Topological defects in epithelia govern cell death and extrusion

Organoids

Organoids have attracted increasing attention because they are simple tissue-engineered cell-based in vitro models that recapitulate many aspects of the complex structure and function of the corresponding in vivo tissue. They can be dissected and interrogated for fundamental mechanistic studies on development, regeneration, and repair in human tissues. Organoids can also be used in diagnostics, disease modeling, drug discovery, and personalized medicine. Organoids are derived from either pluripotent or tissue-resident stem (embryonic or adult) or progenitor or differentiated cells from healthy or diseased tissues, such as tumors. To date, numerous organoid engineering strategies that support organoid culture and growth, proliferation, differentiation and maturation have been reported. This Primer serves to highlight the rationale underlying the selection and development of these materials and methods to control the cellular/tissue niche; and therefore, structure and function of the engineered organoid. We also discuss key considerations for generating robust organoids, such as those related to cell isolation and seeding, matrix and soluble factor selection, physical cues and integration. The general standards for data quality, reproducibility and deposition within the organoid community is also outlined. Lastly, we conclude by elaborating on the limitations of organoids in different applications, and key priorities in organoid engineering for the coming years.

Mechanical regulation of the early stages of angiogenesis

Favouring or thwarting the development of a vascular network is essential in fields as diverse as oncology, cardiovascular disease or tissue engineering. As a result, understanding and controlling angiogenesis has become a major scientific challenge. Mechanical factors play a fundamental role in angiogenesis and can potentially be exploited for optimizing the architecture of the resulting vascular network. Largely focusing on in vitro systems but also supported by some in vivo evidence, the aim of this Highlight Review is dual. First, we describe the current knowledge with particular focus on the effects of fluid and solid mechanical stimuli on the early stages of the angiogenic process, most notably the destabilization of existing vessels and the initiation and elongation of new vessels. Second, we explore inherent difficulties in the field and propose future perspectives on the use of in vitro and physics-based modelling to overcome these difficulties.

Spontaneous multi-scale void formation and closure in densifying epithelial and fibroblast monolayers from the sub-confluent state

Using time-lapse phase contrast microscopy, the formation and closure of spontaneously generated voids in the densifying monolayers of isotropic epithelial cells (ECs) and elongated fibroblast cells (FCs) through proliferation from the sub-confluent state are investigated. It is found that, in both types of monolayers after forming a connected network composed of nematic patches with different orientations, numerous multi-scale voids can be spontaneously formed and gradually close with increasing time. The isotropic fluctuations of deformation and crawling of ECs and the anisotropic axial motion/alignment polarizations of FCs are the two keys leading to the following different generic dynamical behaviors. In EC monolayers, voids exhibit irregular boundary fluctuations and easier cell re-orientation of front layer cells (FLCs) surrounding void boundaries. Void closures are mainly through pinching the gap between the opposite fluctuating void boundaries, and the inward crawling of FLCs to reduce void area associated with topological rearrangement to reduce FLC number. In FC monolayers, large voids have piecewise smooth convex boundaries, and cusp-shaped concave boundaries with cells orienting toward the void at cusp tips. The extension of a thin cell bridge from the cusp tip can bisect a large void into smaller voids. For smaller FC voids dominated by convex boundaries, along which cell alignment prohibits inward crawling, the reduction of FLC number through successive outward squeezing of single FLCs by neighboring FLCs sliding along the void boundary plays an important role for topological rearrangement and void closure. Unlike those surrounding artificial wounds in dense EC monolayers, the absence of ring-like purse-strings surrounding EC and FC voids allows topological rearrangements for reducing void perimeter and void area.

Defect dynamics in active polar fluids vs. active nematics

Topological defects play a key role in two-dimensional active nematics, and a transient role in two-dimensional active polar fluids. Using a variational method, we study both the transient and long-time behavior of defects in two-dimensional active polar fluids in the limit of strong order and overdamped, compressible flow, and compare the defect dynamics with the corresponding active nematics model studied recently. One result is non-central interactions between defect pairs for active polar fluids, and by extending our analysis to allow orientation dynamics of defects, we find that the orientation of +1 defects, unlike that of ±1/2 defects in active nematics, is not locked to defect positions and relaxes to asters. Moreover, using a scaling argument, we explain the transient feature of active polar defects and show that in the steady state, active polar fluids are either devoid of defects or consist of a single aster. We argue that for contractile (extensile) active nematic systems, +1 vortices (asters) should emerge as bound states of a pair of +1/2 defects, which has been recently observed. Moreover, unlike the polar case, we show that for active nematics, a linear chain of equally spaced bound states of pairs of +1/2 defects can screen the activity term. A common feature in both models is the appearance of +1 defects (elementary in polar and composite in nematic) in the steady state.

Active nematic defects in compressible and incompressible flows

We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint. Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case, while they become unstable under the incompressibility constraint. For compressible flows at high enough activity, stable arches organize themselves into a smecticlike pattern, which induce an associated global polar ordering of +1/2 nematic defects. By contrast, divergence-free flows give rise to a local nematic order of the +1/2 defects, consisting of antialigned pairs of neighboring defects, as established in previous studies.

The Nematic Chiral Liquid Crystal Structure of the Cardiac Myoarchitecture: Disclinations and Topological Singularities

This is our second article devoted to the cardiac myoarchitecture considered as a nematic chiral liquid crystal (NCLC). While the first article focused on the myoarchitecture of the left ventricle (LV), this new article extends to the whole ventricular mass and introduces the concept of disclinations and topological singularities, which characterize the differences and relationships between the left and right ventricles (RV). At the level of the ventricular apices, we constantly observed a vortex shape at the LV apex, corresponding, in the terminology of liquid crystals, to a "+1 disclination"; we never observed this at the RV apex. At the level of the interventricular septum (IVS), we identified "-1/2 disclinations" at the anterior and posterior parts. During the perinatal period, there was a significant difference in their distribution, with more "-1/2 disclinations" in the posterior part of the IVS. After birth, concomitant to major physiological changes, the number of "-1/2 disclinations" significantly decreased, both in the anterior and posterior parts of the IVS. Finally, the description of the disclinations must be considered in any attempt to segment the whole ventricular mass, in biomechanical studies, and, more generally, for the characterization of myocardial remodeling.

Scaling and spontaneous symmetry restoring of topological defect dynamics in liquid crystal

Topological defects-locations of local mismatch of order-are a universal concept playing important roles in diverse systems studied in physics and beyond, including the universe, various condensed matter systems, and recently, even life phenomena. Among these, liquid crystal has been a platform for studying topological defects via visualization, yet it has been a challenge to resolve three-dimensional structures of dynamically evolving singular topological defects. Here, we report a direct confocal observation of nematic liquid crystalline defect lines, called disclinations, relaxing from an electrically driven turbulent state. We focus in particular on reconnections, characteristic of such line defects. We find a scaling law for in-plane reconnection events, by which the distance between reconnecting disclinations decreases by the square root of time to the reconnection. Moreover, we show that apparently asymmetric dynamics of reconnecting disclinations is actually symmetric in a comoving frame, in marked contrast to the two-dimensional counterpart whose asymmetry is established. We argue, with experimental supports, that this is because of energetically favorable symmetric twist configurations that disclinations take spontaneously, thanks to the topology that allows for rotation of the winding axis. Our work illustrates a general mechanism of such spontaneous symmetry restoring that may apply beyond liquid crystal, which can take place if topologically distinct asymmetric defects in lower dimensions become homeomorphic in higher dimensions and if the symmetric intermediate is energetically favorable.

Fluctuation-induced dynamics of nematic topological defects

Topological defects are increasingly being identified in various biological systems, where their characteristic flow fields and stress patterns are associated with continuous active stress generation by biological entities. Here, using numerical simulations of continuum fluctuating nematohydrodynamics, we show that even in the absence of any specific form of active stresses associated with self-propulsion, mesoscopic fluctuations in either orientational alignment or hydrodynamics can independently result in flow patterns around topological defects that resemble the ones observed in active systems. Our simulations further show the possibility of extensile- and contractile-like motion of fluctuation-induced positive half-integer topological defects. Remarkably, isotropic stress fields also reproduce the experimentally measured stress patterns around topological defects in epithelia. Our findings further reveal that extensile- or contractile-like flow and stress patterns around fluctuation-induced defects are governed by passive elastic stresses and flow-aligning behavior of the nematics.

Local Yield and Compliance in Active Cell Monolayers

The rheology of biological tissue plays an important role in many processes, from organ formation to cancer invasion. Here, we use a multiphase field model of motile cells to simulate active microrheology within a tissue monolayer. When unperturbed, the tissue exhibits a transition between a solidlike state and a fluidlike state tuned by cell motility and deformability-the ratio of the energetic costs of steric cell-cell repulsion and cell-edge tension. When perturbed, solid tissues exhibit local yield-stress behavior, with a threshold force for the onset of motion of a probe particle that vanishes upon approaching the solid-to-liquid transition. This onset of motion is qualitatively different in the low and high deformability regimes. At high deformability, the tissue is amorphous when solid, it responds compliantly to deformations, and the probe transition to motion is smooth. At low deformability, the monolayer is more ordered translationally and stiffer, and the onset of motion appears discontinuous. Our results suggest that cellular or nanoparticle transport in different types of tissues can be fundamentally different and point to ways in which it can be controlled.

Dominant geometrical factors of collective cell migration in flexible 3D gelatin tube structures

Collective cell migration is a dynamic and interactive behavior of cell cohorts essential for diverse physiological developments in living organisms. Recent studies have revealed the importance of three-dimensional (3D) topographical confinements to regulate the migration modes of cell cohorts in tubular confinement. However, conventional in vitro assays fail to observe cells' behavior in response to 3D structural changes, which is necessary for examining the geometric regulation factors of collective migration. Here, we introduce a newly developed assay for fabricating flexible 3D structures of capillary microtunnels to examine the behavior of vascular endothelial cells (ECs) as they progress through the successive transition across wide or narrow tube structures. The microtunnels with altered diameters were formed inside gelatin-gel blocks by photo-thermal etching with micrometer-sized spot heating of the focused infrared laser absorption. The ECs migrated and spread two-dimensionally on the inner surface of gelatin capillary microtunnels as a monolayer instead of filling the entire capillary. In the straight cylindrical topographical constraint, leading ECs exhibited no apparent diameter dependence for the maximum peak migration velocity. However, widening the diameter in the narrow-wide structures caused a decrease in migration velocity following in direct proportion to the diameter increase ratio, whereas narrowing the diameter in wide-narrow microtunnels increased the speed without obvious correlation between velocity change and diameter change. The results demonstrated the ability of the newly developed flexible 3D gelatin tube structures for collective cell migration, and the findings provide insights into the dominant geometric factor of the emerging migratory modes for endothelial migration as asymmetric fluid flow-like behavior in the borderless cylindrical cell sheets.

Active Nematic Flows over Curved Surfaces

Cell monolayers are a central model system in the study of tissue biophysics. In vivo, epithelial tissues are curved on the scale of microns, and the curvature's role in the onset of spontaneous tissue flows is still not well understood. Here, we present a hydrodynamic theory for an apical-basal asymmetric active nematic gel on a curved strip. We show that surface curvature qualitatively changes monolayer motion compared with flat space: the resulting flows can be thresholdless, and the transition to motion may change from continuous to discontinuous. Surface curvature, friction, and active tractions are all shown to control the flow pattern selected, from simple shear to vortex chains.

Active Nematic Defects and Epithelial Morphogenesis

Inspired by recent experiments that highlight the role of nematic defects in the morphogenesis of epithelial tissues, we develop a minimal framework to study the dynamics of an active curved surface driven by its nematic texture. Allowing the surface to evolve via relaxational dynamics leads to a theory linking nematic defect dynamics, cellular division rates, and Gaussian curvature. Regions of large positive (negative) curvature and positive (negative) growth are colocalized with the presence of positive (negative) defects. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.

Activity gradients in two- and three-dimensional active nematics

We numerically investigate how spatial variations of extensile or contractile active stress affect bulk active nematic systems in two and three dimensions. In the absence of defects, activity gradients drive flows which re-orient the nematic director field and thus act as an effective anchoring force. At high activity, defects are created and the system transitions into active turbulence, a chaotic flow state characterized by strong vorticity. We find that in two-dimensional (2D) systems active torques robustly align +1/2 defects parallel to activity gradients, with defect heads pointing towards contractile regions. In three-dimensional (3D) active nematics disclination lines preferentially lie in the plane perpendicular to activity gradients due to active torques acting on line segments. The average orientation of the defect structures in the plane perpendicular to the line tangent depends on the defect type, where wedge-like +1/2 defects align parallel to activity gradients, while twist defects are aligned anti-parallel. Understanding the response of active nematic fluids to activity gradients is an important step towards applying physical theories to biology, where spatial variations of active stress impact morphogenetic processes in developing embryos and affect flows and deformations in growing cell aggregates, such as tumours.

Plasticity of body axis polarity in Hydra regeneration under constraints

One of the major events in animal morphogenesis is the emergence of a polar body axis. Here, we combine classic grafting techniques with live imaging to explore the plasticity of polarity determination during whole body regeneration in Hydra. Composite tissues are made by fusing two rings, excised from separate animals, in different configurations that vary in the polarity and original positions of the rings along the body axes of the parent animals. Under frustrating initial configurations, body axis polarity that is otherwise stably inherited from the parent animal, can become labile and even be reversed. Importantly, the site of head regeneration exhibits a strong bias toward the edges of the tissue, even when this involves polarity reversal. In particular, we observe head formation at an originally aboral tissue edge, which is not compatible with models of Hydra regeneration based only on preexisting morphogen gradients or an injury response. The site of the new head invariably contains an aster-like defect in the organization of the supra-cellular ectodermal actin fibers. While a defect is neither required nor sufficient for head formation, we show that the defect at the new head site can arise via different routes, either appearing directly following excision as the tissue seals at its edge or through de novo defect formation at the fusion site. Altogether, our results show that the emergence of a polar body axis depends on the original polarity and position of the excised tissues as well as structural factors, suggesting that axis determination is an integrated process that arises from the dynamic interplay of multiple biochemical and mechanical processes.

Defect absorption and emission for p-atic liquid crystals on cones

We investigate the ground-state configurations of two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on fixed curved surfaces. We focus on the intrinsic geometry and show that isothermal coordinates are particularly convenient as they explicitly encode a geometric contribution to the elastic potential. In the special case of a cone with half-angle β, the apex develops an effective topological charge of -χ, where 2πχ=2π(1-sinβ) is the deficit angle of the cone, and a topological defect of charge σ behaves as if it had an effective topological charge Q_{eff}=(σ-σ^{2}/2) when interacting with the apex. The effective charge of the apex leads to defect absorption and emission at the cone apex as the deficit angle of the cone is varied. For total topological defect charge 1, e.g., imposed by tangential boundary conditions at the edge, we find that for a disk the ground-state configuration consists of p defects each of charge +1/p lying equally spaced on a concentric ring of radius d=(p-1/3p-1)^{1/2p}R, where R is the radius of the disk. In the case of a cone with tangential boundary conditions at the base, we find three types of ground-state configurations as a function of cone angle: (i) for sharp cones, all of the +1/p defects are absorbed by the apex; (ii) at intermediate cone angles, some of the +1/p defects are absorbed by the apex and the rest lie equally spaced along a concentric ring on the flank; and (iii) for nearly flat cones, all of the +1/p defects lie equally spaced along a concentric ring on the flank. Here the defect positions and the absorption transitions depend intricately on p and the deficit angle, which we analytically compute. We check these results with numerical simulations for a set of commensurate cone angles and find excellent agreement.

Impact of dipole-dipole interactions on motility-induced phase separation

We present a hydrodynamic theory for systems of dipolar active Brownian particles which, in the regime of weak dipolar coupling, predicts the onset of motility-induced phase separation (MIPS), consistent with Brownian dynamics (BD) simulations. The hydrodynamic equations are derived by explicitly coarse-graining the microscopic Langevin dynamics, thus allowing for a mapping of the coarse-grained model and particle-resolved simulations. Performing BD simulations at fixed density, we find that dipolar interactions tend to hinder MIPS, as first reported in [Liao et al., Soft Matter, 2020, 16, 2208]. Here we demonstrate that the theoretical approach indeed captures the suppression of MIPS. Moreover, the analysis of the numerically obtained, angle-dependent correlation functions sheds light into the underlying microscopic mechanisms leading to the destabilization of the homogeneous phase.

Coupling the topological defect phase to the extrinsic curvature in nematic shells

In two dimensional nematics, topological defects are point like singularities with both a charge and a phase. We study the topological defects within curved nematic textures on the surface of a cylinder. This allows us to isolate the effect of extrinsic curvature on the structure of the topological defect. By minimizing the energy associated with distortions in the nematic director around the core of a defect, we show that the phase of the topological defect is coupled to the orientation of the cylinder. This coupling depends on the relative energetic cost associated with splay, bend and twist distortions of the nematic director. We identify a bistability in the phase of the defects when twist deformations dominate. Finally, we show a similar effect for integer charge topological defects.

Nematic order condensation and topological defects in inertial active nematics

Living materials at different length scales manifest active nematic features such as orientational order, nematic topological defects, and active nematic turbulence. Using numerical simulations we investigate the impact of fluid inertia on the collective pattern formation in active nematics. We show that an incremental increase in inertial effects due to reduced viscosity results in gradual melting of nematic order with an increase in topological defect density before a discontinuous transition to a vortex-condensate state. The emergent vortex-condensate state at low enough viscosities coincides with nematic order condensation within the giant vortices and the drop in the density of topological defects. We further show flow field around topological defects is substantially affected by inertial effects. Moreover, we demonstrate the strong dependence of the kinetic energy spectrum on the inertial effects, recover the Kolmogorov scaling within the vortex-condensate phase, but find no evidence of universal scaling at higher viscosities. The findings reveal complexities in active nematic turbulence and emphasize the important cross-talk between active and inertial effects in setting flow and orientational organization of active particles.

Bridging microscopic cell dynamics to nematohydrodynamics of cell monolayers

It is increasingly being realized that liquid-crystalline features can play an important role in the properties and dynamics of cell monolayers. Here, we present a cell-based model of cell layers, based on the phase-field formulation, that connects cell-cell interactions specified at the single cell level to large-scale nematic and hydrodynamic properties of the tissue. In particular, we present a minimal formulation that reproduces the well-known bend and splay hydrodynamic instabilities of the continuum nemato-hydrodynamic formulation of active matter, together with an analytical description of the instability threshold in terms of activity and elasticity of the cells. Furthermore, we provide a quantitative characterisation and comparison of flows and topological defects for extensile and contractile stress generation mechanisms, and demonstrate activity-induced heterogeneity and spontaneous formation of gaps within a confluent monolayer. Together, these results contribute to bridging the gap between cell-scale dynamics and tissue-scale collective cellular organisation.

Mechanical Forces Govern Interactions of Host Cells with Intracellular Bacterial Pathogens

To combat infectious diseases, it is important to understand how host cells interact with bacterial pathogens. Signals conveyed from pathogen to host, and vice versa, may be either chemical or mechanical. While the molecular and biochemical basis of host-pathogen interactions has been extensively explored, relatively less is known about mechanical signals and responses in the context of those interactions. Nevertheless, a wide variety of bacterial pathogens appear to have developed mechanisms to alter the cellular biomechanics of their hosts in order to promote their survival and dissemination, and in turn many host responses to infection rely on mechanical alterations in host cells and tissues to limit the spread of infection. In this review, we present recent findings on how mechanical forces generated by host cells can promote or obstruct the dissemination of intracellular bacterial pathogens. In addition, we discuss how in vivo extracellular mechanical signals influence interactions between host cells and intracellular bacterial pathogens. Examples of such signals include shear stresses caused by fluid flow over the surface of cells and variable stiffness of the extracellular matrix on which cells are anchored. We highlight bioengineering-inspired tools and techniques that can be used to measure host cell mechanics during infection. These allow for the interrogation of how mechanical signals can modulate infection alongside biochemical signals. We hope that this review will inspire the microbiology community to embrace those tools in future studies so that host cell biomechanics can be more readily explored in the context of infection studies.

Thickness of epithelia on wavy substrates: measurements and continuous models

We measured the thickness of MDCK epithelia grown on substrates with a sinusoidal profile. We show that while at long wavelength the profile of the epithelium follows that of the substrate, at short wavelengths cells are thicker in valleys than on ridges. This is reminiscent of the so-called «healing length in the case of a thin liquid film wetting a rough solid substrate. We explore the ability of continuum mechanics models to account for these observations. Modeling the epithelium as a thin liquid film, with surface tension, does not fully account for the measurements. Neither does modeling the epithelium as a thin incompressible elastic film. On the contrary, the addition of an apical active stress gives satisfactory agreement with measurements, with one fitting parameter, the ratio between the active stress and the elastic modulus.

Defect loops in three-dimensional active nematics as active multipoles

We develop a description of defect loops in three-dimensional active nematics based on a multipole expansion of the far-field director and show how this leads to a self-dynamics dependent on the loop's geometric type. The dipole term leads to active stresses that generate a global self-propulsion for splay and bend loops. The quadrupole moment is nonzero only for nonplanar loops and generates a net "active torque," such that defect loops are both self-motile and self-orienting. Our analysis identifies right- and left-handed twist loops as the only force- and torque-free geometries, suggesting a mechanism for generating an excess of twist loops. Finally, we determine the Stokesian flows created by defect loops and describe qualitatively their hydrodynamics.

Quadrupolar active stress induces exotic patterns of defect motion in compressible active nematics

A wide range of living and artificial active matter exists in close contact with substrates and under strong confinement, where in addition to dipolar active stresses, quadrupolar active stresses can become important. Here, we numerically investigate the impact of quadrupolar non-equilibrium stresses on the emergent patterns of self-organisation in non-momentum conserving active nematics. Our results reveal that beyond having stabilising effects, the quadrupolar active forces can induce various modes of topological defect motion in active nematics. In particular, we find the emergence of both polar and nematic ordering of the defects, as well as new patterns of self-organisation that comprise topological defect chains and transient topological defect asters. The results contribute to further understanding of emergent patterns of collective motion and non-equilibrium self-organisation in active matter.

Self-rotation regulates interface evolution in biphasic active matter through taming defect dynamics

Chirality can endow nonequilibrium active matter with unique features and functions. Here, we explore the chiral dynamics in biphasic active nematics composed of self-rotating units that continuously inject energy and angular momentum at the microscale. We show that the self-rotation of units can regularize the boundaries between two phases, rendering sinusoidal-like interfaces, which allow lateral wave propagation and are characterized by chains of ordered antiferromagnetic cross-interface flow vortices. Through the spontaneous coordination of counter-rotating units across the interfaces, topological defects excited by activity are sorted spatiotemporally, where positive defects are locally trapped at the interfaces but, unexpectedly, are transported laterally in a unidirectional rather than wavy mode, whereas inertial negative defects remain spinning in the bulks. Our findings reveal that individual chirality could be harnessed to modulate interfacial morphodynamics in active systems and suggest a potential approach toward controlling topological defects for programmable microfluidics and logic operations.

Integer topological defects organize stresses driving tissue morphogenesis

Tissues acquire function and shape via differentiation and morphogenesis. Both processes are driven by coordinating cellular forces and shapes at the tissue scale, but general principles governing this interplay remain to be discovered. Here we report that self-organization of myoblasts around integer topological defects, namely spirals and asters, suffices to establish complex multicellular architectures. In particular, these arrangements can trigger localized cell differentiation or, alternatively, when differentiation is inhibited, they can drive the growth of swirling protrusions. Both localized differentiation and growth of cellular vortices require specific stress patterns. By analysing the experimental velocity and orientational fields through active gel theory, we show that integer topological defects can generate force gradients that concentrate compressive stresses. We reveal these gradients by assessing spatial changes in nuclear volume and deformations of elastic pillars. We propose integer topological defects as mechanical organizing centres controlling differentiation and morphogenesis.

Fractional defect charges in liquid crystals with p-fold rotational symmetry on cones

Conical surfaces, with a δ function of Gaussian curvature at the apex, are perhaps the simplest example of geometric frustration. We study two-dimensional liquid crystals with p-fold rotational symmetry (p-atics) on the surfaces of cones. For free boundary conditions at the base, we find both the ground state(s) and a discrete ladder of metastable states as a function of both the cone angle and the liquid crystal symmetry p. We find that these states are characterized by a set of fractional defect charges at the apex and that the ground states are in general frustrated due to effects of parallel transport along the azimuthal direction of the cone. We check our predictions for the ground-state energies numerically for a set of commensurate cone angles (corresponding to a set of commensurate Gaussian curvatures concentrated at the cone apex), whose surfaces can be polygonized as a perfect triangular or square mesh, and find excellent agreement with our theoretical predictions.

Bistability of Dielectrically Anisotropic Nematic Crystals and the Adaptation of Endothelial Collectives to Stress Fields

Endothelial monolayers physiologically adapt to flow and flow-induced wall shear stress, attaining ordered configurations in which elongation, orientation, and polarization are coherently organized over many cells. Here, with the flow direction unchanged, a peculiar bi-stable (along the flow direction or perpendicular to it) cell alignment is observed, emerging as a function of the flow intensity alone, while cell polarization is purely instructed by flow directionality. Driven by the experimental findings, the parallelism between endothelia is delineated under a flow field and the transition of dual-frequency nematic liquid crystals under an external oscillatory electric field. The resulting physical model reproduces the two stable configurations and the energy landscape of the corresponding system transitions. In addition, it reveals the existence of a disordered, metastable state emerging upon system perturbation. This intermediate state, experimentally demonstrated in endothelial monolayers, is shown to expose the cellular system to a weakening of cell-to-cell junctions to the detriment of the monolayer integrity. The flow-adaptation of monolayers composed of healthy and senescent endothelia is successfully predicted by the model with adjustable nematic parameters. These results may help to understand the maladaptive response of in vivo endothelial tissues to disturbed hemodynamics and the progressive functional decay of senescent endothelia.

Motile Topological Defects Hinder Dynamical Arrest in Dense Liquids of Active Ellipsoids

Recent numerical studies have identified the persistence time of active motion as a critical parameter governing glassy dynamics in dense active matter. Here we studied dynamics in liquids of granular active ellipsoids with tunable persistence and velocity. We show that increasing the persistence time at moderate supercooling is equivalent to increasing the strength of attraction in equilibrium liquids and results in reentrant dynamics not just in the translational degrees of freedom, as anticipated, but also in the orientational ones. However, at high densities, motile topological defects, unique to active liquids of elongated particles, hindered dynamical arrest. Most remarkably, for the highest activity, we observed intermittent dynamics due to the jamming-unjamming of these defects for the first time.

Theory of defect-mediated morphogenesis

Growing experimental evidence indicates that topological defects could serve as organizing centers in the morphogenesis of tissues. Here, we provide a quantitative explanation for this phenomenon, rooted in the buckling theory of deformable active polar liquid crystals. Using a combination of linear stability analysis and computational fluid dynamics, we demonstrate that active layers, such as confined cell monolayers, are unstable to the formation of protrusions in the presence of disclinations. The instability originates from an interplay between the focusing of the elastic forces, mediated by defects, and the renormalization of the system's surface tension by the active flow. The posttransitional regime is also characterized by several complex morphodynamical processes, such as oscillatory deformations, droplet nucleation, and active turbulence. Our findings offer an explanation of recent observations on tissue morphogenesis and shed light on the dynamics of active surfaces in general.

Modelling of filamentous phage-induced antibiotic tolerance of P. aeruginosa

Filamentous molecules tend to spontaneously assemble into liquid crystalline droplets with a tactoid morphology in environments with high concentration on non-adsorbing molecules. Tactoids of filamentous Pf bacteriophage, such as those produced by Pseudomonas aeruginosa, have been linked to increased antibiotic tolerance. We modelled this system and show that tactoids composed of filamentous Pf virions can lead to antibiotic tolerance by acting as an adsorptive diffusion barrier. The continuum model, reminiscent of descriptions of reactive diffusion in porous media, has been solved numerically and good agreement was found with the analytical results, obtained using a homogenisation approach. We find that the formation of tactoids significantly increases antibiotic diffusion times which may lead to stronger antibiotic resistance.

Spontaneous flow created by active topological defects

Topological defects are at the root of the large-scale organization of liquid crystals. In two-dimensional active nematics, two classes of topological defects of charges [Formula: see text] are known to play a major role due to active stresses. Despite this importance, few analytical results have been obtained on the flow-field and active-stress patterns around active topological defects. Using the generic hydrodynamic theory of active systems, we investigate the flow and stress patterns around these topological defects in unbounded, two-dimensional active nematics. Under generic assumptions, we derive analytically the spontaneous velocity and stall force of self-advected defects in the presence of both shear and rotational viscosities. Applying our formalism to the dynamics of monolayers of elongated cells at confluence, we show that the non-conservation of cell number generically increases the self-advection velocity and could provide an explanation for their observed role in cellular extrusion and multilayering. We finally investigate numerically the influence of the Ericksen stress. Our work paves the way to a generic study of the role of topological defects in active nematics, and in particular in monolayers of elongated cells.

The mechanical forces that shape our senses

Developing organs are shaped, in part, by physical interaction with their environment in the embryo. In recent years, technical advances in live-cell imaging and material science have greatly expanded our understanding of the mechanical forces driving organ formation. Here, we provide a broad overview of the types of forces generated during embryonic development and then focus on a subset of organs underlying our senses: the eyes, inner ears, nose and skin. The epithelia in these organs emerge from a common origin: the ectoderm germ layer; yet, they arrive at unique and complex forms over developmental time. We discuss exciting recent animal studies that show a crucial role for mechanical forces in, for example, the thickening of sensory placodes, the coiling of the cochlea and the lengthening of hair. Finally, we discuss how microfabricated organoid systems can now provide unprecedented insights into the physical principles of human development.

Recyclable Periodic Nanostructure Formed by Sublimable Liquid Crystals for Robust Cell Alignment

We demonstrate a facile method to fabricate a recyclable cell-alignment scaffold using nanogrooves based on sublimable liquid crystal (LC) material. Randomly and uniaxially arranged smectic LC structures are obtained, followed by sublimation and recondensation processes, which directly produce periodic nanogrooves with dimensions of a couple of hundreds of nanometers. After treatment with osmium tetroxide (OsO₄), the nanogroove can serve as a scaffold to efficiently induce directed cell growth without causing cytotoxicity, and it can be used repeatedly. Together, various cell types are applied to the nanogroove, proving the scaffold's broad applicability. Depending on the nanotopography of the LC structures, cells exhibit different morphologies and gene expression patterns, compared to cells on standard glass substrates, according to microscopic observation and qPCR. Furthermore, cell sheets can be formed, which consist of oriented cells that can be repeatedly formed and transferred to other substrates, while maintaining its organization. We believe that our cell-aligning scaffold may pave the way for the soft material field to bioengineering, which can involve fundamentals in cell behavior and function, as well as applications for regenerative medicine.

Singularity identification for the characterization of topology, geometry, and motion of nematic disclination lines

We introduce a characterization of disclination lines in three dimensional nematic liquid crystals as a tensor quantity related to the so called rotation vector around the line. This quantity is expressed in terms of the nematic tensor order parameter Q, and shown to decompose as a dyad involving the tangent vector to the disclination line and the rotation vector. Further, we derive a kinematic law for the velocity of disclination lines by connecting this tensor to a topological charge density as in the Halperin-Mazenko description of defects in vector models. Using this framework, analytical predictions for the velocity of interacting line disclinations and of self-annihilating disclination loops are given and confirmed through numerical computation.

Epithelial folding of alveolar cells derived from human induced pluripotent stem cells on artificial basement membrane

Epithelial folding depends on mechanical properties of both epithelial cells and underlying basement membrane (BM). While folding is essential for tissue morphogenesis and functions, it is difficult to recapitulate features of a growing epithelial monolayer for in vitro modeling due to lack of in vivo like BM. Herein, we report a method to overcome this difficulty by culturing on an artificial basement membrane (ABM) the primordial lung progenitors (PLPs) from human induced pluripotent stem cells (hiPSCs). The ABM was achieved by self-assembling collagen IV and laminin, the two principal natural BM proteins, in the pores of a monolayer of crosslinked gelatin nanofibers deposited on a honeycomb micro-frame. The hiPSC-PLPs were seeded on the ABM for alveolar differentiation under submerged and air-liquid interface culture conditions. As results, the forces generated by the growing epithelial monolayer led to a geometry-dependent folding. Analysis of strain distribution in a clamped membrane provided instrumental insights into some of the observed phenomena. Moreover, the forces generated by the growing epithelial layer led to a high-level expression of surfactant protein C and a high percentage of aquaporin 5 positive cells compared with the results obtained with a nanofiber-covered bulk substrate. Thus, this work demonstrated the importance of recapitulating natural BM for advanced epithelial modeling. STATEMENT OF SIGNIFICANCE: The effort to develop in vitro epithelial models has not been entirely successful to date, due to lack of in vivo like basement membrane (BM). This lack has been overcome by using a microfabricated dense thin and pliable sheet like structure made of natural BM proteins. With such an artificial BM, alveolar epithelial deformation and folding could be studied and date could be correlated to numerical analyses of a plate theory. This method is simple and effective, enabling further developments in epithelial tissue modeling.

Large-scale orientational order in bacterial colonies during inward growth

During colony growth, complex interactions regulate the bacterial orientation, leading to the formation of large-scale ordered structures, including topological defects, microdomains, and branches. These structures may benefit bacterial strains, providing invasive advantages during colonization. Active matter dynamics of growing colonies drives the emergence of these ordered structures. However, additional biomechanical factors also play a significant role during this process. Here, we show that the velocity profile of growing colonies creates strong radial orientation during inward growth when crowded populations invade a closed area. During this process, growth geometry sets virtual confinement and dictates the velocity profile. Herein, flow-induced alignment and torque balance on the rod-shaped bacteria result in a new stable orientational equilibrium in the radial direction. Our analysis revealed that the dynamics of these radially oriented structures, also known as aster defects, depend on bacterial length and can promote the survival of the longest bacteria around localized nutritional hotspots. The present results indicate a new mechanism underlying structural order and provide mechanistic insights into the dynamics of bacterial growth on complex surfaces.

Appreciating the role of cell shape changes in the mechanobiology of epithelial tissues

The wide range of epithelial cell shapes reveals the complexity and diversity of the intracellular mechanisms that serve to construct their morphology and regulate their functions. Using mechanosensitive steps, epithelial cells can sense a variety of different mechanochemical stimuli and adapt their behavior by reshaping their morphology. These changes of cell shape rely on a structural reorganization in space and time that generates modifications of the tensional state and activates biochemical cascades. Recent studies have started to unveil how the cell shape maintenance is involved in mechanical homeostatic tasks to sustain epithelial tissue folding, identity, and self-renewal. Here, we review relevant works that integrated mechanobiology to elucidate some of the core principles of how cell shape may be conveyed into spatial information to guide collective processes such as epithelial morphogenesis. Among many other parameters, we show that the regulation of the cell shape can be understood as the result of the interplay between two counteracting mechanisms: actomyosin contractility and intercellular adhesions, and that both do not act independently but are functionally integrated to operate on molecular, cellular, and tissue scales. We highlight the role of cadherin-based adhesions in force-sensing and mechanotransduction, and we report recent developments that exploit physics of liquid crystals to connect cell shape changes to orientational order in cell aggregates. Finally, we emphasize that the further intermingling of different disciplines to develop new mechanobiology assays will lead the way toward a unified picture of the contribution of cell shape to the pathophysiological behavior of epithelial tissues.

Dynamic self-organization of migrating cells under constraints by spatial confinement and epithelial integrity

Understanding how migrating cells can establish both dynamic structures and coherent dynamics may provide mechanistic insights to study how living systems acquire complex structures and functions. Recent studies revealed that intercellular contact communication plays a crucial role for establishing cellular dynamic self-organization (DSO) and provided a theoretical model of DSO for migrating solitary cells in a free space. However, to apply those understanding to situations in living organisms, we need to know the role of cell-cell communication for tissue dynamics under spatial confinements and epithelial integrity. Here, we expand the previous numerical studies on DSO to migrating cells subjected spatial confinement and/or epithelial integrity. An epithelial monolayer is simulated by combining the model of cellular DSO and the cellular vertex model in two dimensions for apical integrity. Under confinement to a small space, theoretical models of both solitary and epithelial cells exhibit characteristic coherent dynamics, including apparent swirling. We also find that such coherent dynamics can allow the cells to overcome the strong constraint due to spatial confinement and epithelial integrity. Furthermore, we demonstrate how epithelial cell clusters behave without spatial confinement and find various cluster dynamics, including spinning, migration and elongation.

Polar Fluctuations Lead to Extensile Nematic Behavior in Confluent Tissues

How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions of confluent tissues, in both liquid and solid states. Specifically, we show that a collection of microscopic constituents with no inherently nematic extensile forces can exhibit active extensile nematic behavior when subject to polar fluctuating forces. We further support our findings by performing cell level simulations of minimal models of confluent tissues.

Ferroelectric incommensurate spin crystals

Ferroics, especially ferromagnets, can form complex topological spin structures such as vortices¹ and skyrmions^2,3 when subjected to particular electrical and mechanical boundary conditions. Simple vortex-like, electric-dipole-based topological structures have been observed in dedicated ferroelectric systems, especially ferroelectric-insulator superlattices such as PbTiO₃/SrTiO₃, which was later shown to be a model system owing to its high depolarizing field^4-8. To date, the electric dipole equivalent of ordered magnetic spin lattices driven by the Dzyaloshinskii-Moriya interaction (DMi)^9,10 has not been experimentally observed. Here we examine a domain structure in a single PbTiO₃ epitaxial layer sandwiched between SrRuO₃ electrodes. We observe periodic clockwise and anticlockwise ferroelectric vortices that are modulated by a second ordering along their toroidal core. The resulting topology, supported by calculations, is a labyrinth-like pattern with two orthogonal periodic modulations that form an incommensurate polar crystal that provides a ferroelectric analogue to the recently discovered incommensurate spin crystals in ferromagnetic materials^11-13. These findings further blur the border between emergent ferromagnetic and ferroelectric topologies, clearing the way for experimental realization of further electric counterparts of magnetic DMi-driven phases.

Nematic Templated Complex Nanofiber Structures by Projection Display

Oriented arrays of nanofibers are ubiquitous in nature and have been widely used in recreation of the biological functions such as bone and muscle tissue regenerations. However, it remains a challenge to produce nanofiber arrays with a complex organization by using current fabrication techniques such as electrospinning and extrusion. In this work, we propose a method to fabricate the complex organization of nanofiber structures templated by a spatially varying ordered liquid crystal host, which follows the pattern produced by a maskless projection display system. By programming the synchronization of the rotated polarizer and projected segments with different shapes, various configurations of nanofiber organization ranging from a single to two-dimensional lattice of arbitrary topological defects are created in a deterministic manner. The nanofiber arrays can effectively guide and promote neurite outgrowth. The application of nanofibers with arced profiles and topological defects on neural tissue organization is also demonstrated. This finding, combined with the versatility and programmability of nanofiber structures, suggests that they will help solve challenges in nerve repair, neural regeneration, and other related tissue engineering fields.

Sculpting tissues by phase transitions

Biological systems display a rich phenomenology of states that resemble the physical states of matter - solid, liquid and gas. These phases result from the interactions between the microscopic constituent components - the cells - that manifest in macroscopic properties such as fluidity, rigidity and resistance to changes in shape and volume. Looked at from such a perspective, phase transitions from a rigid to a flowing state or vice versa define much of what happens in many biological processes especially during early development and diseases such as cancer. Additionally, collectively moving confluent cells can also lead to kinematic phase transitions in biological systems similar to multi-particle systems where the particles can interact and show sub-populations characterised by specific velocities. In this Perspective we discuss the similarities and limitations of the analogy between biological and inert physical systems both from theoretical perspective as well as experimental evidence in biological systems. In understanding such transitions, it is crucial to acknowledge that the macroscopic properties of biological materials and their modifications result from the complex interplay between the microscopic properties of cells including growth or death, neighbour interactions and secretion of matrix, phenomena unique to biological systems. Detecting phase transitions in vivo is technically difficult. We present emerging approaches that address this challenge and may guide our understanding of the organization and macroscopic behaviour of biological tissues.

Macroscopic current generated by local division and apoptosis in a minimal model of tissue dynamics

It has been known that the motion of self-propelled particles inside an asymmetric channel can be rectified to give rise to a macroscopic and unidirectional current. In this paper, we show that division and apoptosis process alone (which are ubiquitous in all living systems), without any self-propulsion, are sufficient to give rise to a macroscopic and unidirectional current in a similar channel. More specifically, we consider a minimal computational model of two-dimensional living tissues, with two active ingredients: local particle division and apoptosis, and we found a net steady state current along the channel. This mechanism is fundamentally different from that of self-propelled particles, since this requires the system to be dense. Finally, our results might have applications in tissue engineering such as controlling tissue growth via a geometrically non-uniform substrate.

Active Extensile Stress Promotes 3D Director Orientations and Flows

We use numerical simulations and linear stability analysis to study an active nematic layer where the director is allowed to point out of the plane. Our results highlight the difference between extensile and contractile systems. Contractile stress suppresses the flows perpendicular to the layer and favors in-plane orientations of the director. By contrast extensile stress promotes instabilities that can turn the director out of the plane, leaving behind a population of distinct, in-plane regions that continually elongate and divide. This supports extensile forces as a mechanism for the initial stages of layer formation in living systems, and we show that a planar drop with extensile (contractile) activity grows into three dimensions (remains in two dimensions). The results also explain the propensity of disclination lines in three dimensional active nematics to be of twist type in extensile or wedge type in contractile materials.

Regulating life after death: how mechanical communication mediates the epithelial response to apoptosis

It is increasingly evident that cells in tissues and organs can communicate with one another using mechanical forces. Such mechanical signalling can serve as a basis for the assembly of cellular communities. For this to occur, there must be local instabilities in tissue mechanics that are the source of the signals, and mechanisms for changes in mechanical force to be transmitted and detected within tissues. In this review, we discuss these principles using the example of cell death by apoptosis, when it occurs in epithelia. This elicits the phenomenon of apical extrusion, which can rapidly eliminate apoptotic cells by expelling them from the epithelium. Apoptotic extrusion requires that epithelial cells detect the presence of nearby apoptotic cells, something which can be elicited by the mechanotransduction of tensile instabilities caused by the apoptotic cell. We discuss the central role that adherens junctions can play in the transmission and detection of mechanical signals from apoptotic cells.

Implementation of cellular bulk stresses in vertex models of biological tissues

Vertex models describe biological tissues as tilings of polygons. In standard vertex models, the tissue dynamics result from a balance between isotropic stresses, which are associated with the bulk of the cells, and tensions associated with cell-cell interfaces. However, in this framework it is less obvious how to describe anisotropic stresses arising from the bulk of cells. In epithelia, such bulk anisotropic stresses could arise for instance through medial myosin fluctuations. Two recent publications-Tlili et al. (Proc Natl Acad Sci USA 116(51):25430-25439, 2019) and Comelles et al. (eLife 10:e57730, 2021)-have proposed different schemes to implement bulk anisotropic stresses in vertex models. Here we show that while both schemes transform in the same way under affine deformations, they lead to significantly different tissue dynamics. Our results are consistent with the interpretation that the Tilli et al. scheme describes bulk stresses that are uniform within each cell, while the Comelles et al. scheme corresponds to non-uniform bulk stresses. Finally, we wondered whether a standard vertex model can be fully expressed in terms of bulk cellular stresses alone. We find that, in general, neither scheme can mimic the vertex forces created by cell-cell interface tensions.

Aster repulsion drives short-ranged ordering in the Drosophila syncytial blastoderm

Biological systems are highly complex, yet notably ordered structures can emerge. During syncytial stage development of the Drosophila melanogaster embryo, nuclei synchronously divide for nine cycles within a single cell, after which most of the nuclei reach the cell cortex. The arrival of nuclei at the cortex occurs with remarkable positional order, which is important for subsequent cellularisation and morphological transformations. Yet, the mechanical principles underlying this lattice-like positional order of nuclei remain untested. Here, using quantification of nuclei position and division orientation together with embryo explants, we show that short-ranged repulsive interactions between microtubule asters ensure the regular distribution and maintenance of nuclear positions in the embryo. Such ordered nuclear positioning still occurs with the loss of actin caps and even the loss of the nuclei themselves; the asters can self-organise with similar distribution to nuclei in the wild-type embryo. The explant assay enabled us to deduce the nature of the mechanical interaction between pairs of nuclei. We used this to predict how the nuclear division axis orientation changes upon nucleus removal from the embryo cortex, which we confirmed in vivo with laser ablation. Overall, we show that short-ranged microtubule-mediated repulsive interactions between asters are important for ordering in the early Drosophila embryo and minimising positional irregularity.