Biological Tissues as Active Nematic Liquid Crystals

Confinement promotes nematic alignment of spindle-shaped cells during Drosophila embryogenesis

Tissue morphogenesis is often controlled by actomyosin networks pulling on adherens junctions (AJs), but junctional myosin levels vary. At an extreme, the Drosophila embryo amnioserosa forms a horseshoe-shaped strip of aligned, spindle-shaped cells lacking junctional myosin. What are the bases of amnioserosal cell interactions and alignment? Compared with surrounding tissue, we find that amnioserosal AJ continuity has lesser dependence on α-catenin, the mediator of AJ-actomyosin association, and greater dependence on Bazooka/Par-3, a junction-associated scaffold protein. Microtubule bundles also run along amnioserosal AJs and support their long-range curvilinearity. Amnioserosal confinement is apparent from partial overlap of its spindle-shaped cells, its outward bulging from surrounding tissue and from compressive stress detected within the amnioserosa. Genetic manipulations that alter amnioserosal confinement by surrounding tissue also result in amnioserosal cells losing alignment and gaining topological defects characteristic of nematically ordered systems. With Bazooka depletion, confinement by surrounding tissue appears to be relatively normal and amnioserosal cells align despite their AJ fragmentation. Overall, the fully elongated amnioserosa appears to form through tissue-autonomous generation of spindle-shaped cells that nematically align in response to confinement by surrounding tissue.

Perspectives in collective cell migration - moving forward

Collective cell migration, where cells move as a cohesive unit, is a vital process underlying morphogenesis and cancer metastasis. Thanks to recent advances in imaging and modelling, we are beginning to understand the intricate relationship between a cell and its microenvironment and how this shapes cell polarity, metabolism and modes of migration. The use of biophysical and mathematical models offers a fresh perspective on how cells migrate collectively, either flowing in a fluid-like state or transitioning to more static states. Continuing to unite researchers in biology, physics and mathematics will enable us to decode more complex biological behaviours that underly collective cell migration; only then can we understand how this coordinated movement of cells influences the formation and organisation of tissues and directs the spread of metastatic cancer. In this Perspective, we highlight exciting discoveries, emerging themes and common challenges that have arisen in recent years, and possible ways forward to bridge the gaps in our current understanding of collective cell migration.

Computational tools for cellular scale biophysics

Mathematical models are indispensable for disentangling the interactions through which biological components work together to generate the forces and flows that position, mix, and distribute proteins, nutrients, and organelles within the cell. To illuminate the ever more specific questions studied at the edge of biological inquiry, such models inevitably become more complex. Solving, simulating, and learning from these more realistic models requires the development of new analytic techniques, numerical methods, and scalable software. In this review, we discuss some recent developments in tools for understanding how large numbers of cytoskeletal filaments, driven by molecular motors and interacting with the cytoplasm and other structures in their environment, generate fluid flows, instabilities, and material deformations which help drive crucial cellular processes.

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

The ability of cells to organize into tissues with proper structure and function requires the effective coordination of proliferation, migration, polarization, and differentiation across length scales. Skeletal muscle is innately anisotropic; however, few biomaterials can emulate mechanical anisotropy to determine its influence on tissue patterning without introducing confounding topography. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topography, C2C12 myoblasts collectively polarize in the stiffest direction. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of the same chemical formulation. These findings provide valuable insights for designing biomaterials that mimic anisotropic microenvironments and underscore the importance of stiffness anisotropy in orchestrating tissue morphogenesis.

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.

Controlling active turbulence by activity patterns

By patterning activity in space, one can control active turbulence. To show this, we use Doi's hydrodynamic equations of a semidilute solution of active rods. A linear stability analysis reveals the resting isotropic fluid to be unstable above an absolute pusher activity. The emergent activity-induced paranematic state displays active turbulence, which we characterize by different quantities including the energy spectrum, which shows the typical power-law decay with exponent -4. Then, we control the active turbulence by a square lattice of circular spots where activity is switched off. In the parameter space lattice constant versus surface-to-surface distance of the spots, we identify different flow states. Most interestingly, for lattice constants below the vorticity correlation length and for spot distances smaller than the nematic coherence length, we observe a multi-lane flow state, where flow lanes with alternating flow directions are separated by a street of vortices. The flow pattern displays pronounced multistability and also appears transiently at the transition to the isotropic active-turbulence state. At larger lattice constants a trapped vortex state is identified with a non-Gaussian vorticity distribution due to the low flow vorticity at the spots. It transitions to conventional active turbulence for increasing spot distance.

Coarse-graining the vertex model and its response to shear

Tissue dynamics and collective cell motion are crucial biological processes. Their biological machinery is mostly known, and simulation models such as the active vertex model exist and yield reasonable agreement with experimental observations such as tissue fluidization or fingering. However, a good and well-founded continuum description for tissues remains to be developed. In this work, we derive a macroscopic description for a two-dimensional cell monolayer by coarse-graining the vertex model through the Poisson bracket approach. We obtain equations for cell density, velocity, and the cellular shape tensor. We then study the homogeneous steady states, their stability (which coincides with thermodynamic stability), and especially their behavior under an externally applied shear. Our results contribute to elucidate the interplay between flow and cellular shape. The obtained macroscopic equations present a good starting point for adding cell motion, morphogenetic, and other biologically relevant processes.

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.

Active nematics with deformable particles

The hydrodynamic theory of active nematics has been often used to describe the spatio-temporal dynamics of cell flows and motile topological defects within soft confluent tissues. Those theories, however, often rely on the assumption that tissues consist of cells with a fixed, anisotropic shape and do not resolve dynamical cell shape changes due to flow gradients. In this paper we extend the continuum theory of active nematics to include cell shape deformability. We find that circular cells in tissues must generate sufficient active stress to overcome an elastic barrier to deforming their shape in order to drive tissue-scale flows. Above this threshold the systems enter a dynamical steady-state with regions of elongated cells and strong flows coexisting with quiescent regions of isotropic cells.

Stiffness anisotropy coordinates supracellular contractility driving long-range myotube-ECM alignment

In skeletal muscle tissue, injury-related changes in stiffness activate muscle stem cells through mechanosensitive signaling pathways. Functional muscle tissue regeneration also requires the effective coordination of myoblast proliferation, migration, polarization, differentiation, and fusion across multiple length scales. Here, we demonstrate that substrate stiffness anisotropy coordinates contractility-driven collective cellular dynamics resulting in C2C12 myotube alignment over millimeter-scale distances. When cultured on mechanically anisotropic liquid crystalline polymer networks (LCNs) lacking topographic features that could confer contact guidance, C2C12 myoblasts collectively polarize in the stiffest direction of the substrate. Cellular coordination is amplified through reciprocal cell-ECM dynamics that emerge during fusion, driving global myotube-ECM ordering. Conversely, myotube alignment was restricted to small local domains with no directional preference on mechanically isotropic LCNs of same chemical formulation. These findings reveal a role for stiffness anisotropy in coordinating emergent collective cellular dynamics, with implications for understanding skeletal muscle tissue development and regeneration.

Reconfigurable scaffolds for adaptive tissue regeneration

Tissue engineering and regenerative medicine have offered promising alternatives for clinical treatment of body tissue traumas, losses, dysfunctions, or diseases, where scaffold-based strategies are particularly popular and effective. Over the decades, scaffolds for tissue regeneration have been remarkably evolving. Nevertheless, conventional scaffolds still confront grand challenges in bio-adaptions in terms of both tissue-scaffold and cell-scaffold interplays, for example complying with complicated three-dimensional (3D) shapes of biological tissues and recapitulating the ordered cell regulation effects of native cell microenvironments. Benefiting from the recent advances in "intelligent" biomaterials, reconfigurable scaffolds have been emerging, demonstrating great promise in addressing the bio-adaption challenges through altering their macro-shapes and/or micro-structures. This mini-review article presents a brief overview of the cutting-edge research on reconfigurable scaffolds, summarizing the materials for forming reconfigurable scaffolds and highlighting their applications for adaptive tissue regeneration. Finally, the challenges and prospects of reconfigurable scaffolds are also discussed, shedding light on the bright future of next-generation reconfigurable scaffolds with upgrading adaptability.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

Taxis orientation is common in microorganisms, and it provides feasible strategies to operate active colloids as small-scale robots. Collective taxes involve numerous units that collectively perform taxis motion, whereby the collective cooperation between individuals enables the group to perform efficiently, adaptively, and robustly. Hence, analyzing and designing collectives is crucial for developing and advancing microswarm toward practical or clinical applications. In this review, natural taxis behaviors are categorized and synthetic microrobotic collectives are discussed as bio-inspired realizations, aiming at closing the gap between taxis strategies of living creatures and those of functional active microswarms. As collective behaviors emerge within a group, the global taxis to external stimuli guides the group to conduct overall tasks, whereas the local taxis between individuals induces synchronization and global patterns. By encoding the local orientations and programming the global stimuli, various paradigms can be introduced for coordinating and controlling such collective microrobots, from the viewpoints of fundamental science and practical applications. Therefore, by discussing the key points and difficulties associated with collective taxes of different paradigms, this review potentially offers insights into mimicking natural collective behaviors and constructing intelligent microrobotic systems for on-demand control and preassigned tasks.

Activity-driven tissue alignment in proliferating spheroids

We extend the continuum theory of active nematic fluids to study cell flows and tissue dynamics inside multicellular spheroids, spherical, self-assembled aggregates of cells that are widely used as model systems to study tumour dynamics. Cells near the surface of spheroids have better access to nutrients and therefore proliferate more rapidly than those in the resource-depleted core. Using both analytical arguments and three-dimensional simulations, we find that the proliferation gradients result in flows and in gradients of activity both of which can align the orientation axis of cells inside the aggregates. Depending on environmental conditions and the intrinsic tissue properties, we identify three distinct alignment regimes: spheroids in which all the cells align either radially or tangentially to the surface throughout the aggregate and spheroids with angular cell orientation close to the surface and radial alignment in the core. The continuum description of tissue dynamics inside spheroids not only allows us to infer dynamic cell parameters from experimentally measured cell alignment profiles, but more generally motivates novel mechanisms for controlling the alignment of cells within aggregates which has been shown to influence the mechanical properties and invasive capabilities of tumors.

Defect self-propulsion in active nematic films with spatially varying activity

We study the dynamics of topological defects in active nematic films with spatially varying activity and consider two set-ups: (i) a constant activity gradient and (ii) a sharp jump in activity. A constant gradient of extensile (contractile) activity endows the comet-like +1/2 defect with a finite vorticity that drives the defect to align its nose in the direction of decreasing (increasing) gradient. A constant gradient does not, however, affect the known self-propulsion of the +1/2 defect and has no effect on the -1/2 that remains a non-motile particle. A sharp jump in activity acts like a wall that traps the defects, affecting the translational and rotational motion of both charges. The +1/2 defect slows down as it approaches the interface and the net vorticity tends to reorient the defect polarization so that it becomes perpendicular to the interface. The -1/2 defect acquires a self-propulsion towards the activity interface, while the vorticity-induced active torque tends to align the defect to a preferred orientation. This effective attraction of the negative defects to the wall is consistent with the observation of an accumulation of negative topological charge at both active/passive interfaces and physical boundaries.

Collective rotational motion of freely expanding T84 epithelial cell colonies

Coordinated rotational motion is an intriguing, yet still elusive mode of collective cell migration, which is relevant in pathological and morphogenetic processes. Most of the studies on this topic have been carried out on epithelial cells plated on micropatterned substrates, where cell motion is confined in regions of well-defined shapes coated with extracellular matrix adhesive proteins. The driver of collective rotation in such conditions has not been clearly elucidated, although it has been speculated that spatial confinement can play an essential role in triggering cell rotation. Here, we study the growth of epithelial cell colonies freely expanding (i.e. with no physical constraints) on the surface of cell culture plates and focus on collective cell rotation in such conditions, a case which has received scarce attention in the literature. One of the main findings of our work is that coordinated cell rotation spontaneously occurs in cell clusters in the free growth regime, thus implying that cell confinement is not necessary to elicit collective rotation as previously suggested. The extent of collective rotation was size and shape dependent: a highly coordinated disc-like rotation was found in small cell clusters with a round shape, while collective rotation was suppressed in large irregular cell clusters generated by merging of different clusters in the course of their growth. The angular motion was persistent in the same direction, although clockwise and anticlockwise rotations were equally likely to occur among different cell clusters. Radial cell velocity was quite low as compared to the angular velocity, in agreement with the free expansion regime where cluster growth is essentially governed by cell proliferation. A clear difference in morphology was observed between cells at the periphery and the ones in the core of the clusters, the former being more elongated and spread out as compared to the latter. Overall, our results, to our knowledge, provide the first quantitative and systematic evidence that coordinated cell rotation does not require a spatial confinement and occurs spontaneously in freely expanding epithelial cell colonies, possibly as a mechanism for the system.

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.

Phase Equilibria and Critical Behavior in Nematogenic MBBA-Isooctane Monotectic-Type Mixtures

The transition from the isotropic (I) liquid to the nematic-type (N) uniaxial phase appearing as the consequence of the elongated geometry of elements seems to be a universal phenomenon for many types of suspensions, from solid nano-rods to biological particles based colloids. Rod-like thermotropic nematogenic liquid crystalline (LC) compounds and their mixtures with a molecular solvent (Sol) can be a significant reference for this category, enabling insights into universal features. The report presents studies in 4'-methoxybenzylidene-4-n-butylaniline (MBBA) and isooctane (Sol) mixtures, for which the monotectic-type phase diagram was found. There are two biphasic regions (i) for the low (TP1, isotropic liquid-nematic coexistence), and (ii) high (TP2, liquid-liquid coexistence) concentrations of isooctane. For both domains, biphasic coexistence curves' have been discussed and parameterized. For TP2 it is related to the order parameter and diameter tests. Notable is the anomalous mean-field type behavior near the critical consolute temperature. Regarding the isotropic liquid phase, critical opalescence has been detected above both biphasic regions. For TP2 it starts ca. 20 K above the critical consolute temperature. The nature of pretransitional fluctuations in the isotropic liquid phase was tested via nonlinear dielectric effect (NDE) measurements. It is classic (mean-field) above TP1 and non-classic above the TP2 domain. The long-standing problem regarding the non-critical background effect was solved to reach this result.

Molecular cluster analysis using local order parameters selected by machine learning

Accurately extracting local molecular structures is essential for understanding the mechanisms of phase and structural transitions. A promising method to characterize the local molecular structure is defining the value of the local order parameter (LOP) for each particle. This work develops the Molecular Assembly structure Learning package for Identifying Order parameters (MALIO), a machine learning package that can propose an optimal (set of) LOP(s) quickly and automatically for a huge number of LOP species and various methods of selecting neighboring particles for the calculation. We applied this package to distinguish between the nematic and smectic phases of uniaxial liquid crystal molecules, and selected candidate LOPs that could be used to precisely observe the nematic-smectic phase transition. The LOP candidates were used to observe the nucleation and subsequent percolation transition, and the effect of the choice of LOP species and neighboring particles on the statistics of local molecular structures (clusters) was examined. The procedure revealed the time evolution of the number of clusters and the dependence of the percolation curve on the number of neighboring particles for each LOP species. The LOP species with the lowest dependence on the number of neighboring particles was the best-performing LOP species in the MALIO screening strategy. These results not only show that machine learning can powerfully screen a huge number of LOP species and suggest only a few promising candidates, but also indicate that MALIO can select the best LOP species.

Tilt-induced polar order and topological defects in growing bacterial populations

Rod-shaped bacteria, such as Escherichia coli, commonly live forming mounded colonies. They initially grow two-dimensionally on a surface and finally achieve three-dimensional growth. While it was recently reported that three-dimensional growth is promoted by topological defects of winding number +1/2 in populations of motile bacteria, how cellular alignment plays a role in nonmotile cases is largely unknown. Here, we investigate the relevance of topological defects in colony formation processes of nonmotile E. coli populations, and found that both ±1/2 topological defects contribute to the three-dimensional growth. Analyzing the cell flow in the bottom layer of the colony, we observe that +1/2 defects attract cells and -1/2 defects repel cells, in agreement with previous studies on motile cells, in the initial stage of the colony growth. However, later, cells gradually flow toward -1/2 defects as well, exhibiting a sharp contrast to the existing knowledge. By investigating three-dimensional cell orientations by confocal microscopy, we find that vertical tilting of cells is promoted near the defects. Crucially, this leads to the emergence of a polar order in the otherwise nematic two-dimensional cell orientation. We extend the theory of active nematics by incorporating this polar order and the vertical tilting, which successfully explains the influx toward -1/2 defects in terms of a polarity-induced force. Our work reveals that three-dimensional cell orientations may result in qualitative changes in properties of active nematics, especially those of topological defects, which may be generically relevant in active matter systems driven by cellular growth instead of self-propulsion.

Vector formalism for active nematic liquid crystals in two dimensions

Specific features of two-dimensional nematodynamics give rise to shortfalls of the tensor representation of the nematic order parameter commonly used in computations, especially in theory of active matter. The alternative representation in terms of the vector order parameter follows with small adjustments the classical director-based theory, but is applicable to 2D problems where both nematic alignment and deviation from the isotropic state are variable. Stability analysis of nematic alignment and flow is used as a testing ground. A director-based analysis demonstrates a shortfall of the standard theory, which does not ensure relaxation to equilibrium in a passive system. It also demonstrates the inadequacy of the director-based description, which misses a stabilizing effect of perturbations of the modulus ensuring stability of a passive system on scales far exceeding the healing length.

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.

Liquid Crystal Modified Polylactic Acid Improves Cytocompatibility and M2 Polarization of Macrophages to Promote Osteogenesis

Liquid crystalline phases (LC phases) are widely present in an organism. The well-aligned domain and liquidity of the LC phases are necessary for various biological functions. How to stabilize the floating LC phases and maintain their superior biology is still under study. In addition, it is unclear whether the exogenous LC state can regulate the immune process and improve osteogenesis. In this work, a series of composite films (PLLA/LC) were prepared using cholesteryl oleyl carbonate (COC), cholesteryl pelargonate (CP), and polylactic acid (PLLA) via a controlled facile one-pot approach. The results showed that the thermo-responsive PLLA/LC films exhibited stable LC phases at human body temperature and the cytocompatibility of the composites was improved significantly after modification by the LC. In addition, the M2 polarization of macrophages (RAW264.7) was enhanced in PLLA/LC films, and the osteogenic differentiation of bone marrow mesenchymal stem cells (BMSCs) was improved as co-cultured with macrophages. The in vivo bone regeneration of the materials was verified by calvarial repair, in which the amount of new bone in the PLLA-30% LC group was greater than that in the PLLA group. This work revealed that the liquid crystal-modified PLLA could promote osteogenesis through immunomodulation.

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.

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.

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.

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.

Explicit calculation method for cell alignment in non-circular geometries

The alignment of spindle-shaped cells in two-dimensional geometries induces singular points called topological defects, at which the alignment angle of the cell cannot be defined. To control defects related to biological roles such as cell apoptosis, calculation methods for predicting the defect positions are required. This study proposes an explicit calculation method for predicting cell alignment and defect positions in non-circular geometries. First, a complex potential is introduced to describe the alignment angles of cells, which is used to derive an explicit formula for cell alignment in a unit disc. Then, the derived formula for the unit disc is extended to the case for non-circular geometries using a numerical conformal mapping. Finally, the complex potential allows a calculation of the Frank elastic energy, which can be minimized with respect to the defect positions to predict their equilibrium state in the geometry. The proposed calculation method is used to demonstrate a numerical prediction of multiple defects in circular and non-circular geometries, which are consistent with previous experimental results.

Flow around topological defects in active nematic films

We study the active flow around isolated defects and the self-propulsion velocity of +1/2 defects in an active nematic film with both viscous dissipation (with viscosity η) and frictional damping Γ with a substrate. The interplay between these two dissipation mechanisms is controlled by the hydrodynamic dissipation length ℓd=η/Γ that screens the flows. For an isolated defect, in the absence of screening from other defects, the size of the shear vorticity around the defect is controlled by the system size R. In the presence of friction that leads to a finite value of ℓd, the vorticity field decays to zero on the lengthscales larger than ℓd. We show that the self-propulsion velocity of +1/2 defects grows with R in small systems where R<ℓd, while in the infinite system limit or when R≫ℓd, it approaches a constant value determined by ℓd.

The Myosin Myocardial Mesh Interpreted as a Biological Analogous of Nematic Chiral Liquid Crystals

There are still grey areas in the understanding of the myoarchitecture of the ventricular mass. This is despite the progress of investigation methods since the beginning of the 21st century (diffusion tensor magnetic resonance imaging, microcomputed tomography, and polarised light imaging). The objective of this article is to highlight the specificities and the limitations of polarised light imaging (PLI) of the unstained myocardium embedded in methyl methacrylate (MMA). Thus, to better differentiate our method from other PLI modes, we will refer to it by the acronym PLI-MMA. PLI-MMA shows that the myosin mesh of the compact left ventricular wall behaves like a biological analogous of a nematic chiral liquid crystal. Results obtained by PLI-MMA are: the main direction of the myosin molecules contained in an imaged voxel, the crystal liquid director n, and a regional isotropy index RI that is an orientation tensor, the equivalent of the crystal liquid order parameter. The vector n is collinear with the first eigenvector of diffusion tensor imaging (DTI-MRI). The RI has not been confounded with the diffusion tensor of DTI that gives information about the three eigenvectors of the ellipsoid of diffusion. PLI-MMA gives no information about the collagen network. The physics of soft matter has allowed the revisiting of Streeter’s conjecture on the myoarchitecture of the compact left ventricular wall: “geodesics on a nested set of toroidal surfaces”. Once the torus topology is understood, this characterisation of the myoarchitecture is more accurate and parsimonious than former descriptions. Finally, this article aims to be an enthusiastic invitation to a transdisciplinary approach between physicists of liquid crystals, anatomists, and specialists of imaging.

The role of pectin phase separation in plant cell wall assembly and growth

A rapidly increasing body of literature suggests that many biological processes are driven by phase separation within polymer mixtures. Liquid-liquid phase separation can lead to the formation of membrane-less organelles, which are thought to play a wide variety of roles in cell metabolism, gene regulation or signaling. One of the characteristics of these systems is that they are poised at phase transition boundaries, which makes them perfectly suited to elicit robust cellular responses to often very small changes in the cell's "environment". Recent observations suggest that, also in the semi-solid environment of plant cell walls, phase separation not only plays a role in wall patterning, hydration and stress relaxation during growth, but also may provide a driving force for cell wall expansion. In this context, pectins, the major polyanionic polysaccharides in the walls of growing cells, appear to play a critical role. Here, we will discuss (i) our current understanding of the structure-function relationship of pectins, (ii) in vivo evidence that pectin modification can drive critical phase transitions in the cell wall, (iii) how such phase transitions may drive cell wall expansion in addition to turgor pressure and (iv) the periodic cellular processes that may control phase transitions underlying cell wall assembly and expansion.

Data-driven criterion for the solid-liquid transition of two-dimensional self-propelled colloidal particles far from equilibrium

We establish an explicit data-driven criterion for identifying the solid-liquid transition of two-dimensional self-propelled colloidal particles in the far from equilibrium parameter regime, where the transition points predicted by different conventional empirical criteria for melting and freezing diverge. This is achieved by applying a hybrid machine learning approach that combines unsupervised learning with supervised learning to analyze a huge amount of the system's configurations in the nonequilibrium parameter regime on an equal footing. Furthermore, we establish a generic data-driven evaluation function, according to which the performance of different empirical criteria can be systematically evaluated and improved. In particular, by applying this evaluation function, we identify a new nonequilibrium threshold value for the long-time diffusion coefficient, based on which the predictions of the corresponding empirical criterion are greatly improved in the far from equilibrium parameter regime. These data-driven approaches provide a generic tool for investigating phase transitions in complex systems where conventional empirical ones face difficulties.

Physics of liquid crystals in cell biology

The past decade has witnessed a rapid growth in understanding of the pivotal roles of mechanical stresses and physical forces in cell biology. As a result, an integrated view of cell biology is evolving, where genetic and molecular features are scrutinised hand in hand with physical and mechanical characteristics of cells. Physics of liquid crystals has emerged as a burgeoning new frontier in cell biology over the past few years, fuelled by an increasing identification of orientational order and topological defects in cell biology, spanning scales from subcellular filaments to individual cells and multicellular tissues. Here, we provide an account of the most recent findings and developments, together with future promises and challenges in this rapidly evolving interdisciplinary research direction.

Polar swimmers induce several phases in active nematics

Swimming bacteria in passive nematics in the form of lyotropic liquid crystals are defined as a new class of active matter known as living liquid crystals in recent studies. It has also been shown that liquid crystal solutions are promising candidates for trapping and detecting bacteria. We ask the question, can a similar class of matter be designed for background nematics which are also active? Hence, we developed a minimal model for the mixture of polar particles in active nematics. It is found that the active nematics in such a mixture are highly sensitive to the presence of polar particles and show the formation of large scale higher order structures for a relatively low polar particle density. Upon increasing the density of polar particles, different phases of active nematics are found and it is observed that the system shows two phase transitions. The first phase transition is a first order transition from quasi-long-ranged ordered active nematics to disordered active nematics with larger scale structures. On further increasing density of polar particles, the system transitions to a third phase, where polar particles form large, mutually aligned clusters. These clusters sweep the whole system and enforce local order in the nematics. The current study can be helpful for detecting the presence of very low densities of polar swimmers in active nematics and can be used to design and control different structures in active nematics.

Multistep nucleation of anisotropic molecules

Phase transition of anisotropic materials is ubiquitously observed in physics, biology, materials science, and engineering. Nevertheless, how anisotropy of constituent molecules affects the phase transition dynamics is still poorly understood. Here we investigate numerically the phase transition of a simple model system composed of anisotropic molecules, and report on our discovery of multistep nucleation of nuclei with layered positional ordering (smectic ordering), from a fluid-like nematic phase with orientational order only (no positional order). A trinity of molecular dynamics simulation, machine learning, and molecular cluster analysis yielding free energy landscapes unambiguously demonstrates the dynamics of multistep nucleation process involving characteristic metastable clusters that precede supercritical smectic nuclei and cannot be accounted for by the classical nucleation theory. Our work suggests that molecules of simple shape can exhibit rich and complex nucleation processes, and our numerical approach will provide deeper understanding of phase transitions and resulting structures in anisotropic materials such as biological systems and functional materials.

Topological defects of integer charge in cell monolayers

Many cell types spontaneously order like nematic liquid crystals, and, as such, they form topological defects, which influence the cell organization. While defects with topological charge ±1/2 are common in cell monolayers, defects with charge ±1, which are thought to be relevant in the formation of protrusions in living systems, are more elusive. We use topographical patterns to impose topological charge of ±1 in controlled locations in cell monolayers. We study two types of cells, 3T6 fibroblasts and EpH-4 epithelial cells, and we compare their behavior on such patterns, characterizing the degree of alignment, the cell density near the defects, and their behavior at the defect core. We observe density variation in the 3T6 monolayers near both types of defects over the same length-scale. By choosing appropriate geometrical parameters of our topographical features, we identify a new behavior of 3T6 cells near the defects with topological charge +1, leading to a change in the cells' preferred shape. Our strategy allows a fine control of cell alignment near defects as a platform to study liquid crystalline properties of cells.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Spatiotemporal Oscillation in Confined Epithelial Motion upon Fluid-to-Solid Transition

Fluid-to-solid phase transition in multicellular assembly is crucial in many developmental biological processes, such as embryogenesis and morphogenesis. However, biomechanical studies in this area are limited, and little is known about factors governing the transition and how cell behaviors are regulated. Due to different stresses present, cells could behave distinctively depending on the nature of tissue. Here we report a fluid-to-solid transition in geometrically confined multicellular assemblies. Under circular confinement, Madin-Darby canine kidney (MDCK) monolayers undergo spatiotemporally oscillatory motions that are strongly dependent on the confinement size and distance from the periphery of the monolayers. Nanomechanical mapping reveals that epithelial tensional stress and traction forces on the substrate are both dependent on confinement size. The oscillation pattern and cellular nanomechanics profile appear well correlated with stress fiber assembly and cell polarization. These experimental observations imply that the confinement size-dependent surface tension regulates actin fiber assembly, cellular force generation, and cell polarization. Our analyses further suggest a characteristic confinement size (approximates to MDCK's natural correlation length) below which surface tension is sufficiently high and triggers a fluid-to-solid transition of the monolayers. Our findings may shed light on the geometrical and nanomechanical control of tissue morphogenesis and growth.

A Lyotropic Liquid Crystal from a Flexible Oligopeptide Amphiphile in Dimethyl Sulfoxide

Despite the rapid progress in peptide liquid crystals (LCs) due to their prominent properties, our investigation on flexible peptide-based LCs is incomplete, mainly resulted from their unclear formation mechanisms and unexploited applications in organic solvents. Here, we develop a lyotropic LC based on a flexible oligopeptide amphiphile, which aggregates into aligned cylinder-like nanostructures in dimethyl sulfoxide (DMSO). The formation mechanism of lyotropic LC in DMSO was probed by the experimental investigation and molecular dynamics simulation, indicating that the hydrogen bonding and hydrophobic and electrostatic interactions contribute to the formation of ordered nanostructures in the organic solvent. Arising from the orientational order and suitable fluidity, we exploit the application of lyotropic LC as an aligned medium to measure the residual dipolar couplings of bioactive molecules. This study not only offers the understanding of the mechanism to create LC systems without rigid aromatic groups but also expands the applications of ordered bottom-up nanomaterials in organic solvents.

Biomimetic Design for Bio-Matrix Interfaces and Regenerative Organs

The urgent demand for transplanted organs has motivated the development of regenerative medicine to biomimetically reconstruct the structure and function of natural tissues or organs. The prerequisites for constructing multicellular organs include specific cell sources, suitable scaffolding material, and interconnective biofunctional interfaces. As some of the most complex systems in nature, human organs, tissues, and cellular units have unique "bio-matrix" physicochemical interfaces. Human tissues support a large number of cells with distinct biofunctional interfaces for compartmentalization related to metabolism, material exchange, and physical barriers. These naturally shaped biofunctional interfaces support critical metabolic functions that drive adaptive human behavior. In contrast, mutations and disorders during organogenesis can disrupt these interfaces as a consequence of disease and trauma. To replicate the appropriate structure and physiological function of tissues and organs, the biomaterials used in these approaches should have properties that mimic those of natural biofunctional interfaces. In this review, the focus is on the biomimetic design of functional interfaces and hierarchical structures for four regenerative organs, liver, kidney, lung, heart, and the immune system. Research on these organs provides understanding of cell-matrix interactions for hierarchically bioinspired material engineering, and guidance for the design of bioartificial organs. Finally, we provide perspectives on future challenges in biofunctional interface designs and discuss the obstacles that remain toward the generation of functional bioartificial organs.

Src kinases relax adherens junctions between the neighbors of apoptotic cells to permit apical extrusion

Epithelia can eliminate apoptotic cells by apical extrusion. This is a complex morphogenetic event where expulsion of the apoptotic cell is accompanied by rearrangement of its immediate neighbors to form a rosette. A key mechanism for extrusion is constriction of an actomyosin network that neighbor cells form at their interface with the apoptotic cell. Here we report a complementary process of cytoskeletal relaxation that occurs when cortical contractility is down-regulated at the junctions between those neighbor cells themselves. This reflects a mechanosensitive Src family kinase (SFK) signaling pathway that is activated in neighbor cells when the apoptotic cell relaxes shortly after injury. Inhibiting SFK signaling blocks both the expulsion of apoptotic cells and the rosette formation among their neighbor cells. This reveals the complex pattern of spatially distinct contraction and relaxation that must be established in the neighboring epithelium for apoptotic cells to be extruded.

Topology control of human fibroblast cells monolayer by liquid crystal elastomer

Eukaryotic cells in living tissues form dynamic patterns with spatially varying orientational order that affects important physiological processes such as apoptosis and cell migration. The challenge is how to impart a predesigned map of orientational order onto a growing tissue. Here, we demonstrate an approach to produce cell monolayers of human dermal fibroblasts with predesigned orientational patterns and topological defects using a photoaligned liquid crystal elastomer (LCE) that swells anisotropically in an aqueous medium. The patterns inscribed into the LCE are replicated by the tissue monolayer and cause a strong spatial variation of cells phenotype, their surface density, and number density fluctuations. Unbinding dynamics of defect pairs intrinsic to active matter is suppressed by anisotropic surface anchoring allowing the estimation of the elastic characteristics of the tissues. The demonstrated patterned LCE approach has potential to control the collective behavior of cells in living tissues, cell differentiation, and tissue morphogenesis.

Substrate curvature as a cue to guide spatiotemporal cell and tissue organization

Recent evidence clearly shows that cells respond to various physical cues in their environments, guiding many cellular processes and tissue morphogenesis, pathology, and repair. One aspect that is gaining significant traction is the role of local geometry as an extracellular cue. Elucidating how geometry affects cell and tissue behavior is, indeed, crucial to design artificial scaffolds and understand tissue growth and remodeling. Perhaps the most fundamental descriptor of local geometry is surface curvature, and a growing body of evidence confirms that surface curvature affects the spatiotemporal organization of cells and tissues. While well-defined in differential geometry, curvature remains somewhat ambiguously treated in biological studies. Here, we provide a more formal curvature framework, based on the notions of mean and Gaussian curvature, and summarize the available evidence on curvature guidance at the cell and tissue levels. We discuss the involved mechanisms, highlighting the interplay between tensile forces and substrate curvature that forms the foundation of curvature guidance. Moreover, we show that relatively simple computational models, based on some application of curvature flow, are able to capture experimental tissue growth remarkably well. Since curvature guidance principles could be leveraged for tissue regeneration, the implications for geometrical scaffold design are also discussed. Finally, perspectives on future research opportunities are provided.

Active matter invasion

Biologically active materials such as bacterial biofilms and eukaryotic cells thrive in confined micro-spaces. Here, we show through numerical simulations that confinement can serve as a mechanical guidance to achieve distinct modes of collective invasion when combined with growth dynamics and the intrinsic activity of biological materials. We assess the dynamics of the growing interface and classify these collective modes of invasion based on the activity of the constituent particles of the growing matter. While at small and moderate activities the active material grows as a coherent unit, we find that blobs of active material collectively detach from the cohort above a well-defined activity threshold. We further characterise the mechanical mechanisms underlying the crossovers between different modes of invasion and quantify their impact on the overall invasion speed.

Liquid-crystal organization of liver tissue

Functional tissue architecture originates by self-assembly of distinct cell types, following tissue-specific rules of cell-cell interactions. In the liver, a structural model of the lobule was pioneered by Elias in 1949. This model, however, is in contrast with the apparent random 3D arrangement of hepatocytes. Since then, no significant progress has been made to derive the organizing principles of liver tissue. To solve this outstanding problem, we computationally reconstructed 3D tissue geometry from microscopy images of mouse liver tissue and analyzed it applying soft-condensed-matter-physics concepts. Surprisingly, analysis of the spatial organization of cell polarity revealed that hepatocytes are not randomly oriented but follow a long-range liquid-crystal order. This does not depend exclusively on hepatocytes receiving instructive signals by endothelial cells, since silencing Integrin-β1 disrupted both liquid-crystal order and organization of the sinusoidal network. Our results suggest that bi-directional communication between hepatocytes and sinusoids underlies the self-organization of liver tissue.

Micro-deposition control of polysaccharides on evaporative air-LC interface to design quickly swelling hydrogels

Uniaxial orientation is highly desirable for fabricating advanced soft materials. Liquid crystal (LC) polymer deposition was strategically manipulated at the air-LC interface, by controlling the drying temperature and initial concentration of aqueous solution of xanthan gum in a limited space. Interface-assisted orientation led to membrane-like depositions bridging the millimeter-scale gap between the substrates both, vertically and horizontally. The applicability of this approach lies in synchronization of the molecular orientation beyond their individual LC domains into the condensed state. Cross-polarized microscopy and SEM analysis correlated the orientation of the deposited polymer with the controlled mobility of xanthan gum LC domains at the evaporative interface. Subsequently, a phase diagram was prepared for the variety of oriented structures, depending upon the drying conditions. The deposited membrane behaved as an oriented hydrogel showing reversible anisotropic swelling/deswelling only along its thickness.

Liquid Crystal-Induced Myoblast Alignment

The ability to control cell alignment represents a fundamental requirement toward the production of tissue in vitro but also to create biohybrid materials presenting the functional properties of human organs. However, cell cultures on standard commercial supports do not provide a selective control on the cell organization morphology, and different techniques, such as the use of patterned or stimulated substrates, are developed to induce cellular alignment. In this work, a new approach toward in vitro muscular tissue morphogenesis is presented exploiting liquid crystalline networks. By using smooth polymeric films with planar homogeneous alignment, a certain degree of cellular order is observed in myoblast cultures with direction of higher cell alignment corresponding to the nematic director. The molecular organization inside the polymer determines such effects since no cell organization is observed using homeotropic or isotropic samples. These findings represent the first example of cellular alignment induced by the interaction with a nematic polymeric scaffold, setting the stage for new applications of liquid crystal polymers as active matter to control tissue growth.