Nematic Defects Research Articles

Confinement Modulates Axial Patterning in Regenerating Hydra

The establishment of the body plan is a major step in animal morphogenesis. The role of mechanical forces and feedback in patterning the body plan remains unclear. Here we explore this question by studying regenerating Hydra tissues confined in narrow cylindrical channels, which constrain their morphology. We find that frustration between the orientation of the channel and the inherited axis in the regenerating tissues can lead to the formation of a multiaxial body plan. The morphological outcome is directly related to the pattern of nematic topological defects that emerges in the organization of the supracellular actomyosin fibers. When the inherited axis, which can be read out from the initial alignment of the supracellular fibers in the confined spheroid, is parallel to the channel's axis, the tissue regenerates normally into animals with a single body axis aligned with the channel. However, regenerating spheroids that are confined in a frustrated perpendicular configuration often develop excess defects (including negatively charged −1/2 defects) and regenerate into multiaxial morphologies. The influence of mechanical constraints on the regenerated body plan argues against an axial patterning mechanism that is based solely on inherited gradients of biochemical morphogens. We further show that the dependence of the regeneration outcomes on the initial tissue orientation can be recapitulated by a biophysical model, which considers the coupled dynamics of the nematic organization of the actomyosin fibers and a morphogen concentration field, incorporating a mechanochemical feedback loop involving strain-dependent morphogen production at defect sites. Published by the American Physical Society 2024

Intercellular friction and motility drive orientational order in cell monolayers

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

Ordered structures formed by nematic topological defects and their transformation with changing the Euler characteristics.

Ordered chain structures from topological defects of opposite charges ("necklaces" of defects) were prepared and their dynamics and cooperative rearrangement were investigated. We studied topological defects in nematic films with change of the Euler characteristic induced by temperature. Topological defects emerged due to competing surface anchoring on the nematic-isotropic and nematic-solid interfaces. Transformation of the structure with a circular chain from topological defects to the structure with a single defect and then to a structure without defects takes place as the nematic geometry changes. The temporal evolution of the number of topological defects at their annihilation in the chains differs from coarsening in two-dimensional (2D) and 3D geometry.

Growth-induced collective bending and kinetic trapping of cytoskeletal filaments.

Growth and turnover of actin filaments play a crucial role in the construction and maintenance of actin networks within cells. Actin filament growth occurs within limited space and finite subunit resources in the actin cortex. To understand how filament growth shapes the emergent architecture of actin networks, we developed a minimal agent-based model coupling filament mechanics and growth in a limiting subunit pool. We find that rapid filament growth induces kinetic trapping of highly bent actin filaments. Such collective bending patterns are long-lived, organized around nematic defects, and arise from competition between filament polymerization and bending elasticity. The stability of nematic defects and the extent of kinetic trapping are amplified by an increase in the abundance of the actin pool and by crosslinking the network. These findings suggest that kinetic trapping is a robust consequence of growth in crowded environments, providing a route to program shape memory in actin networks.

Periodic orbits, pair nucleation, and unbinding of active nematic defects on cones.

Geometric confinement and topological constraints present promising means of controlling active materials. By combining analytical arguments derived from the Born-Oppenheimer approximation with numerical simulations, we investigate the simultaneous impact of confinement together with curvature singularity by characterizing the dynamics of an active nematic on a cone. Here, the Born-Oppenheimer approximation means that textures can follow defect positions rapidly on the timescales of interest. Upon imposing strong anchoring boundary conditions at the base of a cone, we find a rich phase diagram of multidefect dynamics, including exotic periodic orbits of one or two +1/2 flank defects, depending on activity and nonquantized geometric charge at the cone apex. By characterizing the transitions between these ordered dynamical states, we present detailed understanding of (i) defect unbinding, (ii) defect absorption, and (iii) defect pair nucleation at the apex. Numerical simulations confirm theoretical predictions of not only the nature of the circular orbits but also defect unbinding from the apex.

The role of aspect ratio and activity on how active nematic defects distribute on toroidal surfaces

Active topological defects are one of the most exciting non-equilibrium systems of recent times. In our experiments, we confine an active nematic populated by positive and negative topological defects to a toroidal surface, and explore how the local geometry, parameterised by the Gaussian curvature, influences the distribution of defects. We find curvature-induced defect unbinding, for relatively thick tori and low activities. In contrast, for high activity and thin tori, which serve to locally approach the cylindrical limit, the relevance of the defect-curvature coupling is lost. Overall, our results illustrate how curvature and activity can both be used to affect how defects distribute on surfaces with varying curvature.

Topological Defects in Tactoid Nematic Phase

The purpose research of the work is to illustrate the role of point surface topological defects in nematics in phase transitions using the example of inorganic sols of vanadium pentoxide in water V2O5/H2O.Methods. Basing on the measurements on polarization light microscopy and theoretically, in frames of the Landau-de Gennes model and the Kibble-Zurek model for defects, the influence of point topological defects at the surface of nematic colloid of lyotropic liquid crystals, in particular, in inorganic sols of the V2O5/H2O system, on their critical thermodynamic, electric, optical, elastic and mechanical properties is estimated. For the system V2O5/H2O, we study the developed models of nematic colloid phases with non-trivial topology composed of spindle-shaped particles, in which their topological defects are classified; geometrical parameters of nematic particles in dynamics and evolution depending on physicochemical conditions, phase stability criteria, conditions for coalescence of particles, including, under external magnetic field, and also, experimental observations confirmed the proposed theories and models, are considered.Results. With a glance of coalescence regime, the critical size of a colloid particle of the system V2O5/H2O, ~ 10 nm in the long axis direction, in which the value of magnetic energy equals to the sum of elastic and surface energy of acolloid particle, is estimated.Conclusion. We confirmed, that the prerequisite of sol particle coalescence in the system V2O5/H2O in the magnetic field is annihilation of the point topological defects at their poles, the geometrical criterion of tactoid coalescence in magnetic field is established basing on the different theories of their surface defects.

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 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.

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.

Formation and annihilation of electrically driven defects in nematic liquid crystals with negative dielectric anisotropy

Orientationally ordered liquid crystals (LCs) exhibit remarkable physical anisotropy and responsiveness to external fields, which give rise to distinguished physical effects and have led to the emergence of a new generation of electric-optical applications. The LCs are also renowned for their abundance of phases and topological defects, which are of significance in studying both fundamental science and practical technology. One simple approach to generating umbilic defects involves applying an electric field to a homeotropically aligned nematic LC with negative dielectric anisotropy <inline-formula><tex-math id="M8">\begin{document}$\Delta \varepsilon $\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M8.png"/></alternatives></inline-formula>. However, the influence of material properties and external conditions on the dynamic process of nematic LC defects remains unclear. Here, we select seven kinds of nematic LCs with negative dielectrically anisotropy, ranging from –1.1 to –11.5, to explore the dynamics of electric-field-induced umbilics. By using a linearly increasing electric field parallel to the molecular orientation of LC, we systematically investigate the effects of material property (dielectric anisotropy) and external conditions (temperature and electric field parameters) on the formation and annihilation of umbilic defects. The experimental results show that the dynamic process of forming the umbilic defects in nematic LCs is independent of dielectric anisotropy, temperature, and electric field frequency, but follows the Kibble-Zurek mechanism, in which the density of generated umbilic defects exhibits a power-law scaling with the change of the electric field ramp rate, with a scaling exponent of approximately <inline-formula><tex-math id="M9">\begin{document}$1/2$\end{document}</tex-math><alternatives><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.jpg"/><graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="5-20231655_M9.png"/></alternatives></inline-formula>. Interestingly, a stronger dielectric anisotropy leads to a higher density of umbilic defects. Additionally, a change in temperature has a significant influence on the density of umbilic defects , in which higher temperature leads to greater defect density under the same external electric field conditions. Furthermore, the annihilation rate of umbilic defects is closely related to the material properties and the ramp of the applied electric field. Specifically, the annihilation rate of umbilic defects becomes faster when dielectric anisotropy is stronger or the electric field ramp is larger. This study provides valuable insights into the relationship between the formation and annihilation of defects, material properties, and external conditions in nematic LCs with dielectrically negative anisotropy, contributing to our comprehensive understanding of the dynamic process of topological defects in soft matter.

Particle-based and continuum models for confined nematics in two dimensions.

We use the particle-based stochastic multi-particle collision dynamics (N-MPCD) algorithm to simulate confined nematic liquid crystals in regular two-dimensional polygons such as squares, pentagons and hexagons. We consider a range of values of the nematicities, U, and simulation domain sizes, R, that canvass nano-sized polygons to micron-sized polygons. We use closure arguments to define mappings between the N-MPCD parameters and the parameters in the continuum deterministic Landau-de Gennes framework. The averaged N-MPCD configurations agree with those predicted by Landau-de Gennes theory, at least for large polygons. We study relaxation dynamics or the non-equilibrium dynamics of confined nematics in polygons, in the N-MPCD framework, and the kinetic traps bear strong resemblance to the unstable saddle points in the Landau-de Gennes framework. Finally, we study nematic defect dynamics inside the polygons in the N-MPCD framework and the finite-size effects slow down the defects and attract them to polygon vertices. Our work is a comprehensive comparison between particle-based stochastic N-MPCD methods and deterministic/continuum Landau-de Gennes methods, and this comparison is essential for new-age multiscale theories.

Effect of internal energy depletion on active nematic texture and dynamics

ABSTRACTActive nematics represent a relatively new class of materials with liquid crystalline properties that rely on an energy source to maintain their structure and dynamics. In this paper, we focus on the well-known microtubule-kinesin-based active nematic, powered by chemical energy as ATP (Adenosine triphosphate), and report on how ATP depletion impacts active nematic defect dynamics and texture. Using fluorescence microscope video imaging, we measure the time averaged mean defect separations and root mean square velocities of the active flows as a function of time. We also characterise textural changes and the growth of void space in the network after ATP depletion using an image binarization technique.

Anomalous Spectral Shift of o-Modes in Multilayer Photonic Structure Induced by Homeotropic–Homeoplanar Transition in Chiral–Nematic Defect Layer

Anomalous Spectral Shift of o-Modes in Multilayer Photonic Structure Induced by Homeotropic–Homeoplanar Transition in Chiral–Nematic Defect Layer

Geometrical control of interface patterning underlies active matter invasion

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Polarity and chirality control of an active fluid by passive nematic defects

Much like passive materials, active systems can be affected by the presence of imperfections in their microscopic order, called defects, that influence macroscopic properties. This suggests the possibility to steer collective patterns by introducing and controlling defects in an active system. Here we show that a self-assembled, passive nematic is ideally suited to control the pattern formation process of an active fluid. To this end, we force microtubules to glide inside a passive nematic material made from actin filaments. The actin nematic features self-assembled half-integer defects that steer the active microtubules and lead to the formation of macroscopic polar patterns. Moreover, by confining the nematic in circular geometries, chiral loops form. We find that the exact positioning of nematic defects in the passive material deterministically controls the formation and the polarity of the active flow, opening the possibility of efficiently shaping an active material using passive defects.

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.

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.

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.

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.