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.

Velocity correlations in an active nematic

The flow properties of a continuum model for an active nematic are studied and compared with recent experiments on suspensions of microtubule bundles and molecular motors. The velocity correlation length is found to be independent of the strength of the activity while the characteristic velocity scale increases monotonically as the activity is increased, both in agreement with the experimental observations. We interpret our results in terms of the creation and annihilation dynamics of a gas of topological defects.

Stabilization of active matter by flow-vortex lattices and defect ordering

Active systems, from bacterial suspensions to cellular monolayers, are continuously driven out of equilibrium by local injection of energy from their constituent elements and exhibit turbulent-like and chaotic patterns. Here we demonstrate both theoretically and through numerical simulations, that the crossover between wet active systems, whose behaviour is dominated by hydrodynamics, and dry active matter where any flow is screened, can be achieved by using friction as a control parameter. Moreover, we discover unexpected vortex ordering at this wet-dry crossover. We show that the self organization of vortices into lattices is accompanied by the spatial ordering of topological defects leading to active crystal-like structures. The emergence of vortex lattices, which leads to the positional ordering of topological defects, suggests potential applications in the design and control of active materials.

Defect-Mediated Morphologies in Growing Cell Colonies

Morphological trends in growing colonies of living cells are at the core of physiological and evolutionary processes. Using active gel equations, which include cell division, we show that shape changes during the growth can be regulated by the dynamics of topological defects in the orientation of cells. The friction between the dividing cells and underlying substrate drives anisotropic colony shapes toward more isotropic morphologies, by mediating the number density and velocity of topological defects. We show that the defects interact with the interface at a specific interaction range, set by the vorticity length scale of flows within the colony, and that the cells predominantly reorient parallel to the interface due to division-induced active stresses.

Vorticity, defects and correlations in active turbulence

We describe a numerical investigation of a continuum model of an active nematic, concentrating on the regime of active turbulence. Results are presented for the effect of three parameters, activity, elastic constant and rotational diffusion constant, on the order parameter and flow fields. Defects and distortions in the director field act as sources of vorticity, and thus vorticity is strongly correlated to the director field. In particular, the characteristic length of decay of vorticity and order parameter correlations is controlled by the defect density. By contrast, the decay of velocity correlations is determined by a balance between activity and dissipation. We highlight the role of microscopic flow generation mechanisms in determining the flow patterns and characteristic scales of active turbulence and contrast the behaviour of extensile and contractile active nematics.

Biphasic, lyotropic, active nematics

We perform dynamical simulations of a two-dimensional active nematic fluid in coexistence with an isotropic fluid. Drops of active nematic become elongated, and an effective anchoring develops at the nematic-isotropic interface. The activity also causes an undulatory instability of the interface. This results in defects of positive topological charge being ejected into the nematic, leaving the interface with a diffuse negative charge. Quenching the active lyotropic fluid results in a steady state in which phase-separating domains are elongated and then torn apart by active stirring.

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

We introduce the notion of cell division-induced activity and show that the cell division generates extensile forces and drives dynamical patterns in cell assemblies. Extending the hydrodynamic models of lyotropic active nematics we describe turbulent-like velocity fields that are generated by the cell division in a confluent monolayer of cells. We show that the experimentally measured flow field of dividing Madin-Darby Canine Kidney (MDCK) cells is reproduced by our modeling approach. Division-induced activity acts together with intrinsic activity of the cells in extensile and contractile cell assemblies to change the flow and director patterns and the density of topological defects. Finally we model the evolution of the boundary of a cellular colony and compare the fingering instabilities induced by cell division to experimental observations on the expansion of MDCK cell cultures.

Battling COVID-19: critical care and peri-operative healthcare resource management strategies in a tertiary academic medical centre in Singapore

In December 2019, a cluster of atypical pneumonia cases were reported in Wuhan, China, and a novel coronavirus elucidated as the aetiologic agent. Although most initial cases occurred in China, the disease, termed coronavirus disease 2019, has become a pandemic and continues to spread rapidly with human-to-human transmission in many countries. This is the third novel coronavirus outbreak in the last two decades and presents an ensuing healthcare resource burden that threatens to overwhelm available healthcare resources. A study of the initial Chinese response has shown that there is a significant positive association between coronavirus disease 2019 mortality and healthcare resource burden. Based on the Chinese experience, some 19% of coronavirus disease 2019 cases develop severe or critical disease. This results in a need for adequate preparation and mobilisation of critical care resources to anticipate and adapt to a surge in coronavirus disease 2019 case-load in order to mitigate morbidity and mortality. In this article, we discuss some of the peri-operative and critical care resource planning considerations and management strategies employed in a tertiary academic medical centre in Singapore in response to the coronavirus disease 2019 outbreak.

Active micromachines: Microfluidics powered by mesoscale turbulence

Dense active matter, from bacterial suspensions and microtubule bundles driven by motor proteins to cellular monolayers and synthetic Janus particles, is characterized by mesoscale turbulence, which is the emergence of chaotic flow structures. By immersing an ordered array of symmetric rotors in an active fluid, we introduce a microfluidic system that exploits spontaneous symmetry breaking in mesoscale turbulence to generate work. The lattice of rotors self-organizes into a spin state where neighboring discs continuously rotate in permanent alternating directions due to combined hydrodynamic and elastic effects. Our virtual prototype demonstrates a new research direction for the design of micromachines powered by the nematohydrodynamic properties of active turbulence.

Patterns in Drying Drops Dictated by Curvature-Driven Particle Transport

Patterns generated by controlled evaporation of droplets containing colloids are dictated by internally generated flows. This advective particle transport is crucial to the efficacy of printing and coating processes and is also an elegant route to the self-assembly of particles. We propose a novel particle transport route, which involves adsorption of particles to the interface and subsequent curvature-driven migration of the particles along the interface. This interface-mediated transport can be exploited to control the distribution of particles in the dried patterns, which we experimentally elucidate by achieving gravity-induced drop shape changes. Our experiments demonstrate that the interplay between the bulk and the interfacial transport leads to strikingly different patterns: while dried aqueous sessile drops of colloidal dispersions produce well known "coffee-rings", dried pendant drops lead to "coffee-eyes". We support our experimental findings using scaling arguments. In previous studies, the effect of gravity-induced change in drop shape on the patterns formed in drying drops has been neglected. However, we show that the structure of the patterns formed by the colloidal particles after solvent evaporation is markedly different when the drops are deformed by gravity.

Pervaporation from a dense membrane: roles of permeant-membrane interactions, Kelvin effect, and membrane swelling

Dense polymeric membranes with extremely small pores in the form of free volume are used widely in the pervaporative separation of liquid mixtures. The membrane permeation of a component followed by its vaporization on the opposite face is governed by the solubility and downstream pressure. We measured the evaporative flux of pure methanol and 2-propanol using dense membranes with different free volumes and different affinities (wettabilities and solubilities) for the permeant. Interestingly, the evaporative flux for different membranes vanished substantially (10-75%) below the equilibrium vapor pressure in the bulk. The discrepancy was larger for a smaller pore size and for more wettable membranes (higher positive spreading coefficients). This observation, which cannot be explained by the existing (mostly solution-diffusion type) models ofpervaporation, suggests an important role for the membrane-permeant interactions in nanopores that can lower the equilibrium vapor pressure. The pore sizes, as estimated from the positron annihilation, ranged from 0.2 to 0.6 nm for the dry membranes. Solubilities of methanol in different composite membranes were estimated from the Flory-Huggins theory. The interaction parameter was obtained from the surface properties measured by the contact angle goniometry in conjunction with the acid-base theory of polar surface interactions. For the membranes examined, the increase in the "wet" pore volume due to membrane swelling correlates almost linearly with the solubility of methanol in these membranes. Indeed, the observations are found to be consistent with the lowering of the equilibrium vapor pressure on the basis of the Kelvin equation. Thus, a higher solubility or selectivity of a membrane also implies stronger permeant-membrane interactions and a greater retention of the permeant by the membrane, thus decreasing its evaporative flux. This observation has important implications for the interpretation of existing experiments and in the separation of liquid mixtures by pervaporation.

Lattice-Boltzmann-Langevin simulations of binary mixtures

We report a hybrid numerical method for the solution of the Model H fluctuating hydrodynamic equations for binary mixtures. The momentum conservation equations with Landau-Lifshitz stresses are solved using the fluctuating lattice Boltzmann equation while the order parameter conservation equation with Langevin fluxes is solved using stochastic method of lines. Two methods, based on finite difference and finite volume, are proposed for spatial discretization of the order parameter equation. Special care is taken to ensure that the fluctuation-dissipation theorem is maintained at the lattice level in both cases. The methods are benchmarked by comparing static and dynamic correlations and excellent agreement is found between analytical and numerical results. The Galilean invariance of the model is tested and found to be satisfactory. Thermally induced capillary fluctuations of the interface are captured accurately, indicating that the model can be used to study nonlinear fluctuations.

Flow States and Transitions of an Active Nematic in a Three-Dimensional Channel

We use active nematohydrodynamics to study the flow of an active fluid in a 3D microchannel, finding a transition between active turbulence and regimes where there is a net flow along the channel. We show that the net flow is only possible if the active nematic is flow aligning and that, in agreement with experiments, the appearance of the net flow depends on the aspect ratio of the channel cross section. We explain our results in terms of when the hydrodynamic screening due to the channel walls allows the emergence of vortex rolls across the channel.

Active nematic materials with substrate friction

Active turbulence in dense active systems is characterized by high vorticity on a length scale that is large compared to that of individual entities. We describe the properties of active turbulence as momentum propagation is screened by frictional damping. As friction is increased, the spacing between the walls in the nematic director field decreases as a consequence of the more rapid velocity decays. This leads to, first, a regime with more walls and an increased number of topological defects, and then to a jammed state in which the walls deliminate bands of opposing flow, analogous to the shear bands observed in passive complex fluids.

Active transport in a channel: stabilisation by flow or thermodynamics

Recent experiments on active materials, such as dense bacterial suspensions and microtubule-kinesin motor mixtures, show a promising potential for achieving self-sustained flows. However, to develop active microfluidics it is necessary to understand the behaviour of active systems confined to channels. Therefore here we use continuum simulations to investigate the behaviour of active fluids in a two-dimensional channel. Motivated by the fact that most experimental systems show no ordering in the absence of activity, we concentrate on temperatures where there is no nematic order in the passive system, so that any nematic order is induced by the active flow. We systematically analyze the results, identify several different stable flow states, provide a phase diagram and show that the key parameters controlling the flow are the ratio of channel width to the length scale of active flow vortices, and whether the system is flow aligning or flow tumbling.

Beyond Coffee Rings: Drying Drops of Colloidal Dispersions on Inclined Substrates

The patterns resulting from drying particle-laden sessile drops (for example, coffee rings, where the particles are concentrated more at the edge, and their complete suppression, where the particles are uniformly distributed throughout the pattern) have been well studied for more than two decades. For the ubiquitous instance of occurrence of drying of drops containing nonvolatile species (either dissolved or dispersed) on substrates oriented at different angles with respect to gravity, the investigation of resulting evaporative patterns has not received much attention. This mini-review addresses the need to investigate the drying of drops residing on inclined surfaces and highlights recent advances in this field.

Morphological evolution of domains in spinodal decomposition

Domain growth in spinodal decomposition is usually described by a single time-evolving length scale. We show that the evolution of morphology of domains is nonmonotonic. The domains elongate rapidly at first and then, with the help of hydrodynamics, return to a more circular shape. The initial elongation phase does not alter with hydrodynamics. A small deviation from critical composition changes the morphology dramatically.

Do liquid drops roll or slide on inclined surfaces?

We study the motion of a two-dimensional droplet on an inclined surface, under the action of gravity, using a diffuse interface model which allows for arbitrary equilibrium contact angles. The kinematics of motion is analyzed by decomposing the gradient of the velocity inside the droplet into a shear and a residual flow. This decomposition helps in distinguishing sliding versus rolling motion of the drop. Our detailed study confirms intuition, in that rolling motion dominates as the droplet shape approaches a circle, and the viscosity contrast between the droplet and the ambient fluid becomes large. As a consequence of kinematics, the amount of rotation in a general droplet shape follows a universal curve characterized by geometry, and independent of Bond number, surface inclination and equilibrium contact angle, but determined by the slip length and viscosity contrast. Our results open the way toward a rational design of droplet-surface properties, both when rolling motion is desirable (as in self-cleaning hydrophobic droplets) and when it must be prevented (as in insecticide sprays on leaves).

Robust Method to Determine Critical Micelle Concentration via Spreading Oil Drops on Surfactant Solutions

The spreading of a liquid on another is often encountered in oil spills and coatings and is also of industrial relevance in pharmaceuticals and petrochemicals. In this study, the spreading of oil drops on aqueous solutions containing cationic, anionic, and nonionic surfactants over a wide range of surfactant concentrations is investigated. The spreading behavior quantified by measuring the time evolution of the projected area of the oil lens reveals the occurrence of a maximum, which is strongly dependent on the concentration of the surfactant in the aqueous solution. Our experiments show that this dependence is different at concentrations above and below the critical micelle concentration (CMC) of the surfactant and can be captured by two straight lines of different slopes. Interestingly, these two straight lines intersect at a concentration that coincides with the CMC of the surfactants in solution. We find that this behavior is universal as shown by performing experiments with different types of surfactants, their purity, and other system variables. Thus, we propose a method to unambiguously determine the CMC of surfactant solutions compared to the conventional techniques. The proposed method is simple, versatile, and applicable for the determination of CMC of both ionic and nonionic surfactants.

Sparse Game Changers Restore Collective Motion in Panicked Human Crowds

Using a dynamic variant of the Vicsek model, we show that the emergence of disorder from an orderly moving human crowd is a nonequilibrium first-order phase transition. We also show that this transition can be reversed by modifying the dynamics of a few agents, deemed as game changers. Surprisingly, the optimal placement of these game changers is found to be in regions of maximum local crowd speed. The presence of such game changers is effective owing to the discontinuous nature of the underlying phase transition. Thus our generic approach provides strategies to (i) delay crowd crush and (ii) design safe evacuation procedures, two aspects that are of paramount importance in maintaining safety of mass gatherings of people.

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.

Minimum energy shapes of one-side-pinned static drops on inclined surfaces

The shape that a liquid drop will assume when resting statically on a solid surface inclined to the horizontal is studied here in two dimensions. Earlier experimental and numerical studies yield multiple solutions primarily because of inherent differences in surface characteristics. On a solid surface capable of sustaining any amount of hysteresis, we obtain the global, and hence unique, minimum energy shape as a function of equilibrium contact angle, drop volume, and plate inclination. It is shown, in the energy minimization procedure, how the potential energy of this system is dependent on the basis chosen to measure it from, and two realistic bases, front-pinned and back-pinned, are chosen for consideration. This is at variance with previous numerical investigations where both ends of the contact line are pinned. It is found that the free end always assumes Young's equilibrium angle. Using this, simple equations that describe the angles and the maximum volume are then derived. The range of parameters where static drops are possible is presented. We introduce a detailed force balance for this problem and study the role of the wall in supporting the drop. We show that a portion of the wall reaction can oppose gravity while the other portion aids it. This determines the maximum drop volume that can be supported at a given plate inclination. This maximum volume is the least for a vertical wall, and is higher for all other wall inclinations. This study can be extended to three-dimensional drops in a straightforward manner and, even without this, lends itself to experimental verification of several of its predictions.

Patterns from drops drying on inclined substrates

The coffee ring effect results from the migration of particles in a drying particle laden drop and their subsequent deposition at the three phase contact line. The evaporative flux during the drying of sessile drops and the spatial distribution of particles in the coffee ring patterns exhibit azimuthal symmetry. It is possible to break this symmetry with the help of gravity by simply manipulating the inclination of the substrate on which the colloidal droplet undergoes drying. However, the effect of particle size, substrate wettability and inclination angle on the extent of asymmetry in the spatial distribution of particles over the deposit patterns has not been explored and is the subject of the current work. Our experiments on the drying of aqueous dispersions of polystyrene particles show that (i) asymmetry in the deposition of particles is observed irrespective of the diameter of the dispersed particles in the drying drop (ii) the degree of asymmetry increases with a decrease in wettability of the drop on the substrate and (iii) it is a non-monotonic function of the inclination angle of the substrate. These results indicate the possibility of additional particle transport mechanisms working in tandem with evaporation driven capillary flows and demand further investigation of the physics of pattern formation in drops drying on oriented substrates.

Helical flow states in active nematics

We show that confining extensile nematics in three-dimensional (3D) channels leads to the emergence of two self-organized flow states with nonzero helicity. The first is a pair of braided antiparallel streams-this double helix occurs when the activity is moderate, anchoring negligible, and reduced temperature high. The second consists of axially aligned counter-rotating vortices-this grinder train arises between spontaneous axial streaming and the vortex lattice. These two unanticipated helical flow states illustrate the potential of active fluids to break symmetries and form complex but organized spatiotemporal structures in 3D fluidic devices.