Celebrating Soft Matter's 10th Anniversary: Cell division: a source of active stress in cellular monolayers

Aspect-ratio-dependent void formation in active rhomboidal and elliptical particle systems

We execute a numerical simulation of active nematics with particles interacting by an excluded-volume effect. Systems with rhomboidal particles and with elliptical particles are considered in order to investigate the effect of the direct contact of particles. In our simulation, the void regions, where the local number density is almost zero, appear in both systems when the aspect ratio of the particles is high. We focus on the relationship between the void regions and the particle orientation of the bulk. The particle number density, particle orientation, topological defects, and void regions are analyzed for different aspect ratios in both systems. The systems with rhomboidal particles have characteristic void sizes, which increase with an increase in the aspect ratio. In contrast, the distribution of the void-region size in the systems with elliptical particles is broad. The present results suggest that the void size in the systems with rhomboidal particles is determined by the correlation length of the particle orientational field around the void regions, while the void size might be determined by the system size in the systems with elliptical particles.

Cell Division and Motility Enable Hexatic Order in Biological Tissues

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

Stress and alignment response to curved obstacles in growing bacterial monolayers

Monolayers of growing bacteria, confined within channel geometries, exhibit self-organization into a highly aligned laminar state along the axis of the channel. Although this phenomenon has been observed in experiments and simulations under various boundary conditions, the underlying physical mechanism driving this alignment remains unclear. In this study, we conduct simulations of growing bacteria in two-dimensional channel geometries perturbed by fixed obstacles, either circular or arc shaped, placed at the channel's center. Our findings reveal that even sizable obstacles cause only short-ranged disruptions to the baseline laminar state. These disruptions arise from a competition between local planar anchoring and bulk laminar alignment. At smaller obstacle sizes, bulk alignment fully dominates, while at larger sizes planar anchoring induces increasing local disruptions. Furthermore, our analysis indicates that the resulting configurations of the bacterial system display a striking resemblance to the arrangement of hard-rod smectic liquid crystals around circular obstacles. This suggests that modeling hard-rod bacterial monolayers as smectic, rather than nematic, liquid crystals may yield successful outcomes. The insights gained from our study contribute to the expanding body of research on bacterial growth in channels. Our work provides perspectives on the stability of the laminar state and extends our understanding to encompass more intricate confinement schemes.

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.

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

Objective

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

Methods

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

Results

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

Conclusion

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

Active cell divisions generate fourfold orientationally ordered phase in living tissue

Morphogenesis, the process through which genes generate form, establishes tissue-scale order as a template for constructing the complex shapes of the body plan. The extensive growth required to build these ordered substrates is fuelled by cell proliferation, which, naively, should destroy order. Understanding how active morphogenetic mechanisms couple cellular and mechanical processes to generate order-rather than annihilate it-remains an outstanding question in animal development. We show that cell divisions are the primary drivers of tissue flow, leading to a fourfold orientationally ordered phase. Waves of anisotropic cell proliferation propagate across the embryo with precise patterning. Defects introduced into the nascent lattice by cell divisions are moved out of the tissue bulk towards the boundary by subsequent divisions. Specific cell proliferation rates and orientations enable cell divisions to organize rather than fluidize the tissue. We observe this using live imaging and tissue cartography to analyse the dynamics of fourfold tissue ordering in the trunk segmental ectoderm of the crustacean Parhyale hawaiensis beginning 72 h after egg lay. The result is a robust, active mechanism for generating global orientational order in a non-equilibrium system that sets the stage for the subsequent development of shape and form.

Molecular-scale substrate anisotropy, crowding and division drive collective behaviours in cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. While nematic order is common in biological tissues, it typically only extends to small regions of cells interacting via steric repulsion. On isotropic substrates, elongated cells can co-align due to steric effects, forming ordered but randomly oriented finite-size domains. However, we have discovered that flat substrates with nematic order can induce global nematic alignment of dense, spindle-like cells, thereby influencing cell organization and collective motion and driving alignment on the scale of the entire tissue. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. To quantify the rich set of behaviours afforded by this system, we analyse velocity, positional and orientational correlations for several thousand cells over days. The establishment of global order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of the dynamics of cellular remodelling and organization among weakly interacting cells.

Engineering tools for quantifying and manipulating forces in epithelia

The integrity of epithelia is maintained within dynamic mechanical environments during tissue development and homeostasis. Understanding how epithelial cells mechanosignal and respond collectively or individually is critical to providing insight into developmental and (patho)physiological processes. Yet, inferring or mimicking mechanical forces and downstream mechanical signaling as they occur in epithelia presents unique challenges. A variety of in vitro approaches have been used to dissect the role of mechanics in regulating epithelia organization. Here, we review approaches and results from research into how epithelial cells communicate through mechanical cues to maintain tissue organization and integrity. We summarize the unique advantages and disadvantages of various reduced-order model systems to guide researchers in choosing appropriate experimental systems. These model systems include 3D, 2D, and 1D micromanipulation methods, single cell studies, and noninvasive force inference and measurement techniques. We also highlight a number of in silico biophysical models that are informed by in vitro and in vivo observations. Together, a combination of theoretical and experimental models will aid future experiment designs and provide predictive insight into mechanically driven behaviors of epithelial dynamics.

Mechanical basis and topological routes to cell elimination

Cell layers eliminate unwanted cells through the extrusion process, which underlines healthy versus flawed tissue behaviors. Although several biochemical pathways have been identified, the underlying mechanical basis including the forces involved in cellular extrusion remains largely unexplored. Utilizing a phase-field model of a three-dimensional cell layer, we study the interplay of cell extrusion with cell-cell and cell-substrate interactions in a flat monolayer. Independent tuning of cell-cell versus cell-substrate adhesion forces reveals that extrusion events can be distinctly linked to defects in nematic and hexatic orders associated with cellular arrangements. Specifically, we show that by increasing relative cell-cell adhesion forces the cell monolayer can switch between the collective tendency towards fivefold, hexatic, disclinations relative to half-integer, nematic, defects for extruding a cell. We unify our findings by accessing three-dimensional mechanical stress fields to show that an extrusion event acts as a mechanism to relieve localized stress concentration.

MACC1-induced migration in tumors: Current state and perspective

Malignant tumors are still a global, heavy health burden. Many tumor types cannot be treated curatively, underlining the need for new treatment targets. In recent years, metastasis associated in colon cancer 1 (MACC1) was identified as a promising biomarker and drug target, as it is promoting tumor migration, initiation, proliferation, and others in a multitude of solid cancers. Here, we will summarize the current knowledge about MACC1-induced tumor cell migration with a special focus on the cytoskeletal and adhesive systems. In addition, a brief overview of several in vitro models used for the analysis of cell migration is given. In this context, we will point to issues with the currently most prevalent models used to study MACC1-dependent migration. Lastly, open questions about MACC1-dependent effects on tumor cell migration will be addressed.

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.

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.

Jamming Transitions in Astrocytes and Glioblastoma Are Induced by Cell Density and Tension

Collective behavior of cells emerges from coordination of cell-cell-interactions and is important to wound healing, embryonic and tumor development. Depending on cell density and cell-cell interactions, a transition from a migratory, fluid-like unjammed state to a more static and solid-like jammed state or vice versa can occur. Here, we analyze collective migration dynamics of astrocytes and glioblastoma cells using live cell imaging. Furthermore, atomic force microscopy, traction force microscopy and spheroid generation assays were used to study cell adhesion, traction and mechanics. Perturbations of traction and adhesion were induced via ROCK or myosin II inhibition. Whereas astrocytes resided within a non-migratory, jammed state, glioblastoma were migratory and unjammed. Furthermore, we demonstrated that a switch from an unjammed to a jammed state was induced upon alteration of the equilibrium between cell-cell-adhesion and tension from adhesion to tension dominated, via inhibition of ROCK or myosin II. Such behavior has implications for understanding the infiltration of the brain by glioblastoma cells and may help to identify new strategies to develop anti-migratory drugs and strategies for glioblastoma-treatment.

The emergence of spontaneous coordinated epithelial rotation on cylindrical curved surfaces

Three-dimensional collective epithelial rotation around a given axis represents a coordinated cellular movement driving tissue morphogenesis and transformation. Questions regarding these behaviors and their relationship with substrate curvatures are intimately linked to spontaneous active matter processes and to vital morphogenetic and embryonic processes. Here, using interdisciplinary approaches, we study the dynamics of epithelial layers lining different cylindrical surfaces. We observe large-scale, persistent, and circumferential rotation in both concavely and convexly curved cylindrical tissues. While epithelia of inverse curvature show an orthogonal switch in actomyosin network orientation and opposite apicobasal polarities, their rotational movements emerge and vary similarly within a common curvature window. We further reveal that this persisting rotation requires stable cell-cell adhesion and Rac-1-dependent cell polarity. Using an active polar gel model, we unveil the different relationships of collective cell polarity and actin alignment with curvatures, which lead to coordinated rotational behavior despite the inverted curvature and cytoskeleton order.

Thermodynamic nonequilibrium effects in bubble coalescence: A discrete Boltzmann study

The thermodynamic nonequilibrium (TNE) effects in a coalescence process of two initially static bubbles under thermal conditions are investigated by a discrete Boltzmann model. The spatial distributions of the typical nonequilibrium quantity, i.e., nonorganized momentum fluxes (NOMFs), during evolutions are investigated in detail. The density-weighted statistical method is used to highlight the relationship between the TNE effects and the morphological and kinetics characteristics of bubble coalescence. The results show that the xx component and yy component of NOMFs are antisymmetrical; the xy component changes from an antisymmetric internal and external double quadrupole structure to an outer octupole structure during the coalescence process. Moreover, the evolution of the averaged xx component of NOMFs provides two characteristic instants, which divide the nonequilibrium process into three stages. The first instant, when the averaged xx component of the NOMFs reaches its first local minimum, corresponds to the moment when the mean coalescence speed gets the maximum, and at this time the ratio of minor and major axes is about 1/2. The second instant, when the averaged xx component of the NOMFs gets its second local maximum, corresponds to the moment when the ratio of minor and major axes becomes 1 for the first time. It is interesting to find that the three quantities, TNE intensity, acceleration of coalescence, and the slope of boundary length, show a high degree of correlation and attain their maxima simultaneously. The surface tension and the heat conduction accelerate the process of bubble coalescence, while the viscosity delays it. Both the surface tension and the viscosity enhance the global nonequilibrium intensity, whereas the heat conduction restrains it. These TNE features and findings present some insights into the kinetics of bubble coalescence.

Mechanical regulation of cell-cycle progression and division

Cell-cycle progression and division are fundamental biological processes in animal cells, and their biochemical regulation has been extensively studied. An emerging body of work has revealed how mechanical interactions of cells with their microenvironment in tissues, including with the extracellular matrix (ECM) and neighboring cells, also plays a crucial role in regulating cell-cycle progression and division. We review recent work on how cells interpret physical cues and alter their mechanics to promote cell-cycle progression and initiate cell division, and then on how dividing cells generate forces on their surrounding microenvironment to successfully divide. Finally, the article ends by discussing how force generation during division potentially contributes to larger tissue-scale processes involved in development and homeostasis.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

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.

MACC1-Induced Collective Migration Is Promoted by Proliferation Rather Than Single Cell Biomechanics

Metastasis-associated in colon cancer 1 (MACC1) is a marker for metastasis, tumor cell migration, and increased proliferation in colorectal cancer (CRC). Tumors with high MACC1 expression show a worse prognosis and higher invasion into neighboring structures. Yet, many facets of the pro-migratory effects are not fully understood. Atomic force microscopy and single cell live imaging were used to quantify biomechanical and migratory properties in low- and high-MACC1-expressing CRC cells. Furthermore, collective migration and expansion of small, cohesive cell colonies were analyzed using live cell imaging and particle image velocimetry. Lastly, the impact of proliferation on collective migration was determined by inhibition of proliferation using mitomycin. MACC1 did not affect elasticity, cortex tension, and single cell migration of CRC cells but promoted collective migration and colony expansion in vitro. Measurements of the local velocities in the dense cell layers revealed proliferation events as regions of high local speeds. Inhibition of proliferation via mitomycin abrogated the MACC1-associated effects on the collective migration speeds. A simple simulation revealed that the expansion of cell clusters without proliferation appeared to be determined mostly by single cell properties. MACC1 overexpression does not influence single cell biomechanics and migration but only collective migration in a proliferation-dependent manner. Thus, targeting proliferation in high-MACC1-expressing tumors may offer additional effects on cell migration.

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.

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.

Flow transitions and length scales of a channel-confined active nematic

We perform lattice Boltzmann simulations of an active nematic fluid confined in a two-dimensional channel to study the range of flow states that are stabilised by the confinement: unidirectional flow, oscillatory flow, the dancing state, localised active turbulence and fully-developed active turbulence. We analyse the flows in Fourier space, and measure a range of different length scales which describe the flows. We argue that the different states occur as a result of flow instabilities inherent to the system. As a consequence the characteristic length scale for oscillatory flow, the dancing state and localised active turbulence is set by the channel width. Fully-developed active turbulence occurs only when the channel width is larger than the intrinsic, active length scale of the bulk fluid. The results clarify why the activity number is a control parameter for the flow transitions.

Activity-induced instabilities of brain organoids

We present an analytical and numerical investigation of the activity-induced hydrodynamic instabilities in model brain organoids. While several mechanisms have been introduced to explain the experimental observation of surface instabilities in brain organoids, the role of activity has been largely overlooked. Our results show that the active stress generated by the cells can be a, previously overlooked, contributor to the emergence of surface deformations in brain organoids.

Investigating the nature of active forces in tissues reveals how contractile cells can form extensile monolayers

Actomyosin machinery endows cells with contractility at a single-cell level. However, within a monolayer, cells can be contractile or extensile based on the direction of pushing or pulling forces exerted by their neighbours or on the substrate. It has been shown that a monolayer of fibroblasts behaves as a contractile system while epithelial or neural progentior monolayers behave as an extensile system. Through a combination of cell culture experiments and in silico modelling, we reveal the mechanism behind this switch in extensile to contractile as the weakening of intercellular contacts. This switch promotes the build-up of tension at the cell-substrate interface through an increase in actin stress fibres and traction forces. This is accompanied by mechanotransductive changes in vinculin and YAP activation. We further show that contractile and extensile differences in cell activity sort cells in mixtures, uncovering a generic mechanism for pattern formation during cell competition, and morphogenesis.

The nature of cell division forces in epithelial monolayers

Epithelial cells undergo striking morphological changes during division to ensure proper segregation of genetic and cytoplasmic materials. These morphological changes occur despite dividing cells being mechanically restricted by neighboring cells, indicating the need for extracellular force generation. Beyond driving cell division itself, forces associated with division have been implicated in tissue-scale processes, including development, tissue growth, migration, and epidermal stratification. While forces generated by mitotic rounding are well understood, forces generated after rounding remain unknown. Here, we identify two distinct stages of division force generation that follow rounding: (1) Protrusive forces along the division axis that drive division elongation, and (2) outward forces that facilitate postdivision spreading. Cytokinetic ring contraction of the dividing cell, but not activity of neighboring cells, generates extracellular forces that propel division elongation and contribute to chromosome segregation. Forces from division elongation are observed in epithelia across many model organisms. Thus, division elongation forces represent a universal mechanism that powers cell division in confining epithelia.

Self-generated persistent random forces drive phase separation in growing tumors

A single solid tumor, composed of nearly identical cells, exhibits heterogeneous dynamics. Dynamics of cells in the core is glass-like, whereas those in the periphery undergoes diffusive or super-diffusive behavior. Quantification of heterogeneity using the mean square displacement or the self-intermediate scattering function, which involves averaging over the cell population, hides the complexity of the collective movement. Using the t-distributed stochastic neighbor embedding (t-SNE), a popular unsupervised machine learning dimensionality reduction technique, we show that the phase space structure of an evolving colony of cells, driven by cell division and apoptosis, partitions into nearly disjoint sets composed principally of the core and periphery cells. The non-equilibrium phase separation is driven by the differences in the persistence of self-generated active forces induced by cell division. Extensive heterogeneity revealed by t-SNE paves the way toward understanding the origins of intratumor heterogeneity using experimental imaging data.

Fluctuations can induce local nematic order and extensile stress in monolayers of motile cells

Recent experiments in various cell types have shown that two-dimensional tissues often display local nematic order, with evidence of extensile stresses manifest in the dynamics of topological defects. Using a mesoscopic model where tissue flow is generated by fluctuating traction forces coupled to the nematic order parameter, we show that the resulting tissue dynamics can spontaneously produce local nematic order and an extensile internal stress. A key element of the model is the assumption that in the presence of local nematic alignment, cells preferentially crawl along the nematic axis, resulting in anisotropy of fluctuations. Our work shows that activity can drive either extensile or contractile stresses in tissue, depending on the relative strength of the contractility of the cortical cytoskeleton and tractions by cells on the extracellular matrix.

Cell cycle-dependent active stress drives epithelia remodeling

Epithelia have distinct cellular architectures which are established in development, reestablished after wounding, and maintained during tissue homeostasis despite cell turnover and mechanical perturbations. In turn, cell shape also controls tissue function as a regulator of cell differentiation, proliferation, and motility. Here, we investigate cell shape changes in a model epithelial monolayer. After the onset of confluence, cells continue to proliferate and change shape over time, eventually leading to a final architecture characterized by arrested motion and more regular cell shapes. Such monolayer remodeling is robust, with qualitatively similar evolution in cell shape and dynamics observed across disparate perturbations. Here, we quantify differences in monolayer remodeling guided by the active vertex model to identify underlying order parameters controlling epithelial architecture. When monolayers are formed atop an extracellular matrix with varied stiffness, we find the cell density at which motion arrests varies significantly, but the cell shape remains constant, consistent with the onset of tissue rigidity. In contrast, pharmacological perturbations can significantly alter the cell shape at which tissue dynamics are arrested, consistent with varied amounts of active stress within the tissue. Across all experimental conditions, the final cell shape is well correlated to the cell proliferation rate, and cell cycle inhibition immediately arrests cell motility. Finally, we demonstrate cell cycle variation in junctional tension as a source of active stress within the monolayer. Thus, the architecture and mechanics of epithelial tissue can arise from an interplay between cell mechanics and stresses arising from cell cycle dynamics.

Migrating Epithelial Monolayer Flows Like a Maxwell Viscoelastic Liquid

We perform a bidimensional Stokes experiment in an active cellular material: an autonomously migrating monolayer of Madin-Darby canine kidney epithelial cells flows around a circular obstacle within a long and narrow channel, involving an interplay between cell shape changes and neighbor rearrangements. Based on image analysis of tissue flow and coarse-grained cell anisotropy, we determine the tissue strain rate, cell deformation, and rearrangement rate fields, which are spatially heterogeneous. We find that the cell deformation and rearrangement rate fields correlate strongly, which is compatible with a Maxwell viscoelastic liquid behavior (and not with a Kelvin-Voigt viscoelastic solid behavior). The value of the associated relaxation time is measured as τ=70±15  min, is observed to be independent of obstacle size and division rate, and is increased by inhibiting myosin activity. In this experiment, the monolayer behaves as a flowing material with a Weissenberg number close to one which shows that both elastic and viscous effects can have comparable contributions in the process of collective cell migration.

Spatially heterogeneous dynamics of cells in a growing tumor spheroid: comparison between theory and experiments

Collective cell movement, characterized by multiple cells that are in contact for substantial periods of time and undergo correlated motion, plays a central role in cancer and embryogenesis. Recent imaging experiments have provided time-dependent traces of individual cells, thus providing an unprecedented picture of tumor spheroid growth. By using simulations of a minimal cell model, we analyze the experimental data that map the movement of cells in a fibrosarcoma tumor spheroid embedded in a collagen matrix. Both simulations and experiments show that cells in the core of the spheroid exhibit subdiffusive glassy dynamics (mean square displacement, Δ(t) ≈ tα with α < 1), whereas cells in the periphery exhibit superdiffusive motion, Δ(t) ≈ tα with α > 1. The motion of most of the cells near the periphery is highly persistent and correlated directional motion due to cell doubling and apoptosis rates, thus explaining the observed superdiffusive behavior. The α values for cells in the core and periphery, extracted from simulations and experiments, are in near quantitative agreement with each other, which is surprising given that no parameter in the model was used to fit the measurements. The qualitatively different dynamics of cells in the core and periphery is captured by the fourth order susceptibility, introduced to characterize metastable states in glass forming systems. Analyses of the velocity autocorrelation of individual cells show remarkable spatial heterogeneity with no two cells exhibiting similar behavior. The prediction that α should depend on the location of the cells in the tumor is amenable to experimental testing. The highly heterogeneous dynamics of cells in the tumor spheroid provides a plausible mechanism for the origin of intratumor heterogeneity.

Unjamming and collective migration in MCF10A breast cancer cell lines

Each cell comprising an intact, healthy, confluent epithelial layer ordinarily remains sedentary, firmly adherent to and caged by its neighbors, and thus defines an elemental constituent of a solid-like cellular collective [1,2]. After malignant transformation, however, the cellular collective can become fluid-like and migratory, as evidenced by collective motions that arise in characteristic swirls, strands, ducts, sheets, or clusters [3,4]. To transition from a solid-like to a fluid-like phase and thereafter to migrate collectively, it has been recently argued that cells comprising the disordered but confluent epithelial collective can undergo changes of cell shape so as to overcome geometric constraints attributable to the newly discovered phenomenon of cell jamming and the associated unjamming transition (UJT) [1,2,5-9]. Relevance of the jamming concept to carcinoma cells lines of graded degrees of invasive potential has never been investigated, however. Using classical in vitro cultures of six breast cancer model systems, here we investigate structural and dynamical signatures of cell jamming, and the relationship between them [1,2,10,11]. In order of roughly increasing invasive potential as previously reported, model systems examined included MCF10A, MCF10A.Vector; MCF10A.14-3-3ζ; MCF10.ErbB2, MCF10AT; and MCF10CA1a [12-15]. Migratory speed depended on the particular cell line. Unsurprisingly, for example, the MCF10CA1a cell line exhibited much faster migratory speed relative to the others. But unexpectedly, across different cell lines higher speeds were associated with enhanced size of cooperative cell packs in a manner reminiscent of a peloton [9]. Nevertheless, within each of the cell lines evaluated, cell shape and shape variability from cell-to-cell conformed with predicted structural signatures of cell layer unjamming [1]. Moreover, both structure and migratory dynamics were compatible with previous theoretical descriptions of the cell jamming mechanism [2,10,11,16,17]. As such, these findings demonstrate the richness of the cell jamming mechanism, which is now seen to apply across these cancer cell lines but remains poorly understood.

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.

Emergence of active nematics in chaining bacterial biofilms

Growing tissue and bacterial colonies are active matter systems where cell divisions and cellular motion generate active stress. Although they operate in the non-equilibrium regime, these biological systems can form large-scale ordered structures. How mechanical instabilities drive the dynamics of active matter systems and form ordered structures are not well understood. Here, we use chaining Bacillus subtilis, also known as a biofilm, to study the relation between mechanical instabilities and nematic ordering. We find that bacterial biofilms have intrinsic length scales above which a series of mechanical instabilities occur. Localized stress and friction drive buckling and edge instabilities which further create nematically aligned structures and topological defects. We also observe that topological defects control stress distribution and initiate the formation of sporulation sites by creating three-dimensional structures. In this study we propose an alternative active matter platform to study the essential roles of mechanics in growing biological tissue.

Active Fingering Instability in Tissue Spreading

During the spreading of epithelial tissues, the advancing tissue front often develops fingerlike protrusions. Their resemblance to traditional viscous fingering patterns in driven fluids suggests that epithelial fingers could arise from an interfacial instability. However, the existence and physical mechanism of such a putative instability remain unclear. Here, based on an active polar fluid model for epithelial spreading, we analytically predict a generic instability of the tissue front. On the one hand, active cellular traction forces impose a velocity gradient that leads to an accelerated front, which is, thus, unstable to long-wavelength perturbations. On the other hand, contractile intercellular stresses typically dominate over surface tension in stabilizing short-wavelength perturbations. Finally, the finite range of hydrodynamic interactions in the tissue selects a wavelength for the fingering pattern, which is, thus, given by the smallest between the tissue size and the hydrodynamic screening length. Overall, we show that spreading epithelia experience an active fingering instability based on a simple kinematic mechanism. Moreover, our results underscore the crucial role of long-range hydrodynamic interactions in the dynamics of tissue morphology.

Emergence of Active Nematic Behavior in Monolayers of Isotropic Cells

There is now growing evidence of the emergence and biological functionality of liquid crystal features, including nematic order and topological defects, in cellular tissues. However, how such features that intrinsically rely on particle elongation emerge in monolayers of cells with isotropic shapes is an outstanding question. In this Letter, we present a minimal model of cellular monolayers based on cell deformation and force transmission at the cell-cell interface that explains the formation of topological defects and captures the flow-field and stress patterns around them. By including mechanical properties at the individual cell level, we further show that the instability that drives the formation of topological defects, and leads to active turbulence, emerges from a feedback between shape deformation and active driving. The model allows us to suggest new explanations for experimental observations in tissue mechanics, and to propose designs for future experiments.

Data-driven quantitative modeling of bacterial active nematics

Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such "active nematics" systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here, we introduce an active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path toward more quantitative active matter research.

Mechanical forces in cell monolayers

In various physiological processes, the cell collective is organized in a monolayer, such as seen in a simple epithelium. The advances in the understanding of mechanical behavior of the monolayer and its underlying cellular and molecular mechanisms will help to elucidate the properties of cell collectives. In this Review, we discuss recent in vitro studies on monolayer mechanics and their implications on collective dynamics, regulation of monolayer mechanics by physical confinement and geometrical cues and the effect of tissue mechanics on biological processes, such as cell division and extrusion. In particular, we focus on the active nematic property of cell monolayers and the emerging approach to view biological systems in the light of liquid crystal theory. We also highlight the mechanosensing and mechanotransduction mechanisms at the sub-cellular and molecular level that are mediated by the contractile actomyosin cytoskeleton and cell-cell adhesion proteins, such as E-cadherin and α-catenin. To conclude, we argue that, in order to have a holistic understanding of the cellular response to biophysical environments, interdisciplinary approaches and multiple techniques - from large-scale traction force measurements to molecular force protein sensors - must be employed.

Biological Tissues as Active Nematic Liquid Crystals

Live tissues can self-organize and be described as active materials composed of cells that generate active stresses through continuous injection of energy. In vitro reconstituted molecular networks, as well as single-cell cytoskeletons show that their filamentous structures can portray nematic liquid crystalline properties and can promote nonequilibrium processes induced by active processes at the microscale. The appearance of collective patterns, the formation of topological singularities, and spontaneous phase transition within the cell cytoskeleton are emergent properties that drive cellular functions. More integrated systems such as tissues have cells that can be seen as coarse-grained active nematic particles and their interaction can dictate many important tissue processes such as epithelial cell extrusion and migration as observed in vitro and in vivo. Here, a brief introduction to the concept of active nematics is provided, and the main focus is on the use of this framework in the systematic study of predominantly 2D tissue architectures and dynamics in vitro. In addition how the nematic state is important in tissue behavior, such as epithelial expansion, tissue homeostasis, and the atherosclerosis disease state, is discussed. Finally, how the nematic organization of cells can be controlled in vitro for tissue engineering purposes is briefly discussed.

A growing bacterial colony in two dimensions as an active nematic

How a single bacterium becomes a colony of many thousand cells is important in biomedicine and food safety. Much is known about the molecular and genetic bases of this process, but less about the underlying physical mechanisms. Here we study the growth of single-layer micro-colonies of rod-shaped Escherichiacoli bacteria confined to just under the surface of soft agarose by a glass slide. Analysing this system as a liquid crystal, we find that growth-induced activity fragments the colony into microdomains of well-defined size, whilst the associated flow orients it tangentially at the boundary. Topological defect pairs with charges \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\pm {\textstyle{1 \over 2}}$$\end{document}±12 are produced at a constant rate, with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$+ {\textstyle{1 \over 2}}$$\end{document}+12 defects being propelled to the periphery. Theoretical modelling suggests that these phenomena have different physical origins from similar observations in other extensile active nematics, and a growing bacterial colony belongs to a new universality class, with features reminiscent of the expanding universe.

Rod-shaped bacteria are an example of active matter. Here the authors find that a growing bacterial colony harbours internal cellular flows affecting orientational ordering in its interior and at the boundary. Results suggest this system may belong to a new active matter universality class.

Inverse tissue mechanics of cell monolayer expansion

Living tissues undergo deformation during morphogenesis. In this process, cells generate mechanical forces that drive the coordinated cell motion and shape changes. Recent advances in experimental and theoretical techniques have enabled in situ measurement of the mechanical forces, but the characterization of mechanical properties that determine how these forces quantitatively affect tissue deformation remains challenging, and this represents a major obstacle for the complete understanding of morphogenesis. Here, we proposed a non-invasive reverse-engineering approach for the estimation of the mechanical properties, by combining tissue mechanics modeling and statistical machine learning. Our strategy is to model the tissue as a continuum mechanical system and to use passive observations of spontaneous tissue deformation and force fields to statistically estimate the model parameters. This method was applied to the analysis of the collective migration of Madin-Darby canine kidney cells, and the tissue flow and force were simultaneously observed by the phase contrast imaging and traction force microscopy. We found that our monolayer elastic model, whose elastic moduli were reverse-engineered, enabled a long-term forecast of the traction force fields when given the tissue flow fields, indicating that the elasticity contributes to the evolution of the tissue stress. Furthermore, we investigated the tissues in which myosin was inhibited by blebbistatin treatment, and observed a several-fold reduction in the elastic moduli. The obtained results validate our framework, which paves the way to the estimation of mechanical properties of living tissues during morphogenesis.

In order to shape the body of a multicellular organism, cells generate mechanical forces and undergo deformation. Although these forces are being increasingly determined, quantitative characterization of the relation between the deformation and forces at the tissue level remains challenging. To estimate these properties, we developed a reverse-engineering method by combining tissue mechanics modeling and statistical machine learning, and then tested this method on a common model system, the expansion of cultured cell monolayer. This statistically sound framework uses the passive observations of spontaneous deformation and force dynamics in tissues, and enables us to elucidate unperturbed mechanical processes underlying morphogenesis.

Edge instability in incompressible planar active fluids

Interfacial instability is highly relevant to many important biological processes. A key example arises in wound healing experiments, which observe that an epithelial layer with an initially straight edge does not heal uniformly. We consider the phenomenon in the context of active fluids. Improving upon the approximation used by Zimmermann, Basan, and Levine [Eur. Phys. J.: Spec. Top. 223, 1259 (2014)1951-635510.1140/epjst/e2014-02189-7], we perform a linear stability analysis on a two-dimensional incompressible hydrodynamic model of an active fluid with an open interface. We categorize the stability of the model and find that for experimentally relevant parameters, fingering instability is always absent in this minimal model. Our results point to the crucial role of density variation in the fingering instability in tissue regeneration.

Emergent patterns of collective cell migration under tubular confinement

Collective epithelial behaviors are essential for the development of lumens in organs. However, conventional assays of planar systems fail to replicate cell cohorts of tubular structures that advance in concerted ways on out-of-plane curved and confined surfaces, such as ductal elongation in vivo. Here, we mimic such coordinated tissue migration by forming lumens of epithelial cell sheets inside microtubes of 1-10 cell lengths in diameter. We show that these cell tubes reproduce the physiological apical-basal polarity, and have actin alignment, cell orientation, tissue organization, and migration modes that depend on the extent of tubular confinement and/or curvature. In contrast to flat constraint, the cell sheets in a highly constricted smaller microtube demonstrate slow motion with periodic relaxation, but fast overall movement in large microtubes. Altogether, our findings provide insights into the emerging migratory modes for epithelial migration and growth under tubular confinement, which are reminiscent of the in vivo scenario.

Motility of active nematic films driven by "active anchoring"

We provide a minimal model for an active nematic film in contact with both a solid substrate and a passive isotropic fluid, and explore its dynamics in one and two dimensions using a combination of hybrid Lattice Boltzmann simulations and analytical calculations. By imposing nematic anchoring at the substrate while active flows induce a preferred alignment at the interface ("active anchoring"), we demonstrate that directed fluid flow spontaneously emerges in cases where the two anchoring types are opposing. In one dimension, our model reduces to an analogue of a loaded elastic column. Here, the transition from a stationary to a motile state is akin to the buckling bifurcation, but offers the possibility to reverse the flow direction for a given set of parameters and boundary conditions solely by changing initial conditions. The two-dimensional variant of our model allows for additional tangential instabilities, and it is found that undulations form in the interface above a threshold activity. Our results might be relevant for the design of active microfluidic geometries or curvature-guided self-assembly.

Cell Division Induces and Switches Coherent Angular Motion within Bounded Cellular Collectives

Collective cell migration underlies many biological processes, including embryonic development, wound healing, and cancer progression. In the embryo, cells have been observed to move collectively in vortices using a mode of collective migration known as coherent angular motion (CAM). To determine how CAM arises within a population and changes over time, here, we study the motion of mammary epithelial cells within engineered monolayers, in which the cells move collectively about a central axis in the tissue. Using quantitative image analysis, we find that CAM is significantly reduced when mitosis is suppressed. Particle-based simulations recreate the observed trends, suggesting that cell divisions drive the robust emergence of CAM and facilitate switches in the direction of collective rotation. Our simulations predict that the location of a dividing cell, rather than the orientation of the division axis, facilitates the onset of this motion. These predictions agree with experimental observations, thereby providing, to our knowledge, new insight into how cell divisions influence CAM within a tissue. Overall, these findings highlight the dynamic nature of CAM and suggest that regulating cell division is crucial for tuning emergent collective migratory behaviors, such as vortical motions observed in vivo.

Topological defects in epithelia govern cell death and extrusion

Epithelial tissues (epithelia) remove excess cells through extrusion, preventing the accumulation of unnecessary or pathological cells. The extrusion process can be triggered by apoptotic signalling, oncogenic transformation and overcrowding of cells. Despite the important linkage of cell extrusion to developmental, homeostatic and pathological processes such as cancer metastasis, its underlying mechanism and connections to the intrinsic mechanics of the epithelium are largely unexplored. We approach this problem by modelling the epithelium as an active nematic liquid crystal (that has a long range directional order), and comparing numerical simulations to strain rate and stress measurements within monolayers of MDCK (Madin Darby canine kidney) cells. Here we show that apoptotic cell extrusion is provoked by singularities in cell alignments in the form of comet-shaped topological defects. We find a universal correlation between extrusion sites and positions of nematic defects in the cell orientation field in different epithelium types. The results confirm the active nematic nature of epithelia, and demonstrate that defect-induced isotropic stresses are the primary precursors of mechanotransductive responses in cells, including YAP (Yes-associated protein) transcription factor activity, caspase-3-mediated cell death, and extrusions. Importantly, the defect-driven extrusion mechanism depends on intercellular junctions, because the weakening of cell-cell interactions in an α-catenin knockdown monolayer reduces the defect size and increases both the number of defects and extrusion rates, as is also predicted by our model. We further demonstrate the ability to control extrusion hotspots by geometrically inducing defects through microcontact printing of patterned monolayers. On the basis of these results, we propose a mechanism for apoptotic cell extrusion: spontaneously formed topological defects in epithelia govern cell fate. This will be important in predicting extrusion hotspots and dynamics in vivo, with potential applications to tissue regeneration and the suppression of metastasis. Moreover, we anticipate that the analogy between the epithelium and active nematic liquid crystals will trigger further investigations of the link between cellular processes and the material properties of epithelia.

Cell growth, division, and death in cohesive tissues: A thermodynamic approach

Cell growth, division, and death are defining features of biological tissues that contribute to morphogenesis. In hydrodynamic descriptions of cohesive tissues, their occurrence implies a nonzero rate of variation of cell density. We show how linear nonequilibrium thermodynamics allows us to express this rate as a combination of relevant thermodynamic forces: chemical potential, velocity divergence, and activity. We illustrate the resulting effects of the nonconservation of cell density on simple examples inspired by recent experiments on cell monolayers, considering first the velocity of a spreading front, and second an instability leading to mechanical waves.

Dancing disclinations in confined active nematics

The spontaneous emergence of collective flows is a generic property of active fluids and often leads to chaotic flow patterns characterised by swirls, jets, and topological disclinations in their orientation field. However, the ability to achieve structured flows and ordered disclinations is of particular importance in the design and control of active systems. By confining an active nematic fluid within a channel, we find a regular motion of disclinations, in conjunction with a well defined and dynamic vortex lattice. As pairs of moving disclinations travel through the channel, they continually exchange partners producing a dynamic ordered state, reminiscent of Ceilidh dancing. We anticipate that this biomimetic ability to self-assemble organised topological disclinations and dynamically structured flow fields in engineered geometries will pave the road towards establishing new active topological microfluidic devices.