The dynamics of epithelial tissues play a key role in tissue organization, both in health and disease. In this Review, the authors discuss materials and techniques for the study of epithelial movement and mechanics and investigate epithelia as active matter from a theoretical and experimental perspective.
Active matter systems are made up of units that consume energy. Physicists group flocks of birds, molecular motors and layers of vibrating grains together in this category because they all extract energy from their surroundings at a single particle level and transform it into mechanical work. By studying the behaviours that emerge, our understanding of these systems can be enhanced and new frameworks for investigating the statistical physics of out-of-equilibrium systems can be built.
This collection brings together research and reviews from across the Nature Research journals covering key aspects of active matter with selected content from Nature Communications, Nature, Nature Physics, Nature Materials, Nature Reviews Materials and Communications Physics.
Comment and reviews
Active matter systems are made up of self-driven components which extract energy from their surroundings to generate mechanical work. Here the authors review the subfield of active nematics and provide a comparison between theoretical findings and the corresponding experimental realisations.
The field of active matter studies how internally driven motile components self-organize into large-scale dynamical states and patterns. This Review discusses how active matter concepts are important for understanding cell biology, and how the use of biochemical components enables the creation of new inherently non-equilibrium materials with unique properties that have so far been mostly restricted to living organisms.
From flocking birds to swarming molecules, physicists are seeking to understand 'active matter' — and looking for a fundamental theory of the living world.
Equilibrium physics is ill-equipped to explain all of life’s subtleties, largely because living systems are out of equilibrium. Attempts to overcome this problem have given rise to a lively field of research—and some surprising biological findings.
Evidence that ants communicate mechanically to move objects several times their size has prompted a theory that places the group near a transition between uncoordinated and coordinated motion. These findings and their implications are reviewed here.
The behaviour of cells and tissues can be understood in terms of emergent mesoscale states that are determined by a set of physical properties. This Review surveys experimental evidence for these states and the physics underpinning them.
Theory and Modelling
Active matter describes a group of interacting units showing collective motions by constantly consuming energy from the environment, but inertia has largely been overlooked in this context. Scholz et al. show how important it can be by characterizing the dynamics of self-propelled particles in a model system.
Adapting statistical physics tools to study active systems is challenging due to their non-equilibrium nature. Here the authors use simulations to present a phase diagram of a 2D active system, showing a two-step melting scenario far from equilibrium along with gas-liquid motility-induced phase separation.
Active chiral fluids are a special case of active matter in which energy is introduced into rotational motion via local application of torque. Here Banerjee et al. develop a hydrodynamic theory of such active fluids and connect it with odd viscosity which was previously considered an abstract concept.
Collective self-organized behavior can be observed in a variety of systems such as colloids and microswimmers. Here O’Keeffe et al. propose a model of oscillators which move in space and tend to synchronize with neighboring oscillators and outline five types of collective self-organized states.
Determining how cellular activity affects the collective properties of growing tissues is key to understanding morphogenesis. An epithelial tissue model shows how active tension can give rise to striking mechanical behaviours seen in experiments.
Ensuring topological protection of the edge states in candidate topological insulators is complicated by the need to break time-reversal symmetry. Polar active liquids present an innovative solution to this problem, as a new metamaterial design shows.
Bacteria continuously inject energy into their surroundings and thus induce chaotic like flows, namely meso-scale turbulence. Here, the authors show that transition to meso-scale turbulence and inertial turbulence observed in pipes share the same scaling behavior that belongs to the directed percolation universality class.
Active fluids consist of self-driven particles that can drive spontaneous flow without the intervention of external forces. Here Woodhouseet al. show how to design logic circuits using this phenomenon in active fluid networks, which could be further exploited for autonomous microfluidic computing.
The dynamics of actin cytoskeleton is essential to the function of living cells. Here, Foffanoet al. describe a nonequilibrium filament model to mimic the formation of cytoskeleton and pinpoint the key role played by the actin entanglement during the transition from homogeneous to bundled networks.
Droplets are an appealing picture for protocells in origin-of-life studies, but it’s unclear how they would have propagated by growth and division. Theory suggests that chemically active droplets spontaneously split into equal daughter droplets.
The collective motion of microswimmers is determined by not only their direct interaction, but also the hydrodynamics forces mediated by the surrounding flow field. Here, the authors detail in simulation the spontaneous assembly and disassembly of magnetic microswimmers into various structures.
In active matter, chemical energy is transformed into mechanical motion; theoretical descriptions of nematic liquids are useful in understanding such phenomena. Here, Zhang et al. model the dynamics of active nematic liquid crystals confined onto a spherical shell in systems that mimic cell motion.
Mapping two-dimensional polar active fluids to two-dimensional soap and one-dimensional sandblasting
In many groups of moving organisms, such as swarms of bacteria, their constituents pack so tightly that density cannot change. Here, Chen et al.map such incompressible flocks in two dimensions onto the growth of a one-dimensional interface, and thereby compute the large-distance behaviour of such flocks.
Active matter can be described as either wet or dry, depending on whether hydrodynamics or frictional damping dominates the interactions. Here, the authors show that an increase in friction can stabilise the chaotic flow observed in wet active systems to give an ordered lattice of topological defects.
The pressure that a fluid of self-propelled particles exerts on its container is shown to depend on microscopic interactions between fluid and container, suggesting that there is no equation of state for mechanical pressure in generic active systems.
Synthetic Active Matter
The “faster is slower” phenomenon expresses a decrease in average velocity of a system of objects as their individual speed increases and can be used to describe a range of scenarios from microscopic particles to sheep. The authors investigate the effects of clogging and jamming in a system of paramagnetic colloids and the relation to the faster is slower phenomenon.
Synthetic active particles with inter-particle propulsion have been served as a model system to study the collective animal behaviors. Here, Khadka et al. add complexity to the model by spatially controlling particle motions through a laser feedback loop in response to the collective dynamics of particles.
Manipulation of paramagnetic microparticles can be exploited for drug delivery. Here the authors manipulate a swarm of such particles and control its shape with a magnetic field so that it can elongate reversibly, split into smaller swarms and thus be guided through a maze with multiple parallel channels.
Bacteria communicate and organize via quorum sensing which is determined by biochemical processes. Here the authors aim to reproduce this behaviour in a system of synthetic active particles whose motion is induced by an external beam which is in turn controlled by a feedback-loop which mimics quorum sensing.
Motile cilia are organelles found in eukaryotic cells and serve to swim or generate surface flows. The paper presents a theoretical and experimental study showing the systematic link between synchronisation state and the beating motion of active biological filaments.
Active systems utilize energy input to realize structural complexity and functional diversity. This work shows that magnetic colloidal rollers spontaneously self-organize into unconfined macroscopic vortices under a magnetic field, which can be used to transport inert particles across a flat surface.
Active rotating particles were shown to undergo a phase separation through numerical simulations. Here the authors provide an experimental realization of this phenomenon by presenting an ensemble of 3D-printed robots that rotate in different directions and interact with each other.
The cluster phase of active particles is one instance of the propensity of active matter to self-organize. Combining high-statistics experiments on Janus colloids and simple modeling, Ginot et al. provide a thorough characterization of cluster’s size and motion.
By designing surfactants that are responsive to an external stimulus, it is possible to manipulate surfactant-stabilized liquid droplets in a variety of ways. For example, we can control the interactions and assembly of the droplets. Bartosz Grzybowski and colleagues take this concept to a higher level of complexity, by synthesizing nanoparticulate surfactants that respond in different ways to multiple stimuli, including light, electric fields and magnetic fields. These multi-responsive surfactants enable an unprecedented level of structural and dynamical control over the resulting surfactant-stabilized systems, in which liquid droplets can be manipulated, assembled and made to react on demand.
A structurally chiral two-dimensional array of nanomagnets is shown to thermally relax its magnetization by rotation in a preferential direction, behaving as a magnetic ratchet.
Bacteria are able to propel themselves and thus drive systems out of equilibrium. Here the authors aim to control this motion and exploit it in microengineered motors which are powered by genetically modified bacteria and driven by light.
Collections of rolling colloids are shown to pinch off into motile clusters resembling droplets sliding down a windshield. These stable dynamic structures are formed through a fingering instability that relies on hydrodynamic interactions alone.
Our understanding of collective animal behaviour generally assumes that flocks and herds move through homogeneous environments. Colloidal experiments suggest that flocking can be distorted or even suppressed by the introduction of disorder.
The capability to move towards or away from light sources, namely phototaxis, is an essential feature of many microorganisms like bacteria or motile cells. Lozano et al. show an artificial phototaxis system that enables autonomous navigation of colloidal Janus spheres in a laser-generated light landscape.
Metal–dielectric Janus colloids subjected to perpendicular a.c. electric fields can self-organize into swarms, chains, clusters and isotropic gases, depending on the frequency of the field.
Active matter, such as swimming bacteria, show unique behaviors under confinement, but it is experimentally challenging to measure them. Takatoriet al. show the use of acoustic tweezers to trap self-propelled Janus particles as an enabling tool to investigate collective motions in living systems.
Many living systems, such as bacterial colonies, exhibit collective and dynamic behaviours that are sensitive to the change in environmental conditions. Here, the authors show that a colloidal active matter system switches between gathering and dispersal of individuals in response to a disordered potential.
Experiments and coarse-grained simulations show, in an active system based on microtubules, a system-spanning phase of motile defects with orientational order that persists over hours despite a defect lifetime of seconds.
Nanocapillarity-mediated magnetic assembly of nanoparticles into ultraflexible filaments and reconfigurable networks
Capillary forces at the nanoscale can be harnessed for the magnetically directed assembly of lipid-shell-coated nanoparticles into ultraflexible microfilaments and network structures.
Confined populations of interacting motile particles often display collective motion in the form of large-scale vortices, such as fish groups and bacteria colonies. Bricard et al.study a model system with self-propelled colloidal rollers and identify the constituents responsible for emergent vortices.
The ability to control the movement of fluid droplets is of practical use in many applications including microfluidic liquid handling. Existing techniques demand large energy gradients on the solid surfaces on which the droplets are placed or a carefully prepared surface to overcome contact line pinning (an effect which usually limits droplet motion). This paper reports a previously unrecognized phenomenon that could provide a convenient means of manipulating fluid droplets. Droplets consisting of two miscible components in which one component has both a higher vapour pressure and higher surface tension than the other — such as water and propylene glycol — exhibit a contact angle when deposited on a high-energy surface (clean glass), but rest on a fluid film so do not suffer from contact line pinning. The droplets are stabilized by evaporation-induced surface tension gradients and can move under the influence of tiny forces, including the vapour emitted by neighbouring droplets. A wide range of interesting interactions is recorded — for example, one droplet bouncing off another, a droplet 'chasing' another in a circle and a rainbow of different droplets sorted according to their surface tensions.
Biological Active Matter
The study of interfaces in bacterial systems is of relevance to the spreading of bacterial colonies and pathological infections. Here the authors investigate the dynamics of active/passive interfaces in bacterial swarms and find that the boundary can be described as a propagating, diffuse elastic interface.
A study of how single C. elegans cells establish the polarity required for cell division reveals a general principle for pattern formation in living systems controlled by biochemical cues.
Single-cell tracking of up to 10,000 bacteria reveals the structure and dynamics of 3D biofilms—providing evidence to suggest that both local ordering and global biofilm architecture emerge from mechanical interactions.
Myosin motors drive the actin cytoskeleton out-of-equilibrium, but the role of myosin-driven active stresses in the accumulation and dissipation of mechanical work is unclear. Here, the authors synthesize an actomyosin material and find that the rate of entropy production increases non-monotonically with increasing accumulation of active stresses.
Geometrically confined suspensions of swimming bacteria can self-organize into an ordered state. Here, the authors use tiny pillars to trigger organization of bacterial motion into a stable lattice of vortices with a long-range antiferromagnetic order and control vortex direction through pillar chirality.
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.
An analogy with wetting has proven apt for describing how groups of cells spread on a substrate. But cells are active: they polarize, generate forces and adhere to their surroundings. Experiments now find agreement with an active update to the theory.
Polygonal motion and adaptable phototaxis via flagellar beat switching in the microswimmer Euglena gracilis
A single-celled organism exhibits complex swimming behaviours in response to changes in light intensity. Modelling and experiments suggest that the swimmer exploits phase relations between its photoreceptor and orientation to enable navigation.
Sokolov et al. have previously shown how bacteria are expelled in response to a rotating microparticle. Here the authors find that when the microparticle is spun at much higher rotation rates bacteria are trapped around it and then are expelled radially upon rotation cessation in an explosion-like manner.
The ability to generate microscale patterns and control microswimmers may be useful for engineering smart materials. Here Arlt et al. use genetically modified bacteria with fast response to changes in light intensity to produce light-induced patterns.
Topological defects in a turbulent active nematic on a toroidal surface are shown to segregate in regions of opposite curvature. Simulations suggest that this behaviour may be controlled — or even suppressed — by tuning the level of activity.
Tissue remodeling involves substantial involvement of the contractile actomyosin cytoskeleton. Here the authors model the spatiotemporal evolution of actomyosin densities during Drosophila germband extension and find affine and nonaffine deformations that depend on the magnitude of local contractile stress.
Active nematics consist of self-driven components that develop orientational order and turbulent flow. Here Guillamat et al. investigate an active nematic constrained in a quasi-2D geometrical setup and show that there exists an intrinsic length scale that determines the geometry in all forcing regimes.
Self-organization is observed in cytoskeletal systems but emergence of order from disorder is poorly understood. Using a high density actomyosin system, the authors capture the transition from disorder to order, which is driven by enhanced alignment effects caused by increase in multi-filament collisions.
Epithelial monolayers remove excess cells by extrusion. Benoit Ladoux and colleagues now report a purely mechanical route to cell extrusion at the site of topological defects within the cell monolayer. By modelling the epithelium as an active nematic liquid crystal, they show that cell extrusion is driven by stresses induced by distortions in cell orientation. Extrusion hotspots were controlled by geometrically inducing defects through microcontact printing of patterned monolayers. The authors also investigated the mechanotransductive effect of stress localization and found that signals related to cell death were induced at these sites of compressive stress. Additionally, tampering with the intercellular adhesion complexes led to a weakening of cell–cell interactions and resulted in an increased number of defects and extrusions. This finding is in line with nematic theory, which predicts that the number of topological defects is inversely related to the orientational elasticity.
Kyogo Kawaguchi et al. show that particular sorts of defect structures in cultures of neural progenitor cells can act as 'sources' and 'sinks' of cell flow, depending on the direction of movement of cells around the defects. The alignment of cells around these defect structures (which correspond to topological defects) is similar to that seen in artificial extensile active nematic liquid-crystal systems. The authors observed that the cells either piled up into mounds or decreased in density around the defects, affecting the flow of the cells. The authors suggest that it is the interplay between the active forces from cell motility and frictional forces that lead to the changes in cell flow and density.
In vitro models of actin organization show the formation of vortices, asters and stars. Here Fritzsche et al. show that such actin structures form in living cells in a manner dependent on the Arp2/3 complex but not myosin, and such structures influence membrane architecture but not cortex elasticity.
In recent years, various effects of collective behaviour have been reported in 'active matter'—systems that contain large numbers of self-propelled particles. Such studies offer clues to understanding organization in biological systems at various scales and to strategies for designing smart materials. Yilin Wu and colleagues studied dense suspensions of Escherichia coli bacteria and observed a striking effect of collective oscillatory motion. Individual bacteria move in an erratic manner, but when they are averaged over tens or hundreds of micrometres, steady, synchronized oscillations become apparent. The authors present a model of noisy self-propelled particles with strictly local interactions that can account for the observations. Such oscillatory behaviour could point to a new direction for studying self-organization in active matter.
The actomyosin cytoskeleton consists of a contractile array but how it becomes organized is not clear. Here the authors reconstitute a controllable contractile system to show that force balances at boundaries determine contraction dynamics, and spatial anisotropy leads to self-organization or aligned contractile fibres.
Spindle-shaped cells readily form nematic structures marked by topological defects. When confined, the defect distribution is independent of the domain size, activity and type of cell, lending a stability not found in non-cellular active nematics.
The interaction between myosin motors and F-actin is well described, but the impact of actin organization on contractility is not well described. Here the authors use a 2D biomimetic system and computational modelling to show that contractility of isotropic actomyosin is cooperative, and contraction velocity scales with myosin activation area.
Animals moving in groups are expected to differ from their many-body counterparts in equilibrium. A method based on maximum entropy shows that the interactions in starling flocks rearrange slowly enough to permit an equilibrium description locally.
The membranes of red blood cells exhibit a flickering motion that has long been ascribed a thermal origin. Microrheology experiments provide direct evidence that flickering is an active process characterized by non-equilibrium dynamics.
Interplay of active processes modulates tension and drives phase transition in self-renewing, motor-driven cytoskeletal networks
The actin cytoskeleton is a complex network of filaments, cross-linking proteins and motors; although the components are recognised, the behaviour of the network is less understood. Here Mak et al.use a Brownian dynamics model that reveals actin turnover dynamics as a key regulatory mechanism controlling cytoskeletal states.
Hydrodynamic coupling induces a vortex state in bacterial populations. Microfluidic experiments and modelling now demonstrate that lattices of these vortices can self-organize into patterns characterized by ferro- and antiferromagnetic order.
Aggregations of fire ants are viscoelastic with identical elastic and viscous moduli, and exhibit shear-thinning behaviour when deformed beyond the linear regime.
Cells moving in a tissue undergo a rigidity transition resembling that of active particles jamming at a critical density—but the tissue density stays constant. A new type of rigidity transition implicates the physical properties of the cells.
Sperm use external cues to find the egg using ill-defined principles. Here the authors use holographic microscopy and optochemical tools to study sperm swimming in light-sculpted chemical 3D landscapes; they show that sperm translate the temporal stimulation pattern into multiple swimming behaviours to orient deterministically in a gradient.
A simple system for studying self-organization in biology comprises driven actin filaments, thought to interact primarily via binary collisions. Angle-resolved statistics suggest that the transition to polar order is driven by multi-filament events.
A general memoryless molecular mechanism explains the self-organization of Brownian-like steps into truncated Lévy walks in the classic system of intracellular trafficking.
Soft filamentous bundles, including F-actin, microtubules or bacterial flagella, can experience large frictional forces that scale logarithmically with sliding velocity, and such frictional coupling can be tuned by modifying lateral interfilament interactions.