Topological defects in epithelia govern cell death and extrusion

Analysis of the number of topological defects in active nematic fluids under applied shear flow

The number of topological defects in the shear flow of active nematic fluids is numerically investigated in this study. The evolution of the flow state of extensile active nematic fluids is explored by increasing the activity of active nematic fluids. Evidently, medium-activity active nematic fluids exhibit a highly ordered vortex lattice fluid state. However, high-activity active nematic fluids exhibit a meso-scale turbulent flow accompanied by topological defects. The number of topological defects (Ndef) increases with increasing shear Reynolds number (Res). Fluid viscosity strongly influences Ndef, while the influence of fluid density is relatively weak. Ndef decreases with increasing activity length scale (lζ) value. A small Res value strongly influences Ndef, whereas a large lζ value only weakly influences Ndef. As the activity increases, Ndef in contractile active nematic fluids becomes larger than that of extensile active nematic fluids.

Topological defects in multi-layered swarming bacteria

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid dynamics of swarming bacteria. The results are compared to the predictions of two-dimensional active nematics. We show that, even though some of the assumptions underlying the theory do not hold, the swarm dynamics is in agreement with two-dimensional nematic theory. In particular, we look into the multi-layered structure of the swarm, which is an important feature of real, natural colonies, and find a strong coupling between layers. Our results suggest that the defect-charge density is hyperuniform, i.e., that long range density-fluctuations are suppressed.

Cell Division and Motility Enable Hexatic Order in Biological Tissues

Biological tissues transform between solid- and liquidlike states in many fundamental physiological events. Recent experimental observations further suggest that in two-dimensional epithelial tissues these solid-liquid transformations can happen via intermediate states akin to the intermediate hexatic phases observed in equilibrium two-dimensional melting. The hexatic phase is characterized by quasi-long-range (power-law) orientational order but no translational order, thus endowing some structure to an otherwise structureless fluid. While it has been shown that hexatic order in tissue models can be induced by motility and thermal fluctuations, the role of cell division and apoptosis (birth and death) has remained poorly understood, despite its fundamental biological role. Here we study the effect of cell division and apoptosis on global hexatic order within the framework of the self-propelled Voronoi model of tissue. Although cell division naively destroys order and active motility facilitates deformations, we show that their combined action drives a liquid-hexatic-liquid transformation as the motility increases. The hexatic phase is accessed by the delicate balance of dislocation defect generation from cell division and the active binding of disclination-antidisclination pairs from motility. We formulate a mean-field model to elucidate this competition between cell division and motility and the consequent development of hexatic order.

A theoretical model of anaphase

This paper develops a theory for anaphase in cells. After a brief description of microtubules, the mitotic spindle and the centrosome, a mathematical model for anaphase is introduced and developed in the context of the cell cytoplasm and liquid crystalline structures. Prophase, prometaphase and metaphase are then briefly described in order to focus on anaphase, which is the main study of this paper. The entities involved are modelled in terms of liquid crystal defects and microtubules are represented as defect flux lines. The mathematical techniques employed make extensive use of energy considerations based on the work that was developed by Dafermos (1970) from the classical Frank-Oseen nematic liquid crystal energy (Frank, 1958; Oseen, 1933). With regard to liquid crystal theory we introduce the concept of regions of influence for defects which it is believed have important implications beyond the subject of this paper. The results of this paper align with observed biochemical phenomena and are explored in application to HeLa cells and Caenorhabditis elegans. This unified approach offers the possibility of gaining insight into various consequences of mitotic abnormalities which may result in Down syndrome, Hodgkin lymphoma, breast, prostate and various other types of cancer.

Design rules for controlling active topological defects

Topological defects play a central role in the physics of many materials, including magnets, superconductors, and liquid crystals. In active fluids, defects become autonomous particles that spontaneously propel from internal active stresses and drive chaotic flows stirring the fluid. The intimate connection between defect textures and active flow suggests that properties of active materials can be engineered by controlling defects, but design principles for their spatiotemporal control remain elusive. Here, we propose a symmetry-based additive strategy for using elementary activity patterns, as active topological tweezers, to create, move, and braid such defects. By combining theory and simulations, we demonstrate how, at the collective level, spatial activity gradients act like electric fields which, when strong enough, induce an inverted topological polarization of defects, akin to a negative susceptibility dielectric. We harness this feature in a dynamic setting to collectively pattern and transport interacting active defects. Our work establishes an additive framework to sculpt flows and manipulate active defects in both space and time, paving the way to design programmable active and living materials for transport, memory, and logic.

Mechanochemical dynamics of collective cells and hierarchical topological defects in multicellular lumens

Collective cell dynamics is essential for tissue morphogenesis and various biological functions. However, it remains incompletely understood how mechanical forces and chemical signaling are integrated to direct collective cell behaviors underlying tissue morphogenesis. Here, we propose a three-dimensional (3D) mechanochemical theory accounting for biochemical reaction-diffusion and cellular mechanotransduction to investigate the dynamics of multicellular lumens. We show that the interplay between biochemical signaling and mechanics can trigger either pitchfork or Hopf bifurcation to induce diverse static mechanochemical patterns or generate oscillations with multiple modes both involving marked mechanical deformations in lumens. We uncover the crucial role of mechanochemical feedback in emerging morphodynamics and identify the evolution and morphogenetic functions of hierarchical topological defects including cell-level hexatic defects and tissue-level orientational defects. Our theory captures the common mechanochemical traits of collective dynamics observed in experiments and could provide a mechanistic context for understanding morphological symmetry breaking in 3D lumen-like tissues.

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.

Stress-shape misalignment in confluent cell layers

In tissue formation and repair, the epithelium undergoes complex patterns of motion driven by the active forces produced by each cell. Although the principles governing how the forces evolve in time are not yet clear, it is often assumed that the contractile stresses within the cell layer align with the axis defined by the body of each cell. Here, we simultaneously measured the orientations of the cell shape and the cell-generated contractile stresses, observing correlated, dynamic domains in which the stresses were systematically misaligned with the cell body. We developed a continuum model that decouples the orientations of contractile stress and cell body. The model recovered the spatial and temporal dynamics of the regions of misalignment in the experiments. These findings reveal that the cell controls its contractile forces independently from its shape, suggesting that the physical rules relating cell forces and cell shape are more flexible than previously thought.

Non-equilibrium structural and dynamic behaviors of active polymers in complex and crowded environments

Active matter systems, which convert internal chemical energy or energy from the environment into directed motion, are ubiquitous in nature and exhibit a range of emerging non-equilibrium behaviors. However, most of the current works on active matter have been devoted to particles, and the study of active polymers has only recently come into the spotlight due to their prevalence within living organisms. The intricate interplay between activity and conformational degrees of freedom gives rise to novel structural and dynamical behaviors of active polymers. Research in active polymers remarkably broadens diverse concepts of polymer physics, such as molecular architecture, dynamics, scaling and so on, which is of significant importance for the development of new polymer materials with unique performance. Furthermore, active polymers are often found in strongly interacting and crowded systems and in complex environments, so that the understanding of this behavior is essential for future developments of novel polymer-based biomaterials. This review thereby focuses on the study of active polymers in complex and crowded environments, and aims to provide insights into the fundamental physics underlying the adaptive and collective behaviors far from equilibrium, as well as the open challenges that the field is currently facing.

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

Cell morphology heterogeneity within epithelial collectives is a pervasive phenomenon intertwined with tissue mechanical properties. Despite its widespread occurrence, the underlying mechanisms driving cell morphology heterogeneity and its consequential biological ramifications remain elusive. Here, we investigate the dynamic evolution of epithelial cell morphology and nucleus morphology during crowding, unveiling a consistent correlation between the two. Our investigation reveals a persistent log-normal probability distribution characterizing both cell and nucleus areas across diverse crowding stages and epithelial model systems. We showed that this morphological diversity arises from asymmetric partitioning during cell division and is perpetuated through actomyosin-mediated regulation of cell-nucleus size coordination. Moreover, we provide insights into the impact of nucleus morphology on chromatin dynamics, demonstrating that constraining nucleus area leads to downregulation of the euchromatic mark H3K9ac and upregulation of the heterochromatic mark H3K27me3 through modulation of histone demethylase UTX expression. These findings under-score the significance of cell morphology heterogeneity as a driver of chromatin state diversity, shaping functional variability within epithelial tissues.

Topology-guided polar ordering of collective cell migration

The ability of epithelial monolayers to self-organize into a dynamic polarized state, where cells migrate in a uniform direction, is essential for tissue regeneration, development, and tumor progression. However, the mechanisms governing long-range polar ordering of motility direction in biological tissues remain unclear. Here, we investigate the self-organizing behavior of quiescent epithelial monolayers that transit to a dynamic state with long-range polar order upon growth factor exposure. We demonstrate that the heightened self-propelled activity of monolayer cells leads to formation of vortex-antivortex pairs that undergo sequential annihilation, ultimately driving the spread of long-range polar order throughout the system. A computational model, which treats the monolayer as an active elastic solid, accurately replicates this behavior, and weakening of cell-to-cell interactions impedes vortex-antivortex annihilation and polar ordering. Our findings uncover a mechanism in epithelia, where elastic solid material characteristics, activated self-propulsion, and topology-mediated guidance converge to fuel a highly efficient polar self-ordering activity.

Epithelial cells crowded out in asthma

Bronchoconstriction causes epithelial cell extrusion that promotes airway inflammation.

Topological balance of cell distributions in plane monolayers

Most of normal proliferative epithelia of plants and metazoans are topologically invariant and characterized by similar cell distributions according to the number of cell neighbors (DCNs). Here we study peculiarities of these distributions and explain why the DCN obtained from the location of intercellular boundaries and that based on the Voronoi tessellation with nodes located on cell nuclei may differ from each other. As we demonstrate, special microdomains where four or more intercellular boundaries converge are topologically charged. Using this fact, we deduce a new equation describing the topological balance of the DCNs. The developed theory is applied for a series of microphotographs of non-tumoral epithelial cells of the human cervix (HCerEpiC) to improve the image processing near the edges of microphotographs and reveal the topological invariance of the examined monolayers. Special contact microdomains may be present in epithelia of various natures, however, considering the well-known vertex model of epithelium, we show that such contacts are absent in the usual solid-like state of the model and appear only in the liquid-like cancer state. Also, we discuss a possible biological role of special contacts in context of proliferative epithelium dynamics and tissue morphogenesis.

The collective dynamics of frustrated biological neuron networks

To maintain normal functionality, it is necessary for a multicellular organism to generate robust responses to external temporal signals. However, the underlying mechanisms to coordinate the collective dynamics of cells remain poorly understood. Here we study the calcium activity of micropatterned biological neuron networks excited by periodic ATP stimuli. Combining quantitative experiments, physical and biological manipulation of cells, as well as mathematical modeling, we show that isolated cells in a network become more synchronized at longer period of stimuli through noise cancellation. However, slowly varying external signal also increases gap junction coupling between connected nodes in the network; and gap junction mediated communication may destroy network synchronization due to special nonlinear bifurcations exhibited by the excitable dynamics of neuronal cells. Based on our results, we propose that a biological neuron network supported by gap junctional communication encodes external temporal signals in its network dynamics. A sparely connected network approaches synchronization as input signal slows down, whereas a highly connected network enters dynamic frustration in the same situation.

Organoids as preclinical models of human disease: progress and applications

In the field of biomedical research, organoids represent a remarkable advancement that has the potential to revolutionize our approach to studying human diseases even before clinical trials. Organoids are essentially miniature 3D models of specific organs or tissues, enabling scientists to investigate the causes of diseases, test new drugs, and explore personalized medicine within a controlled laboratory setting. Over the past decade, organoid technology has made substantial progress, allowing researchers to create highly detailed environments that closely mimic the human body. These organoids can be generated from various sources, including pluripotent stem cells, specialized tissue cells, and tumor tissue cells. This versatility enables scientists to replicate a wide range of diseases affecting different organ systems, effectively creating disease replicas in a laboratory dish. This exciting capability has provided us with unprecedented insights into the progression of diseases and how we can develop improved treatments. In this paper, we will provide an overview of the progress made in utilizing organoids as preclinical models, aiding our understanding and providing a more effective approach to addressing various human diseases.

Three-Dimensional Chiral Morphogenesis of Active Fluids

Chirality is an essential nature of biological systems. However, it remains obscure how the handedness at the microscale is translated into chiral morphogenesis at the tissue level. Here, we investigate three-dimensional (3D) tissue morphogenesis using an active fluid theory invoking chirality. We show that the coordination of achiral and chiral stresses, arising from microscopic interactions and energy input of individual cells, can engender the self-organization of 3D papillary and helical structures. The achiral active stress drives the nucleation of asterlike topological defects, which initiate 3D out-of-plane budding, followed by rodlike elongation. The chiral active stress excites vortexlike topological defects, which favor the tip spheroidization and twisting of the elongated rod. These results unravel the chiral morphogenesis observed in our experiments of 3D organoids generated by human embryonic stem cells.

Topological defects in self-assembled patterns of mesenchymal stromal cells in vitro are predictive attributes of condensation and chondrogenesis

Mesenchymal stromal cells (MSCs) are promising therapeutic agents for cartilage regeneration, including the potential of cells to promote chondrogenesis in vivo. However, process development and regulatory approval of MSCs as cell therapy products benefit from facile in vitro approaches that can predict potency for a given production run. Current standard in vitro approaches include a 21 day 3D differentiation assay followed by quantification of cartilage matrix proteins. We propose a novel biophysical marker that is cell population-based and can be measured from in vitro monolayer culture of MSCs. We hypothesized that the self-assembly pattern that emerges from collective-cell behavior would predict chondrogenesis motivated by our observation that certain features in this pattern, namely, topological defects, corresponded to mesenchymal condensations. Indeed, we observed a strong predictive correlation between the degree-of-order of the pattern at day 9 of the monolayer culture and chondrogenic potential later estimated from in vitro 3D chondrogenic differentiation at day 21. These findings provide the rationale and the proof-of-concept for using self-assembly patterns to monitor chondrogenic commitment of cell populations. Such correlations across multiple MSC donors and production batches suggest that self-assembly patterns can be used as a candidate biophysical attribute to predict quality and efficacy for MSCs employed therapeutically for cartilage regeneration.

Mechanical convergence in mixed populations of mammalian epithelial cells

Tissues consist of cells with different molecular and/or mechanical properties. Measuring the forces and stresses in mixed-cell populations is essential for understanding the mechanisms by which tissue development, homeostasis, and disease emerge from the cooperation of distinct cell types. However, many previous studies have primarily focused their mechanical measurements on dissociated cells or aggregates of a single-cell type, leaving the mechanics of mixed-cell populations largely unexplored. In the present study, we aimed to elucidate the influence of interactions between different cell types on cell mechanics by conducting in situ mechanical measurements on a monolayer of mammalian epithelial cells. Our findings revealed that while individual cell types displayed varying magnitudes of traction and intercellular stress before mixing, these mechanical values shifted in the mixed monolayer, becoming nearly indistinguishable between the cell types. Moreover, by analyzing a mixed-phase model of active tissues, we identified physical conditions under which such mechanical convergence is induced. Overall, the present study underscores the importance of in situ mechanical measurements in mixed-cell populations to deepen our understanding of the mechanics of multicellular systems.

Toward a predictive understanding of epithelial cell death

Epithelial cell death is highly prevalent during development and tissue homeostasis. While we have a rather good understanding of the molecular regulators of programmed cell death, especially for apoptosis, we still fail to predict when, where, how many and which specific cells will die in a tissue. This likely relies on the much more complex picture of apoptosis regulation in a tissular and epithelial context, which entails cell autonomous but also non-cell autonomous factors, diverse feedback and multiple layers of regulation of the commitment to apoptosis. In this review, we illustrate this complexity of epithelial apoptosis regulation by describing these different layers of control, all demonstrating that local cell death probability is a complex emerging feature. We first focus on non-cell autonomous factors that can locally modulate the rate of cell death, including cell competition, mechanical input and geometry as well as systemic effects. We then describe the multiple feedback mechanisms generated by cell death itself. We also outline the multiple layers of regulation of epithelial cell death, including the coordination of extrusion and regulation occurring downstream of effector caspases. Eventually, we propose a roadmap to reach a more predictive understanding of cell death regulation in an epithelial context.

Machine learning topological defects in confluent tissues

Active nematics is an emerging paradigm for characterizing biological systems. One aspect of particularly intense focus is the role active nematic defects play in these systems, as they have been found to mediate a growing number of biological processes. Accurately detecting and classifying these defects in biological systems is, therefore, of vital importance to improving our understanding of such processes. While robust methods for defect detection exist for systems of elongated constituents, other systems, such as epithelial layers, are not well suited to such methods. Here, we address this problem by developing a convolutional neural network to detect and classify nematic defects in confluent cell layers. Crucially, our method is readily implementable on experimental images of cell layers and is specifically designed to be suitable for cells that are not rod shaped, which we demonstrate by detecting defects on experimental data using the trained model. We show that our machine learning model outperforms current defect detection techniques and that this manifests itself in our method as requiring less data to accurately capture defect properties. This could drastically improve the accuracy of experimental data interpretation while also reducing costs, advancing the study of nematic defects in biological systems.

Probing active nematics with in situ microfabricated elastic inclusions

In this work, we report a direct measurement of the forces exerted by a tubulin/kinesin active nematic gel as well as its complete rheological characterization, including the quantification of its shear viscosity, η, and its activity parameter, α. For this, we develop a method that allows us to rapidly photo-polymerize compliant elastic inclusions in the continuously remodeling active system. Moreover, we quantitatively settle long-standing theoretical predictions, such as a postulated relationship encoding the intrinsic time scale of the active nematic in terms of η and α. In parallel, we infer a value for the nematic elasticity constant, K, by combining our measurements with the theorized scaling of the active length scale. On top of the microrheology capabilities, we demonstrate strategies for defect encapsulation, quantification of defect mechanics, and defect interactions, enabled by the versatility of the microfabrication strategy that allows to combine elastic motifs of different shapes and stiffnesses that are fabricated in situ.

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.

A machine learning approach to robustly determine director fields and analyze defects in active nematics

Active nematics are dense systems of rodlike particles that consume energy to drive motion at the level of the individual particles. They exist in natural systems like biological tissues and artificial materials such as suspensions of self-propelled colloidal particles or synthetic microswimmers. Active nematics have attracted significant attention in recent years due to their spectacular nonequilibrium collective spatiotemporal dynamics, which may enable applications in fields such as robotics, drug delivery, and materials science. The director field, which measures the direction and degree of alignment of the local nematic orientation, is a crucial characteristic of active nematics and is essential for studying topological defects. However, determining the director field is a significant challenge in many experimental systems. Although director fields can be derived from images of active nematics using traditional imaging processing methods, the accuracy of such methods is highly sensitive to the settings of the algorithms. These settings must be tuned from image to image due to experimental noise, intrinsic noise of the imaging technology, and perturbations caused by changes in experimental conditions. This sensitivity currently limits automatic analysis of active nematics. To address this, we developed a machine learning model for extracting reliable director fields from raw experimental images, which enables accurate analysis of topological defects. Application of the algorithm to experimental data demonstrates that the approach is robust and highly generalizable to experimental settings that are different from those in the training data. It could be a promising tool for investigating active nematics and may be generalized to other active matter systems.

Phase behaviour and dynamics of three-dimensional active dumbbell systems

We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial phases. We construct a detailed phase diagram by exploring the effects of the system's activity, density, and attraction strength. We identify several distinct phases, including a disordered, a gel, and a completely phase-separated phase. Additionally, we discover a novel dynamical phase, that we name percolating network, which is characterized by the presence of a spanning network of connected dumbbells. In the phase-separated phase we characterize numerically and describe analytically the helical motion of the dense cluster.

[The Dynamic Model of the Active-Inactive Cell Interface]

Objective

To explore the morphodynamics of the active-inactive cell monolayer interfaces by using the active liquid crystal model.

Methods

A continuum mechanical model was established based on the active liquid crystal theory and the active-inactive cell monolayer interfaces were established by setting the activity difference of cell monolayers. The theoretical equations were solved numerically by the finite difference and the lattice Boltzmann method.

Results

The active-inactive cell interfaces displayed three typical morphologies, namely, flat interface, wavy interface, and finger-like interface. On the flat interfaces, the cells were oriented perpendicular to the interface, the -1/2 topological defects were clustered in the interfaces, and the interfaces were negatively charged. On the wavy interfaces, cells showed no obvious preference for orientation at the interfaces and the interfaces were neutrally charged. On the finger-like interfaces, cells were tangentially oriented at the interfaces, the +1/2 topological defects were collected at the interfaces, driving the growth of the finger-like structures, and the interfaces were positively charged.

Conclusion

The orientation of the cell alignment at the interface can significantly affect the morphologies of the active-inactive cell monolayer interfaces, which is closely associated with the dynamics of topological defects at the interfaces.

Symmetry Breaking of Self-Propelled Topological Defects in Thin-Film Active Chiral Nematics

Active nematics represent a range of dense active matter systems which can engender spontaneous flows and self-propelled topological defects. Two-dimensional (2D) active nematic theory and simulation have been successful in explaining many quasi-2D experiments in which self-propelled +1/2 defects are observed to move along their symmetry axis. However, many active liquid crystals are essentially chiral nematic, but their twist mode becomes irrelevant under the 2D assumption. Here, we use theory and simulation to examine a three-dimensional active chiral nematic confined to a thin film, thus forming a quasi-2D system. We predict that the self-propelled +1/2 disclination in a curved thin film can break its mirror symmetry by moving circularly. Our prediction is confirmed by hydrodynamic simulations of thin spherical-shell and thin cylindrical-shell systems. In the spherical-shell confinement, the four emerged +1/2 disclinations exhibit rich dynamics as a function of activity and chirality. As such, we have proposed a new symmetry-breaking scenario in which self-propelled defects in quasi-2D active nematics can acquire an active angular velocity, greatly enriching their dynamics for finer control and emerging applications.

Machine learning interpretable models of cell mechanics from protein images

Cellular form and function emerge from complex mechanochemical systems within the cytoplasm. Currently, no systematic strategy exists to infer large-scale physical properties of a cell from its molecular components. This is an obstacle to understanding processes such as cell adhesion and migration. Here, we develop a data-driven modeling pipeline to learn the mechanical behavior of adherent cells. We first train neural networks to predict cellular forces from images of cytoskeletal proteins. Strikingly, experimental images of a single focal adhesion (FA) protein, such as zyxin, are sufficient to predict forces and can generalize to unseen biological regimes. Using this observation, we develop two approaches-one constrained by physics and the other agnostic-to construct data-driven continuum models of cellular forces. Both reveal how cellular forces are encoded by two distinct length scales. Beyond adherent cell mechanics, our work serves as a case study for integrating neural networks into predictive models for cell biology.

Vortex Lattices in Active Nematics with Periodic Obstacle Arrays

We numerically model a two-dimensional active nematic confined by a periodic array of fixed obstacles. Even in the passive nematic, the appearance of topological defects is unavoidable due to planar anchoring by the obstacle surfaces. We show that a vortex lattice state emerges as activity is increased, and that this lattice may be tuned from "ferromagnetic" to "antiferromagnetic" by varying the gap size between obstacles. We map the rich variety of states exhibited by the system as a function of distance between obstacles and activity, including a pinned defect state, motile defects, the vortex lattice, and active turbulence. We demonstrate that the flows in the active turbulent phase can be tuned by the presence of obstacles, and explore the effects of a frustrated lattice geometry on the vortex lattice phase.

Mechanical manipulation for ordered topological defects

Randomly distributed topological defects created during the spontaneous symmetry breaking are the fingerprints to trace the evolution of symmetry, range of interaction, and order parameters in condensed matter systems. However, the effective mean to manipulate topological defects into ordered form is elusive due to the topological protection. Here, we establish a strategy to effectively align the topological domain networks in hexagonal manganites through a mechanical approach. It is found that the nanoindentation strain gives rise to a threefold Magnus-type force distribution, leading to a sixfold symmetric domain pattern by driving the vortex and antivortex in opposite directions. On the basis of this rationale, sizeable mono-chirality topological stripe is readily achieved by expanding the nanoindentation to scratch, directly transferring the randomly distributed topological defects into an ordered form. This discovery provides a mechanical strategy to manipulate topological protected domains not only on ferroelectrics but also on ferromagnets/antiferromagnets and ferroelastics.

Density-Polarity Coupling in Confined Active Polar Films: Asters, Spirals, and Biphasic Orientational Phases

Topological defects in active polar fluids can organize spontaneous flows and influence macroscopic density patterns. Both of them play an important role during animal development. Yet the influence of density on active flows is poorly understood. Motivated by experiments on cell monolayers confined to disks, we study the coupling between density and polar order for a compressible active polar fluid in the presence of a +1 topological defect. As in the experiments, we find a density-controlled spiral-to-aster transition. In addition, biphasic orientational phases emerge as a generic outcome of such coupling. Our results highlight the importance of density gradients as a potential mechanism for controlling flow and orientational patterns in biological systems.

Soft-Matter Physics Provides New Insights on Myocardial Architecture: Automatic and Quantitative Identification of Topological Defects in the Trabecular Myocardium

This article is the third in our series dedicated to the analysis of cardiac myoarchitecture as a nematic chiral liquid crystal (NCLC). Previously, we introduced the concept of topological defects (disclinations) and focused on their visual identification inside the compact myocardium. Herein, we investigate these using a mathematical and automated algorithm for the reproducible identification of a larger panel of topological defects throughout the myocardium of 13 perinatal and 11 early infant hearts. This algorithm identified an average of 29 ± 11 topological defects per slice with a 2D topological charge of m = +1/2 and an average of 27 ± 10 topological defects per slice with a 2D topological charge of m = -1/2. The excess of defects per slice with a 2D topological charge of m = +1/2 was statistically significant (p < 0.001). There was no significant difference in the distribution of defects with a 2D topological charge of m = +1/2 and m = -1/2 between perinatal and early infant hearts. These defects were mostly arranged in pairs, as expected in nematics, and located inside the trabecular myocardium. When isolated, defects with a 2D topological charge of m = +1/2 were located near the luminal extremity of the trabeculae and those with a 2D topological charge of m = -1/2 were located at the anterior and posterior part of the interventricular septum. These findings constitute an advance in the characterization of the deep cardiac myoarchitecture for application in developmental and pathological studies.

Interfacial Organization and Forces Arising from Epithelial-Cancerous Monolayer Interactions

The interfacial interactions between epithelia and cancer cells have profound relevance for tumor development and metastasis. Through monolayer confrontation of MCF10A (nontumorigenic human breast epithelial cells) and MDA-MB-231 (human epithelial breast cancer cells) cells, we investigate the epithelial-cancerous interfacial interactions at the tissue level. We show that the monolayer interaction leads to competitive interfacial morphodynamics and drives an intricate spatial organization of MCF10A cells into multicellular finger-like structures, which further branch into multiple subfinger-like structures. These hierarchical interfacial structures penetrate the cancer monolayer and can spontaneously segregate or even envelop cancer cell clusters, consistent with our theoretical prediction. By tracking the substrate displacements via embedded fluorescent nanobeads and implementing nanomechanical modeling that combines atomic force microscopy and finite element simulations, we computed mechanical force patterns, including traction forces and monolayer stresses, caused by the monolayer interaction. It is found that the heterogeneous mechanical forces accumulated in the monolayers are able to squeeze cancer cells, leading to three-dimensional interfacial bulges or cell extrusion, initiating the p53 apoptosis signaling pathways of cancer cells. We reveal that intercellular E-cadherin and P-cadherin of epithelial cells differentially regulate the interfacial organization including migration speed, directionality, spatial correlation, F-actin alignment, and subcellular protrusions of MCF10A cells; whereas E-cadherin governs interfacial geometry that is relevant to force localization and cancer cell extrusion, P-cadherin maintains interfacial integrity that enables long-range force transmission. Our findings suggest that the collaborative molecular and mechanical behaviors are crucial for preventing epithelial tissues from undergoing tumor invasion.

Elasticity tunes mechanical stress localization around active topological defects

Mechanical stresses are increasingly found to be associated with various biological functionalities. At the same time, topological defects are being identified across a diverse range of biological systems and are points of localized mechanical stress. It is therefore important to ask how mechanical stress localization around topological defects is controlled. Here, we use continuum simulations of nonequilibrium, fluctuating and active nematics to explore the patterns of stress localization, as well as their extent and intensity around topological defects. We find that by increasing the orientational elasticity of the material, the isotropic stress pattern around topological defects is changed substantially, from a stress dipole characterized by symmetric compression-tension regions around the core of the defect, to a localized stress monopole at the defect position. Moreover, we show that elastic anisotropy alters the extent and intensity of the stresses, and can result in the dominance of tension or compression around defects. Finally, including both nonequilibrium fluctuations and active stress generation, we find that the elastic constant tunes the relative effect of each, leading to the flipping of tension and compression regions around topological defects. This flipping of the tension-compression regions only by changing the elastic constant presents an interesting, simple, way of switching the dynamic behavior in active matter by changing a passive material property. We expect these findings to motivate further exploration tuning stresses in active biological materials by varying material properties of the constituent units.

Improvement of Intracellular Interactions through Liquid Crystalline Elastomer Scaffolds by the Alteration of Topology

Preparation of inherently bioactive scaffolds has become a challenging issue owing to their complicated synthesis and nonrobust modified cell-actuating property. Liquid crystalline elastomers (LCEs), due to their combined specialties of liquid crystals and elastomers as well as their ability to respond to various kinds of stimuli, have reversibly led to the design of a new class of stimuli-responsive tissue-engineered scaffolds. In this line, in the first stage of this research work, synthesis and evaluation of acrylate-based LCE films (LCEfilm) encompassing mesogenic monomers are carried out. In the second step, the design of an affordable electrospinning technique for preparing LCE nanofibers (LCEfiber) as a problematic topic, thanks to the low molecular weight of the mesogenic chains of LCEs, is investigated. For this purpose, two approaches are considered, including (1) photo-cross-linking of electrospun LCEfiber and (2) blending LCE with poly(ε-caprolactone) (PCL) to produce morphologically stable nanofibers (PCL-LCEfiber). In the following, thermal, mechanical, and morphological evaluations show the optimized crosslinker (mol)/aliphatic spacer (mol) molar ratio of 50:50 for LCEfilm samples. On the other hand, for LCEfiber samples, the appropriate amounts of excessive mesogenic monomer and PCL/LCE (v/v) to fabricate the uniform nanofibers are determined to be 20% and 1:2, respectively. Eventually, PC12 cell compatibility and the impact of the liquid crystalline phase on the PC12 cell dynamic behavior of the samples are examined. The obtained results reveal that PC12 cells cultured on electrospun PCL-LCEfiber nanofibers with an average diameter of ∼659 nm per sample are alive and the scaffold has susceptibility for cell proliferation and actuation because of the rapid increase in cell density and number of singularity points formed in time-lapse cell imaging. Moreover, the PCL-LCEfiber nanofibrous scaffold exhibits a high performance for cell differentiation according to detailed biological evaluations such as gene expression level measurements. The time-lapse evaluation of PC12 cell flow fields confirms the significant influence of the reprogrammable liquid crystalline phase in the PCL-LCEfiber nanofibrous scaffold on topographical cue induction compared to the biodegradable PCL nanofibers.

Mechanochemical Active Feedback Generates Convergence Extension in Epithelial Tissue

Convergence extension, the simultaneous elongation of tissue along one axis while narrowing along a perpendicular axis, occurs during embryonic development. A fundamental process that contributes to shaping the organism, it happens in many different species and tissue types. Here, we present a minimal continuum model, that can be directly linked to the controlling microscopic biochemistry, which shows spontaneous convergence extension. It is comprised of a 2D viscoelastic active material with a mechanochemical active feedback mechanism coupled to a substrate via friction. Robust convergent extension behavior emerges beyond a critical value of the activity parameter and is controlled by the boundary conditions and the coupling to the substrate. Oscillations and spatial patterns emerge in this model when internal dissipation dominates over friction, as well as in the active elastic limit.

Intracellular tension sensor reveals mechanical anisotropy of the actin cytoskeleton

The filamentous actin (F-actin) cytoskeleton is a composite material consisting of cortical actin and bundled F-actin stress fibers, which together mediate the mechanical behaviors of the cell, from cell division to cell migration. However, as mechanical forces are typically measured upon transmission to the extracellular matrix, the internal distribution of forces within the cytoskeleton is unknown. Likewise, how distinct F-actin architectures contribute to the generation and transmission of mechanical forces is unclear. Therefore, we have developed a molecular tension sensor that embeds into the F-actin cytoskeleton. Using this sensor, we measure tension within stress fibers and cortical actin, as the cell is subject to uniaxial stretch. We find that the mechanical response, as measured by FRET, depends on the direction of applied stretch relative to the cell's axis of alignment. When the cell is aligned parallel to the direction of the stretch, stress fibers and cortical actin both accumulate tension. By contrast, when aligned perpendicular to the direction of stretch, stress fibers relax tension while the cortex accumulates tension, indicating mechanical anisotropy within the cytoskeleton. We further show that myosin inhibition regulates this anisotropy. Thus, the mechanical anisotropy of the cell and the coordination between distinct F-actin architectures vary and depend upon applied load.

Effect of contact inhibition locomotion on confined cellular organization

Experiments performed using micro-patterned one dimensional collision assays have allowed a precise quantitative analysis of the collective manifestation of contact inhibition locomotion (CIL) wherein, individual migrating cells reorient their direction of motion when they come in contact with other cells. Inspired by these experiments, we present a discrete, minimal 1D Active spin model that mimics the CIL interaction between cells in one dimensional channels. We analyze the emergent collective behaviour of migrating cells in such confined geometries, as well as the sensitivity of the emergent patterns to driving forces that couple to cell motion. In the absence of vacancies, akin to dense cell packing, the translation dynamics is arrested and the model reduces to an equilibrium spin model which can be solved exactly. In the presence of vacancies, the interplay of activity-driven translation, cell polarity switching, and CIL results in an exponential steady cluster size distribution. We define a dimensionless Péclet number Q-the ratio of the translation rate and directional switching rate of particles in the absence of CIL. While the average cluster size increases monotonically as a function of Q, it exhibits a non-monotonic dependence on CIL strength, when the Q is sufficiently high. In the high Q limit, an analytical form of average cluster size can be obtained approximately by effectively mapping the system to an equivalent equilibrium process involving clusters of different sizes wherein the cluster size distribution is obtained by minimizing an effective Helmholtz free energy for the system. The resultant prediction of exponential dependence on CIL strength of the average cluster size and [Formula: see text] dependence of the average cluster size is borne out to reasonable accuracy as long as the CIL strength is not very large. The consequent prediction of a single scaling function of Q, particle density and CIL interaction strength, characterizing the distribution function of the cluster sizes and resultant data collapse is observed for a range of parameters.

A life off the beaten track in biomechanics: Imperfect elasticity, cytoskeletal glassiness, and epithelial unjamming

Textbook descriptions of elasticity, viscosity, and viscoelasticity fail to account for certain mechanical behaviors that typify soft living matter. Here, we consider three examples. First, strong empirical evidence suggests that within lung parenchymal tissues, the frictional stresses expressed at the microscale are fundamentally not of viscous origin. Second, the cytoskeleton (CSK) of the airway smooth muscle cell, as well as that of all eukaryotic cells, is more solid-like than fluid-like, yet its elastic modulus is softer than the softest of soft rubbers by a factor of 104-105. Moreover, the eukaryotic CSK expresses power law rheology, innate malleability, and fluidization when sheared. For these reasons, taken together, the CSK of the living eukaryotic cell is reminiscent of the class of materials called soft glasses, thus likening it to inert materials such as clays, pastes slurries, emulsions, and foams. Third, the cellular collective comprising a confluent epithelial layer can become solid-like and jammed, fluid-like and unjammed, or something in between. Esoteric though each may seem, these discoveries are consequential insofar as they impact our understanding of bronchospasm and wound healing as well as cancer cell invasion and embryonic development. Moreover, there are reasons to suspect that certain of these phenomena first arose in the early protist as a result of evolutionary pressures exerted by the primordial microenvironment. We have hypothesized, further, that each then became passed down virtually unchanged to the present day as a conserved core process. These topics are addressed here not only because they are interesting but also because they track the journey of one laboratory along a path less traveled by.

A toolbox to analyze collective cell migration, proliferation and cellular organization simultaneously

BACKGROUND

Analyses of collective cell migration and orientation phenomena are needed to assess the behavior of multicellular clusters. While some tools to the authors' knowledge none is capable to analyze collective migration, cellular orientation and proliferation in phase contrast images simultaneously.

METHODS

We provide a tool based to analyze phase contrast images of dense cell layers. PIV is used to calculatevelocity fields, while the structure tensor provides cellular orientation. An artificial neural network is used to identify cell division events, allowing to correlate migratory and organizational phenomena with cell density.

CONCLUSION

The presented tool allows the simultaneous analysis of collective cell behavior from phase contrast images in terms of migration, (self-)organization and proliferation.

Autofluorescence microscopy as a non-invasive probe to characterize the complex mechanical properties of keratin-based integumentary organs: A feather paradigm

Integumentary organs exhibit diverse morphologies and functions. The complex mechanical property of the architecture is mainly contributed by the ingenious multiscale assembly of keratins. A cross-scale characterization on keratin integration in an integument system will help us understand the principles on how keratin-based bio-architecture are built and function in nature. In this study, we used feather as a model integument organ. We develop autofluorescence (AF) microscopy to study the characteristics of its keratin assemblies over a wide range of length scales. The AF intensity of each feather component, following the hierarchy from the rachis to barb to barbule, decreased with the physical dimension. By combining the analysis of AF signal and tensile testing, we can probe regional material density and the associated mechanical strength in a composite feather. We further demonstrated that the AF micro-images could resolve subtle variations in the defective keratin assembly in feathers from frizzled chicken variants with a mutation in α-keratin 75. The distinction between AF patterns and the morphological features of feather components across different length scales indicated a synergetic interplay between material integration and complex morphogenesis during feather development. The work shows AF microscopy can serve as an easy and non-invasive approach to study multiscale keratin organizations and the associated bio-mechanical properties in diverse integumentary organs. This approach will facilitate our learning of many bio-inspired designs in diverse animal integumentary organs/appendages.

Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.

Epithelial homeostasis: Cell size shapes cell fate

A new study shows that cell size, in conjunction with specific signaling pathways, controls apoptosis within developing tissues. Cells with smaller sizes and relatively smaller sizes compared to their neighbors exhibit an increased likelihood of undergoing apoptosis. These processes are regulated by the Hippo/YAP and Notch pathways, respectively.

Epithelial apoptotic pattern emerges from global and local regulation by cell apical area

Geometry is a fundamental attribute of biological systems, and it underlies cell and tissue dynamics. Cell geometry controls cell-cycle progression and mitosis and thus modulates tissue development and homeostasis. In sharp contrast and despite the extensive characterization of the genetic mechanisms of caspase activation, we know little about whether and how cell geometry controls apoptosis commitment in developing tissues. Here, we combined multiscale time-lapse microscopy of developing Drosophila epithelium, quantitative characterization of cell behaviors, and genetic and mechanical perturbations to determine how apoptosis is controlled during epithelial tissue development. We found that early in cell lives and well before extrusion, apoptosis commitment is linked to two distinct geometric features: a small apical area compared with other cells within the tissue and a small relative apical area with respect to the immediate neighboring cells. We showed that these global and local geometric characteristics are sufficient to recapitulate the tissue-scale apoptotic pattern. Furthermore, we established that the coupling between these two geometric features and apoptotic cells is dependent on the Hippo/YAP and Notch pathways. Overall, by exploring the links between cell geometry and apoptosis commitment, our work provides important insights into the spatial regulation of cell death in tissues and improves our understanding of the mechanisms that control cell number and tissue size.

Active nematic liquid crystals simulated by particle-based mesoscopic methods

Two Multi-particle collision dynamics algorithms that simulate nematic liquid crystals are generalised to reproduce active behaviour. One of the algorithms is due to Shendruk and Yeomans and is based on particles that carry an orientation vector ordered by a mean-field energy [T. N. Shendruk and J. M. Yeomans, Soft Matter, 2015, 11, 5101]. In the other algorithm, due to Mandal and Mazza, particles possess an order parameter tensor which evolves according to the Qian-Sheng model of nematohydrodynamics [S. Mandal and M. G. Mazza, Phys. Rev. E, 2019, 99, 063319]. For both methods activity is incorporated through a force proportional to the divergence of the local average order parameter tensor. Both implementations produce disclination curves in the nematic fluid that undergo nucleation and self-annihilation dynamics. Topological defects are found to be consistent with those observed in recent experiments of three-dimensional active nematics. Results permit to compare the length-scales over which the different nematic Multi-particle collision dynamics methods operate. The structure and dynamics of the orientation and flow fields agree with those obtained recently in numerical studies of continuum three-dimensional active nematics. Overall, our results open the opportunity to use mesoscopic particle-based approaches to study active liquid crystals in situations such as nonequilibrium states driven by flow or colloidal particles in active anisotropic solvents.

A mechanism-based theory of cellular and tissue plasticity

Plastic deformation in cells and tissues has been found to play crucial roles in collective cell migration, cancer metastasis, and morphogenesis. However, the fundamental question of how plasticity is initiated in individual cells and then propagates within the tissue remains elusive. Here, we develop a mechanism-based theory of cellular and tissue plasticity that accounts for all key processes involved, including the activation and development of active contraction at different scales as well as the formation of endocytic vesicles on cell junctions and show that this theory achieves quantitative agreement with all existing experiments. Specifically, it reveals that, in response to optical or mechanical stimuli, the myosin contraction and thermal fluctuation-assisted formation and pinching of endocytic vesicles could lead to permanent shortening of cell junctions and that such plastic constriction can stretch neighboring cells and trigger their active contraction through mechanochemical feedbacks and eventually their plastic deformations as well. Our theory predicts that endocytic vesicles with a size around 1 to 2 µm will most likely be formed and a higher irreversible shortening of cell junctions could be achieved if a long stimulation is split into multiple short ones, all in quantitative agreement with experiments. Our analysis also shows that constriction of cells in tissue can undergo elastic/unratcheted to plastic/ratcheted transition as the magnitude and duration of active contraction increases, ultimately resulting in the propagation of plastic deformation waves within the monolayer with a constant speed which again is consistent with experimental observations.

Spontaneous flows and dynamics of full-integer topological defects in polar active matter

Polar active matter of self-propelled particles sustain spontaneous flows through the full-integer topological defects. We study theoretically the incompressible flow profiles around ±1 defects induced by polar and dipolar active forces. We show that dipolar forces induce vortical flows around the +1 defect, while the flow around the -1 defect has an 8-fold rotational symmetry. The vortical flow changes its chirality near the +1 defect core in the absence of the friction with a substrate. We show analytically that the flow induced by polar active forces is vortical near the +1 defect and is 4-fold symmetric near the -1 defect, while it becomes uniform in the far-field. For a pair of oppositely charged defects, this polar flow contributes to a mutual interaction force that depends only on the orientation of the defect pair relative to the background polarization, and that enhances defect pair annihilation. This is in contradiction with the effect of dipolar active forces which decay inversely proportional with the defect separation distance. As such, our analyses reveals a long-ranged mechanism for the pairwise interaction between topological defects in polar active matter.

Mechanically induced pyroptosis enhances cardiosphere oxidative stress resistance and metabolism for myocardial infarction therapy

Current approaches in myocardial infarction treatment are limited by low cellular oxidative stress resistance, reducing the long-term survival of therapeutic cells. Here we develop a liquid-crystal substrate with unique surface properties and mechanical responsiveness to produce size-controllable cardiospheres that undergo pyroptosis to improve cellular bioactivities and resistance to oxidative stress. We perform RNA sequencing and study cell metabolism to reveal increased metabolic levels and improved mitochondrial function in the preconditioned cardiospheres. We test therapeutic outcomes in a rat model of myocardial infarction to show that cardiospheres improve long-term cardiac function, promote angiogenesis and reduce cardiac remodeling during the 3-month observation. Overall, this study presents a promising and effective system for preparing a large quantity of functional cardiospheres, showcasing potential for clinical application.

Dissecting morphogenetic apoptosis through a genetic screen in Drosophila

Apoptosis is an essential cellular process both in normal development and pathological contexts. Screens performed to date have focused on the cell autonomous aspect of the process, deciphering the apoptotic cascade leading to cell destruction through the activation of caspases. However, the nonautonomous aspect of the apoptotic pathway, including signals regulating the apoptotic pattern or those sent by the apoptotic cell to its surroundings, is still poorly understood. Here, we describe an unbiased RNAi-based genetic screen whose goal is to identify elements of the "morphogenetic apoptosis pathway" in an integrated model system, the Drosophila leg. We screened about 1,400 candidates, using adult joint morphology, morphogenetic fold formation, and apoptotic pattern as readouts for the identification of potential apoptosis-related genes. We identified 41 genes potentially involved in specific aspects of morphogenetic apoptosis: (1) regulation of the apoptotic process; (2) formation, extrusion, and elimination of apoptotic bodies; and (3) contribution to morphogenesis downstream of apoptosis.

Cell migration in dense microenvironments

The nucleus has been viewed as a passenger during cell migration that functions merely to protect the genome. However, increasing evidence shows that the nucleus is an active organelle, constantly sensing the surrounding environment and translating extracellular mechanical inputs into intracellular signaling. The nuclear envelope has a large membrane reservoir which serves as a buffer for mechanical inputs as it unfolds without increasing its tension. In contrast, when cells cope with mechanical strain, such as migration through solid tumors or dense interstitial spaces, the nuclear envelope folds stretch, increasing nuclear envelope tension and sometimes causing rupture. Different degrees of nuclear envelope tension regulate cellular behaviors and functions, especially in cells that move and grow within dense matrices. The crosstalk between extracellular mechanical inputs and the cell nucleus is a critical component in the modulation of cell function of cells that navigate within packed microenvironments. Moreover, there is a link between regimes of nuclear envelope unfolding and different cellular behaviors, from orchestrated signaling cascades to cellular perturbations and damage.

Hexanematic crossover in epithelial monolayers depends on cell adhesion and cell density

Changes in tissue geometry during developmental processes are associated with collective migration of cells. Recent experimental and numerical results suggest that these changes could leverage on the coexistence of nematic and hexatic orientational order at different length scales. How this multiscale organization is affected by the material properties of the cells and their substrate is presently unknown. In this study, we address these questions in monolayers of Madin-Darby canine kidney cells having various cell densities and molecular repertoires. At small length scales, confluent monolayers are characterized by a prominent hexatic order, independent of the presence of E-cadherin, monolayer density, and underlying substrate stiffness. However, all three properties affect the meso-scale tissue organization. The length scale at which hexatic order transits to nematic order, the "hexanematic" crossover scale, strongly depends on cell-cell adhesions and correlates with monolayer density. Our study demonstrates how epithelial organization is affected by mechanical properties, and provides a robust description of tissue organization during developmental processes.