynamics of entropy generation, as a consequence of energy dissipation, are characterized in each regime using viscoelastic constitutive models and the surface properties at the cell-matrix biointerface. The focus of this theoretical review is to clarify how cells can modulate their rate of energy dissipation by altering cell-cell and cell-matrix adhesion interactions, undergoing changes in shape, and re-establishing polarity due to the contact inhibition of locomotion. We approach these questions by discussing the physical aspects of these complex phenomena.

Nonreciprocal Interactions Reshape Topological Defect Annihilation

We show how nonreciprocal ferromagnetic interactions between neighboring planar spins in two dimensions, affect the behavior of topological defects. Nonreciprocity is introduced by weighting the coupling strength of the two-dimensional XY model by an anisotropic kernel. As a consequence, in addition to the topological charge q, the actual shape of the defects becomes crucial to faithfully describe their dynamics. Nonreciprocal coupling twists the spin field, selecting specific defect shapes, dramatically altering the pair annihilation process. Defect annihilation can either be enhanced or hindered, depending on the shape of the defects concerned and the degree of nonreciprocity in the system. We introduce a continuous description-for which the phenomenological coefficients can be explicitly written in terms of the microscopic ones-that captures the behavior of the lattice model.

Differential Elasticity Affects Lineage Segregation of Embryonic Stem Cells

The question of what guides lineage segregation is central to development, where cellular differentiation leads to segregated cell populations destined for specialized functions. Here, using optical tweezers measurements of mouse embryonic stem cells, we reveal a mechanical mechanism based on differential elasticity in the second lineage segregation of the embryonic inner cell mass into epiblast (EPI) cells, which will develop into the fetus, and primitive endoderm (PrE), which will form extraembryonic structures such as the yolk sac. Remarkably, we find that these mechanical differences already occur during priming, not just after a cell has committed to differentiation. Specifically, we show that PrE-primed cells exhibit significantly higher elasticity than EPI-primed cells, characterized by lower power spectrum scaling exponents, higher Young's modulus, and lower loss tangent. Using a model of two cell types differing only in elasticity, we show that differential elasticity alone is sufficient to lead to segregation between cell types, suggesting that the mechanical attributes of the cells contribute to the segregation process. Importantly, we find that this process relies on cellular activity. Our findings present differential elasticity as a previously unknown mechanical contributor to lineage segregation during embryo morphogenesis.

Epithelial cell extrusion at a glance

The robustness and plasticity of epithelial tissues rely on the capacity of such tissues to eliminate cells without affecting their sealing. This is achieved by epithelial cell extrusion - a well-orchestrated series of remodelling steps involving the eliminated cell and its neighbours - which ensures the constant maintenance of mechanical and chemical barrier properties while allowing cell expulsion. In this Cell Science at a Glance and the accompanying poster, we describe the remodelling steps that take place within dying or extruding cells, as well as neighbouring cells, outlining the commonalities and variations between tissues and organisms. These steps include reorganization of the cytoskeleton and remodelling of cell-cell junctions that alters their contribution to mechanical coupling and mechanotransduction. We also discuss larger-scale coordination between cells and the contribution of cell extrusion to tissue morphogenesis, epithelial surveillance mechanisms, and pathologies such as cancer and chronic inflammation. Altogether, we outline the complexity and plasticity of this minimalist morphogenetic process.

Epithelial apoptosis: A back-and-forth mechanical interplay between the dying cell and its surroundings

Apoptosis is an essential cellular process corresponding to a programmed cell suicide. It has long been considered as a cell-autonomous process, supposed to have no particular impact on the surrounding tissue. However, it has become clear in the last 15 years that epithelial apoptotic cells interact mechanically and biochemically with their environment. Here, we explore recent literature on apoptotic mechanics from an individual dying cell to the back-and-forth interplay with the neighboring epithelial tissue. Finally, we discuss how caspases, key regulators of apoptosis, appear to have a dual function as a cytoskeleton regulator favoring either cytoskeleton degradation or dynamics independently of their apoptotic or non-apoptotic role.

Tissue Active Matter: Integrating Mechanics and Signaling into Dynamical Models

The importance of physical forces in the morphogenesis, homeostatic function, and pathological dysfunction of multicellular tissues is being increasingly characterized, both theoretically and experimentally. Analogies between biological systems and inert materials such as foams, gels, and liquid crystals have provided striking insights into the core design principles underlying multicellular organization. However, these connections can seem surprising given that a key feature of multicellular systems is their ability to constantly consume energy, providing an active origin for the forces that they produce. Key emerging questions are, therefore, to understand whether and how this activity grants tissues novel properties that do not have counterparts in classical materials, as well as their consequences for biological function. Here, we review recent discoveries at the intersection of active matter and tissue biology, with an emphasis on how modeling and experiments can be combined to understand the dynamics of multicellular systems. These approaches suggest that a number of key biological tissue-scale phenomena, such as morphogenetic shape changes, collective migration, or fate decisions, share unifying design principles that can be described by physical models of tissue active matter.

Active polymer behavior in two dimensions: A comparative analysis of tangential and push-pull models

In this work, we compare the structural and dynamic behavior of active filaments in two dimensions using tangential and push-pull models, including a variant with passive end monomers, to bridge the two frameworks. These models serve as valuable frameworks for understanding self-organization in biological polymers and synthetic materials. At low activity, all models exhibit similar behavior; as activity increases, subtle differences emerge in intermediate regimes, but at high activity, their behaviors converge. Adjusting for differences in mean active force reveals nearly identical behavior across models, even across varying filament configurations and bending rigidities. Our results highlight the importance of force definitions in active polymer simulations and provide insights into phase transitions across varying filament configurations.

Force transmission is a master regulator of mechanical cell competition

Cell competition is a tissue surveillance mechanism for eliminating unwanted cells, being indispensable in development, infection and tumourigenesis. Although studies have established the role of biochemical mechanisms in this process, due to challenges in measuring forces in these systems, how mechanical forces determine the competition outcome remains unclear. Here we report a form of cell competition that is regulated by differences in force transmission capabilities, selecting for cell types with stronger intercellular adhesion. Direct force measurements in ex vivo tissues and different cell lines reveal that there is an increased mechanical activity at the interface between two competing cell types, which can lead to large stress fluctuations resulting in upward forces and cell elimination. We show how a winning cell type endowed with a stronger intercellular adhesion exhibits higher resistance to elimination and benefiting from efficient force transmission to the neighbouring cells. This cell elimination mechanism could have broad implications for keeping the strong force transmission ability for maintaining tissue boundaries and cell invasion pathology.

Evidence of universal conformal invariance in living biological matter

The emergent dynamics of collective cellular movement are typically thought to depend on how cells interact with one another and the mechanisms used to drive motility, both of which exhibit remarkable diversity across different biological systems. Here we report experimental evidence of a universal feature in the patterns of flow that spontaneously emerge in groups of collectively moving cells. Specifically, we demonstrate that the flows generated by collectively moving dog kidney cells, human breast cancer cells and two different strains of pathogenic bacteria exhibit robust conformal invariance. We also show that the precise form of invariance in all four systems is described by the Schramm-Loewner evolution-a family of planar curves defined by a single parameter-and belongs to the percolation universality class. The presence of universal conformal invariance reveals that the macroscopic features of living biological matter exhibit universal translational, rotational and scale symmetries that are independent of the microscopic properties of its constituents. Our results show that flow patterns generated by different systems are highly conserved and that biological systems can be used to experimentally test predictions from the theories for conformally invariant structures.

Integer topological defects offer a methodology to quantify and classify active cell monolayers

Monolayers of confluent elongated cells are frequently considered active nematics, featuring ± 1 2 topological defects. In extensile systems, where cells extend further along their long axis, they can accumulate at + 1 2 defects and escape from - 1 2 defects. Nevertheless, collective dynamics surrounding integer defects remain insufficiently understood. We induce diverse  + 1 topological defects (asters, spirals, and targets) within neural progenitor cell monolayers using microfabricated patterns. Remarkably, cells migrate toward the cores of all  + 1 defects, challenging existing theories and conventional extensile/contractile dichotomy, which predicts escape from highly bent spirals and targets. By combining experiments and a continuum theory derived from a cell-level model, we identify previously overlooked nonlinear active forces driving this unexpected accumulation toward defect cores, providing a unified framework to explain cell behavior across defect types. Our findings establish  + 1 defects as probes to uncover key nonlinear features of active nematics, offering a methodology to characterize and classify cell monolayers.

Fluidization and anomalous density fluctuations in 2D Voronoi cell tissues with pulsating activity

Cells not only can be motile by crawling but are also capable of nonmotility active motions like periodic contraction or pulsation. In this work, based on a Voronoi cell model, we show how this nonmotility activity affects the structure, dynamic, and density fluctuations of cellular monolayers. Our model shows that random cell pulsation fluidizes solid epithelial tissues into a hyperuniform fluid state, while pulsation synchronization inhibits the fluidity and causes a reverse solidification. Our results indicate this solidification is a Berezinskii-Kosterlitz-Thouless-type transition, characterized by strong density/dynamic heterogeneity arising from the annihilation of topological defects in the pulsating phase space. The magnitude and length scale of density heterogeneity diverge with the pulsating period, resulting in an opposite giant density fluctuation or anti-hyperuniformity. We propose a fluctuating hydrodynamic theory that can unify the two opposite anomalous fluctuation phenomena. Our findings can help to understand recent experimental observations in Madin-Darby canine kidney monolayers.

The Mechanics of Building Functional Organs

Organ morphogenesis is multifaceted, multiscale, and fundamentally a robust process. Despite the complex and dynamic nature of embryonic development, organs are built with reproducible size, shape, and function, allowing them to support organismal growth and life. This striking reproducibility of tissue form exists because morphogenesis is not entirely hardwired. Instead, it is an emergent product of mechanochemical information flow, operating across spatial and temporal scales-from local cellular deformations to organ-scale form and function, and back. In this review, we address the mechanical basis of organ morphogenesis, as understood by observations and experiments in living embryos. To this end, we discuss how mechanical information controls the emergence of a highly conserved set of structural motifs that shape organ architectures across the animal kingdom: folds and loops, tubes and lumens, buds, branches, and networks. Moving forward, we advocate for a holistic conceptual framework for the study of organ morphogenesis, which rests on an interdisciplinary toolkit and brings the embryo center stage.

Turbulence-to-order transitions in activity-patterned active nematics

We numerically study two-dimensional active nematics with periodic activity patterning. For stripes of activity, we observe a transition from two-dimensional to one-dimensional active turbulence as the maximum active force and distance between activity stripes increases, followed by a transition to stable vortices ordered antiferromagnetically along the stripes and ferromagnetically transverse to the stripes. By comparing to a triangular lattice of activity circles, we find that transitions to two-dimensional active turbulence emerge from interplays between the active length scale and activity density, independent of the patterning geometry. The vortex ordering, however, is highly sensitive to patterning geometry, which we show by comparing the activity stripes to columns of activity circles, where the vortex ordering is lost. Our results provide a mechanism for inducing nonequilibrium phase transitions in active nematics using activity inhomogeneity, which can be further exploited to create activity patterned ordered phases.

Epithelial Polarity Loss and Multilayer Formation: Insights Into Tumor Growth and Regulatory Mechanisms

Epithelial tissues serve as critical barriers in metazoan organisms, maintaining structural integrity and facilitating essential physiological functions. Epithelial cell polarity regulates mechanical properties, signaling, and transport, ensuring tissue organization and homeostasis. However, the barrier function is challenged by cell turnover during development and maintenance. To preserve tissue integrity while removing dying or unwanted cells, epithelial tissues employ cell extrusion. This process removes both dead and live cells from the epithelial layer, typically causing detached cells to undergo apoptosis. Transformed cells, however, often resist apoptosis, leading to multilayered structures and early carcinogenesis. Malignant cells may invade neighboring tissues. Loss of cell polarity can lead to multilayer formation, cell extrusion, and invasion. Recent studies indicate that multilayer formation in epithelial cells with polarity loss involves a mixture of wild-type and mutant cells, leading to apical or basal accumulation. The directionality of accumulation is regulated by mutations in polarity complex genes. This phenomenon, distinct from traditional apical or basal extrusion, exhibits similarities to the endophytic or exophytic growth observed in human tumors. This review explores the regulation and implications of these phenomena for tissue biology and disease pathology.

Active Nematics Reinforce the Ratchet Flow in Dense Environments Without Jamming

The past decade witnessed a surge in discoveries where biological systems, such as bacteria or living cells, inherently portray active polar or nematic behavior: they prefer to align with each other and form local order during migration. Although the underlying mechanisms remain unclear, utilizing their physical properties to achieve controllable cell-layer transport will be of fundamental importance. In this study, the ratchet effect is harnessed to control the collective motion of neural progenitor cells (NPCs) in vitro. NPCs travel back-and-forth and do not specify head or tail, and therefore regarded as nematics alike liquid crystals. Ratchet and splay-shaped confinements are crafted to modulate collective cell dynamics in dense environments, while jamming is not explicitly spotted. The adaptation of an agent-based simulation further revealed how the ratchet's asymmetry and active forces from nematic order synergistically reinforce the directional cell flow. These findings provide insights into topotaxis in cell populations when restricted to crowded 2D ratchets and the mechanisms that regulate collective behavior of the cells.

Regulation of chromatin modifications through coordination of nucleus size and epithelial cell morphology heterogeneity

Cell morphology heterogeneity is pervasive in epithelial collectives, yet the underlying mechanisms driving such heterogeneity and its consequential biological ramifications remain elusive. Here, we observed a consistent correlation between the epithelial cell morphology and nucleus morphology during crowding, revealing a persistent log-normal probability distribution characterizing both cell and nucleus areas across diverse epithelial model systems. We showed that this morphological diversity arises from asymmetric partitioning during cell division. Next, we provide insights into the impact of nucleus morphology on chromatin modifications. We demonstrated that constraining nucleus leads to downregulation of the euchromatic mark H3K9ac and upregulation of the heterochromatic mark H3K27me3. Furthermore, we showed that nucleus size regulates H3K27me3 levels through histone demethylase UTX. These findings highlight the significance of cell morphology heterogeneity as a driver of chromatin state diversity, shaping functional variability within epithelial tissues.

Regulation of Chromatin Modifications through Coordination of Nucleus Size and Epithelial Cell Morphology Heterogeneity

Cell morphology heterogeneity is pervasive in epithelial collectives, yet the underlying mechanisms driving such heterogeneity and its consequential biological ramifications remain elusive. Here, we observed a consistent correlation between the epithelial cell morphology and nucleus morphology during crowding, revealing a persistent log-normal probability distribution characterizing both cell and nucleus areas across diverse epithelial model systems. We further showed that this morphological diversity arises from asymmetric partitioning during cell division. Moreover, we provide insights into the impact of nucleus morphology on chromatin modifications. We demonstrated that constraining nucleus leads to downregulation of the euchromatic mark H3K9ac and upregulation of the heterochromatic mark H3K27me3. Furthermore, we showed that nucleus size regulates H3K27me3 levels through histone demethylase UTX. These findings highlight the significance of cell morphology heterogeneity as a driver of chromatin state diversity, shaping functional variability within epithelial tissues.

Local polar order controls mechanical stress and triggers layer formation in Myxococcus xanthus colonies

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are substantially larger than the mean due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.

Topology changes of Hydra define actin orientation defects as organizers of morphogenesis

Hydra regenerates one head when cut, but how forces shaping the head are coordinated remains unclear. Soft compression of Hydra's head-regenerating tissues induces the formation of viable, two-headed animals. Compression creates new topological defects in the supracellular orientational order of muscular actin fibers, associated with additional heads. Theory supports that these defects organize muscle stresses required to shape the head. By compressing head-regenerating tissues along their body axis, we formed toroidal tissues, whose unique topology allows for the absence of defects. Toroids with no actin defects did not regenerate. Toroids with actin defects regenerated into viable toroidal animals with a bifurcated body. Topological defects in the actin orientational order are thus necessary for complete regeneration of Hydra, defining actin topological defects as mechanical organizers of morphogenesis.

Vertex model with internal dissipation enables sustained flows

Complex tissue flows in epithelia are driven by intra- and inter-cellular processes that generate, maintain, and coordinate mechanical forces. There has been growing evidence that cell shape anisotropy, manifested as nematic order, plays an important role in this process. Here we extend an active nematic vertex model by replacing substrate friction with internal viscous dissipation, dominant in epithelia not supported by a substrate or the extracellular matrix, which are found in many early-stage embryos. When coupled to cell shape anisotropy, the internal viscous dissipation allows for long-range velocity correlations and thus enables the spontaneous emergence of flows with a large degree of spatiotemporal organisation. We demonstrate sustained flow in epithelial sheets confined to a channel, providing a link between the cell-level vertex model of tissue dynamics and continuum active nematics, whose behaviour in a channel is theoretically understood and experimentally realisable. Our findings also show a simple mechanism that could account for collective cell migration correlated over distances large compared to the cell size, as observed during morphogenesis.

Noise-induced transitions from contractile to extensile active stress in isotropic fluids

Tissues of living cells are a prime example of active fluids. There is experimental evidence that tissues generate extensile active stress even though their constituting cells are contractile. Fluctuating forces that could result from cell-substrate interactions have been proposed to be able to induce a transition from contractile to extensile active stress. We define the notion of contractile and extensile active stress in isotropic and anisotropic active matter. Through analytic calculations and numerical computations, we then show that in isotropic active fluids, nonlinearities and coupling between fluctuating forces and fluid density are necessary for such a transition to occur. Here, both transitions from extensile to contractile and vice versa are possible.

Multiparticle collision framework for active polar fluids

Sufficiently dense intrinsically out-of-equilibrium suspensions, such as those observed in biological systems, can be modeled as active fluids characterized by their orientational symmetry. While mesoscale numerical approaches to active nematic fluids have been developed, polar fluids are simulated as either ensembles of microscopic self-propelled particles or continuous hydrodynamic-scale equations of motion. To better simulate active polar fluids in complex geometries or as a solvent for suspensions, mesoscale numerical approaches are needed. In this work, the coarse-graining multiparticle collision dynamics (MPCD) framework is applied to three active particle models to produce mesoscale simulations of polar active fluids. The first active-polar MPCD (AP-MPCD) is a variant of the Vicsek model, while the second and third variants allow the speed of the particles to relax towards a self-propulsion speed subject to Andersen and Langevin thermostats, respectively. Each of these AP-MPCD variants exhibits a flocking transition at a critical activity and banding in the vicinity of the transition point. We leverage the mesoscale nature of AP-MPCD to explore flocking in the presence of external fields, which destroys banding, and anisotropic obstacles, which act as a ratchet that biases the flocking direction. These results demonstrate the capacity of AP-MPCD to capture the known phenomenology of polar active suspensions and its versatility to study active polar fluids in complex scenarios.

Deviation of a system of nonreciprocally coupled harmonic oscillators from a conservative system

Discrete systems of coupled linear mechanical oscillators with nonreciprocal interaction are a model for a variety of physical systems. In general, the presence of nonreciprocal interactions renders their dynamics nonconservative, but under certain conditions it remains conservative. In this paper we show which thermodynamic properties induced by nonreciprocity can be observed in conservative systems and which are specific to nonconservative systems. To this end, we formulate a criterion for identifying conservative systems and construct a measure to quantify the deviation from conservativity.

Integer Topological Defects Reveal Antisymmetric Forces in Active Nematics

Cell layers are often categorized as contractile or extensile active, nematics but recent experiments on neural progenitor cells with induced +1 topological defects challenge this classification. In a bottom-up approach, we first study a relevant particle-level model and then analyze a continuum theory derived from it. We show that both model and theory account qualitatively for the main experimental result, i.e., accumulation of cells at the core of any type of +1 defect. We argue that cell accumulation is essentially due to two generally ignored antisymmetric active forces. We finally discuss the relevance and consequences of our findings in the context of other cellular active nematics experiments and previously proposed theories.

Analytical model for the motion and interaction of two-dimensional active nematic defects

We develop an approximate, analytical model for the velocity of defects in active nematics by combining recent results for the velocity of topological defects in nematic liquid crystals with the flow field generated from individual defects in active nematics. Importantly, our model takes into account the long-range interactions between defects that result from the flows they produce as well as the orientational coupling between defects inherent in nematics. Our work complements previous studies of active nematic defect motion by introducing a linear approximation that allows us to treat defect interactions as two-body interactions and incorporates the hydrodynamic screening length as a tuning parameter. We show that the model can analytically predict bound states between two +1/2 winding number defects, effective attraction between two -1/2 defects, and the scaling of a critical unbinding length between ±1/2 defects with activity. The model also gives predictions for the trajectories of defects, such as the scattering of +1/2 defects by -1/2 defects at a critical impact parameter that depends on activity. In the presence of circular confinement, the model predicts a braiding motion for three +1/2 defects that was recently seen in experiments, as well as stable and ergodic trajectories for four or more defects.

Cell Sorting in an Active Nematic Vertex Model

We study a mixture of extensile and contractile cells using a vertex model extended to include active nematic stresses. The two cell populations phase separate over time. While phase separation strengthens monotonically with an increasing magnitude of contractile activity, the dependence on extensile activity is nonmonotonic, so that sufficiently high values reduce the extent of sorting. We interpret this by showing that extensile activity renders the system motile, enabling cells to undergo neighbor exchanges. Contractile cells that come into contact as a result are then more likely to stay connected due to an effective attraction arising from contractile activity.

Liquid Crystalline Hydroxyapatite Nanorods Orchestrate Hierarchical Bone-Like Mineralization

Bone matrix exhibits exceptional mechanical properties due to its unique nanocomposite structure of type I collagen fibrils and hydroxyapatite (HAp) nanoparticles in hierarchical liquid crystalline (LC) order. However, the regeneration mechanism of this LC structure is elusive. This study investigates the role of the LC structure of HAp nanorods in guiding aligned mineralization and its underlying molecular mechanism. A unidirectionally oriented LC phase of HAp nanorods is developed through engineering-assisted self-assembling. This is used to study the growth direction of long-range aligned extracellular matrix (ECM) and calcium deposit formation during the osteogenic differentiation of human bone marrow-derived mesenchymal stem cells. It is found that 2 key regulatory genes, COL1A1 and COL4A6, lead to the formation of aligned ECM. Activation of the PI3K-Akt pathway enhances osteogenesis and promotes ordered calcium deposits. This study provides evidence for elucidating the mechanism of LC-induced ordered calcium deposition at hierarchical levels spanning from the molecular to macro-scale, as well as the switch from ordered to disordered mineralization. These findings illuminate bone regeneration, contribute to the development of biomimetic artificial bone with long-range ordered structures, and suggest a basis for therapeutic targeting of microstructure-affected bone disorders and the broader field of cell-ECM interactions.

Spontaneous flows and quantum analogies in heterogeneous active nematic films

Incorporating the inherent heterogeneity of living systems into models of active nematics is essential to provide a more realistic description of biological processes such as bacterial growth, cell dynamics and tissue development. Spontaneous flow of a confined active nematic is a fundamental feature of these systems, in which the role of heterogeneity has not yet been considered. We therefore determine the form of spontaneous flow transition for an active nematic film with heterogeneous activity, identifying a correspondence between the unstable director modes and solutions to Schrödinger's equation. We consider both activity gradients and steps between regions of distinct activity, finding that such variations can change the signature properties of the flow. The threshold activity required for the transition can be raised or lowered, the fluid flux can be reduced or reversed and interfaces in activity induce shear flows. In a biological context fluid flux influences the spread of nutrients while shear flows affect the behaviour of rheotactic microswimmers and can cause the deformation of biofilms. All the effects we identify are found to be strongly dependent on not simply the types of activity present in the film but also on how they are distributed.

Different Biomechanical Cell Behaviors in an Epithelium Drive Collective Epithelial Cell Extrusion

In vertebrates, many organs, such as the kidney and the mammary gland form ductal structures based on the folding of epithelial sheets. The development of these organs relies on coordinated sorting of different cell lineages in both time and space, through mechanisms that remain largely unclear. Tissues are composed of several cell types with distinct biomechanical properties, particularly at cell-cell and cell-substrate boundaries. One hypothesis is that adjacent epithelial layers work in a coordinated manner to shape the tissue. Using in vitro experiments on model epithelial cells, differential expression of atypical Protein Kinase C iota (aPKCi), a key junctional polarity protein, is shown to reinforce cell epithelialization and trigger sorting by tuning cell mechanical properties at the tissue level. In a broader perspective, it is shown that in a heterogeneous epithelial monolayer, in which cell sorting occurs, forces arising from epithelial cell growth under confinement by surrounding cells with different biomechanical properties are sufficient to promote collective cell extrusion and generate emerging 3D organization related to spheroids and buds. Overall, this research sheds light on the role of aPKCi and the biomechanical interplay between distinct epithelial cell lineages in shaping tissue organization, providing insights into the understanding of tissue and organ development.

Curvature-directed anchoring and defect structure of colloidal smectic liquid crystals in confinement

Rod-like objects at high packing fractions can exhibit liquid crystalline ordering. By controlling how the rods align near a boundary, i.e. the anchoring, the defects of a liquid crystal can be selected and tuned. For smectic phases, the rods break rotational and translational symmetry by forming lamellae. Smectic defects thereby include both discontinuities in the rod orientational order (disclinations), as well as in the positional order (dislocations). In this work, we use experiments and simulations to uncover the geometrical conditions necessary for a boundary to set the anchoring of a confined, particle-resolved, smectic liquid crystal. We confine a colloidal smectic within elliptical wells of varying size and shape for a smooth variation of the boundary curvature. We find that the anchoring depends upon the local boundary curvature, with an anchoring transition observed at a critical radius of curvature approximately twice the rod length. Surprisingly, the critical radius of curvature for an anchoring transition holds across a wide range of rod lengths and packing fractions. The anchoring controls the defect structure. By analyzing topological charges and networks composed of maximum density (rod centers) and minimum density (rod ends), we quantify disclinations and dislocations formed with varying confinement geometry. Circular confinements, characterized by planar anchoring, promote disclinations, whereas elliptical confinements, featuring antipodal regions of homeotropic anchoring, promote long-range smectic order and dislocations. Our findings demonstrate how geometrical constraints can control the anchoring and defect structures of liquid crystals-a principle that is applicable from molecular to colloidal length scales.

Energetic scaling behavior of patterned epithelium

Cellular monolayers display various degrees of coordinated motion ranging from the small scale of just a few cells to large multi-cellular scales. This collective migration carries important physical cues for creating proper tissue morphology. Previous studies have demonstrated that the energetics of the epithelial monolayer show a linear variation with time in conjunction with an arrest in monolayer motion after confluency. However, little is known about how the energetics of monolayer development are affected by confined geometries. Here, we demonstrate that micropatterned epithelial monolayers display a non-linear change in energetic variables, which coincides with the large-scale coordination of migration. This non-linear scaling behavior was further seen to be associated with the biased alignment of cells and cell-cell adhesion. These findings provide a new understanding of how developing epithelia may be impacted by different conditions in vivo.

Physical aspects of epithelial cell-cell interactions: hidden system complexities

The maintenance of homeostasis and the retention of ordered epithelial cell self-organization are essential for morphogenesis, wound healing, and the spread of cancer across the epithelium. However, cell-cell interactions in an overcrowded environment introduce a diversity of complications. Such interactions arise from an interplay between the cell compressive and shear stress components that accompany increased cell packing density. They can lead to various kinds of cell rearrangement such as: the epithelial-to-mesenchymal cell state transition; live cell extrusion; and cell jamming. All of these scenarios of cell rearrangement under mechanical stress relate to changes in the strengths of the cell-cell and cell-matrix adhesion contacts. The objective of this review study is twofold: first, to provide a comprehensive summary of the biological and physical factors influencing the effects of cell mechanical stress on cell-cell interactions, and the consequences of these interactions for the status of cell-cell and cell-matrix adhesion contacts; and secondly, to offer a bio-physical/mathematical analysis of the aforementioned biological aspects. By presenting these two approaches in conjunction, we seek to highlight the intricate nature of biological systems, which manifests in the form of complex bio-physical/mathematical equations. Furthermore, the juxtaposition of these apparently disparate approaches underscores the importance of conducting experiments to determine the multitude of parameters that contribute to the development of these intricate bio-physical/mathematical models.

Strain rate controls alignment in growing bacterial monolayers

Growing monolayers of rod-shaped bacteria exhibit local alignment similarly to extensile active nematics. When confined in a channel or growing inward from a ring, the local nematic order of these monolayers changes to a global ordering with cells throughout the monolayer orienting in the same direction. The mechanism behind this phenomenon is so far unclear, as previously proposed mechanisms fail to predict the correct alignment direction in one or more confinement geometries. We present a strain-based model relating net deformation of the growing monolayer to the cell-level deformation resulting from single-cell growth and rotation, producing predictions of cell orientation behavior based on the velocity field in the monolayer. This model correctly predicts the direction of preferential alignment in channel-confined, inward growing, and unconfined colonies. The model also quantitatively predicts orientational order when the velocity field has no net negative strain rate in any direction. We further test our model in simulations of expanding colonies confined to spherical surfaces. Our model and simulations agree that cells away from the origin cell orient radially relative to the colony's center. Additionally, our model's quantitative prediction of the orientational order agrees with the simulation results in the top half of the sphere but fails in the lower half where there is a net negative strain rate. The success of our model bridges the gap between previous works on cell alignment in disparate confinement geometries and provides insight into the underlying physical effects responsible for large-scale alignment.

Active nematics in corrugated channels

Active nematic fluids exhibit complex dynamics in both bulk and in simple confining geometries. However, complex confining geometries could have substantial impact on active spontaneous flows. Using multiparticle collision dynamics simulations adapted for active nematic particles, we study the dynamic behaviour of an active nematic fluid confined in a corrugated channel. The transition from a quiescent state to a spontaneous flow state occurs from a weak swirling flow to a strong coherent flow due to the presence of curved-wall induced active flows. We show that the active nematic fluid flows in corrugated channels can be understood in two different ways: (i) as the result of an early or delayed flow transition when compared with that in a flat-walled channel of appropriate width and (ii) boundary-induced active flows in the corrugations providing an effective slip velocity to the coherent flows in the bulk. Thus, our work illustrates the crucial role of corrugations of the confining boundary in dictating the flow transition and flow states of active fluids.

Reduction of endocytosis and EGFR signaling is associated with the switch from isolated to clustered apoptosis during epithelial tissue remodeling in Drosophila

Epithelial tissues undergo cell turnover both during development and for homeostatic maintenance. Removal of cells is coordinated with the increase in number of newly dividing cells to maintain barrier function of the tissue. In Drosophila metamorphosis, larval epidermal cells (LECs) are replaced by adult precursor cells called histoblasts. Removal of LECs must counterbalance the exponentially increasing adult histoblasts. Previous work showed that the LEC removal accelerates as endocytic activity decreases throughout all LECs. Here, we show that the acceleration is accompanied by a mode switching from isolated single-cell apoptosis to clustered ones induced by the endocytic activity reduction. We identify the epidermal growth factor receptor (EGFR) pathway via extracellular-signal regulated kinase (ERK) activity as the main components downstream of endocytic activity in LECs. The reduced ERK activity, caused by the decrease in endocytic activity, is responsible for the apoptotic mode switching. Initially, ERK is transiently activated in normal LECs surrounding a single apoptotic LEC in a ligand-dependent manner, preventing clustered cell death. Following the reduction of endocytic activity, LEC apoptosis events do not provoke these transient ERK up-regulations, resulting in the acceleration of the cell elimination rate by frequent clustered apoptosis. These findings contrasted with the common perspective that clustered apoptosis is disadvantageous. Instead, switching to clustered apoptosis is required to accommodate the growth of neighboring tissues.

Intercellular friction and motility drive orientational order in cell monolayers

Spatiotemporal patterns in multicellular systems are important to understanding tissue dynamics, for instance, during embryonic development and disease. Here, we use a multiphase field model to study numerically the behavior of a near-confluent monolayer of deformable cells with intercellular friction. Varying friction and cell motility drives a solid-liquid transition, and near the transition boundary, we find the emergence of local nematic order of cell deformation driven by shear-aligning cellular flows. Intercellular friction contributes to the monolayer's viscosity, which significantly increases the spatial correlation in the flow and, concomitantly, the extent of nematic order. We also show that local hexatic and nematic order are tightly coupled and propose a mechanical-geometric model for the colocalization of [Formula: see text] nematic defects and 5-7 disclination pairs, which are the structural defects in the hexatic phase. Such topological defects coincide with regions of high cell-cell overlap, suggesting that they may mediate cellular extrusion from the monolayer, as found experimentally. Our results delineate a mechanical basis for the recent observation of nematic and hexatic order in multicellular collectives in experiments and simulations and pinpoint a generic pathway to couple topological and physical effects in these systems.

Bioprinting of Cells, Organoids and Organs-on-a-Chip Together with Hydrogels Improves Structural and Mechanical Cues

The 3D bioprinting technique has made enormous progress in tissue engineering, regenerative medicine and research into diseases such as cancer. Apart from individual cells, a collection of cells, such as organoids, can be printed in combination with various hydrogels. It can be hypothesized that 3D bioprinting will even become a promising tool for mechanobiological analyses of cells, organoids and their matrix environments in highly defined and precisely structured 3D environments, in which the mechanical properties of the cell environment can be individually adjusted. Mechanical obstacles or bead markers can be integrated into bioprinted samples to analyze mechanical deformations and forces within these bioprinted constructs, such as 3D organoids, and to perform biophysical analysis in complex 3D systems, which are still not standard techniques. The review highlights the advances of 3D and 4D printing technologies in integrating mechanobiological cues so that the next step will be a detailed analysis of key future biophysical research directions in organoid generation for the development of disease model systems, tissue regeneration and drug testing from a biophysical perspective. Finally, the review highlights the combination of bioprinted hydrogels, such as pure natural or synthetic hydrogels and mixtures, with organoids, organoid-cell co-cultures, organ-on-a-chip systems and organoid-organ-on-a chip combinations and introduces the use of assembloids to determine the mutual interactions of different cell types and cell-matrix interferences in specific biological and mechanical environments.

Skyrmion engineering with origami

Skyrmion structures play critical roles in solid-state systems involving electric, magnetic and optical fields. Previous approaches to the study of skyrmions have involved specific structures in magnetic materials, liquid crystals and polymers in addition to two-dimensional arrays used for electrical control. These methods have encountered limitations and constraints on both the microscopic and macroscopic scales related to the physical properties of materials. The present work demonstrates an origami-based skyrmion engineering strategy that suggests a new approach to topological control. This technique utilizes the unique properties of orientational origami, combining polarization techniques with rotationally symmetric, periodically folded designs. This strategy enables the transformation of flat sheets into three-dimensional structures with associated changes in optical topology, similar to the characteristics of proteins. Topological defects such as misalignments and dislocations in folded molecularly oriented sheets lead to the creation of skyrmion clusters at boundaries having different orientational orders. The strategy reported herein involves the construction of unique metamaterial platforms that could provide new applications for twistronics in graphene and photonic crystals.

Spatiotemporal control of structure and dynamics in a polar active fluid

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.

Many-defect solutions in planar nematics: interactions, spiral textures and boundary conditions

From incompressible flows to electrostatics, harmonic functions can provide solutions to many two-dimensional problems and, similarly, the director field of a planar nematic can be determined using complex analysis. We derive a closed-form solution for a quasi-steady state director field induced by an arbitrarily large set of point defects and circular inclusions with or without fixed rotational degrees of freedom, and compute the forces and torques acting on each defect or inclusion. We show that a complete solution must include two types of singularities, generating a defect winding number and its spiral texture, which have a direct effect on defect equilibrium textures and their dynamics. The solution accounts for discrete degeneracy of topologically distinct free energy minima which can be obtained by defect braiding. The derived formalism can be readily applied to equilibrium and slowly evolving nematic textures for active or passive fluids with multiple defects present within the orientational order.

Epithelial cell-cell interactions in an overcrowded environment: jamming or live cell extrusion

Epithelial tissues respond strongly to the mechanical stress caused by collective cell migration and are able to regulate it, which is important for biological processes such as morphogenesis, wound healing, and suppression of the spread of cancer. Compressive, tensional, and shear stress components are produced in cells when epithelial monolayers on substrate matrices are actively or passively wetted or de-wetted. Increased compressive stress on cells leads to enhanced cell-cell interactions by increasing the frequency of change the cell-cell distances, triggering various signalling pathways within the cells. This can ultimately lead either to cell jamming or to the extrusion of live cells. Despite extensive research in this field, it remains unclear how cells decide whether to jam, or to extrude a cell or cells, and how cells can reduce the compressive mechanical stress. Live cell extrusion from the overcrowded regions of the monolayers is associated with the presence of topological defects of cell alignment, induced by an interplay between the cell compressive and shear stress components. These topological defects stimulate cell re-alignment, as a part of the cells' tendency to re-establish an ordered trend of cell migration, by intensifying the glancing interactions in overcrowded regions. In addition to individual cell extrusion, collective cell extrusion has also been documented during monolayer active de-wetting, depending on the cell type, matrix stiffness, and boundary conditions. Cell jamming has been discussed in the context of the cells' contact inhibition of locomotion caused by cell head-on interactions. Since cell-cell interactions play a crucial role in cell rearrangement in an overcrowded environment, this review is focused on physical aspects of these interactions in order to stimulate further biological research in the field.

Patterning in stratified epithelia depends on cell-cell adhesion

Epithelia consist of proliferating and differentiating cells that often display patterned arrangements. However, the mechanism regulating these spatial arrangements remains unclear. Here, we show that cell-cell adhesion dictates multicellular patterning in stratified epithelia. When cultured keratinocytes, a type of epithelial cell in the skin, are subjected to starvation, they spontaneously develop a pattern characterized by areas of high and low cell density. Pharmacological and knockout experiments show that adherens junctions are essential for patterning, whereas the mathematical model that only considers local cell-cell adhesion as a source of attractive interactions can form regions with high/low cell density. This phenomenon, called cell-cell adhesion-induced patterning (CAIP), influences cell differentiation and proliferation through Yes-associated protein modulation. Starvation, which induces CAIP, enhances the stratification of the epithelia. These findings highlight the intrinsic self-organizing property of epithelial cells.

Density and inertia effects on two-dimensional active semiflexible filament suspensions

We examine the influence of density on the transition between chain and spiral structures in planar assemblies of active semiflexible filaments, utilizing detailed numerical simulations. We focus on how increased density, and higher Péclet numbers, affect the activity-induced transition spiral state in a semiflexible, self-avoiding active chain. Our findings show that increasing the density causes the spiral state to break up, reverting to a motile chain-like shape. This results in a density-dependent reentrant phase transition from spirals back to open chains. We attribute this phenomenon to an inertial effect observed at the single polymer level, where increased persistence length due to inertia has been shown in recent three-dimensional studies to cause polymers to open up. Our two-dimensional simulations further reveal that a reduction in the damping coefficient leads to partial unwinding of the spirals, forming longer arms. In suspension, interactions among these extended arms can trigger a complete unwinding of the spirals, driven by the combined effects of density and inertia.

Phase ordering in binary mixtures of active nematic fluids

We use a continuum, two-fluid approach to study a mixture of two active nematic fluids. Even in the absence of thermodynamically driven ordering, for mixtures of different activities we observe turbulent microphase separation, where domains form and disintegrate chaotically in an active turbulent background. This is a weak effect if there is no elastic nematic alignment between the two fluid components, but is greatly enhanced in the presence of an elastic alignment or substrate friction. We interpret the results in terms of relative flows between the two species which result from active anchoring at concentration gradients. Our results may have relevance in interpreting epithelial cell sorting and the dynamics of multispecies bacterial colonies.