Viscoelastic control of spatiotemporal order in bacterial active matter

Spatiotemporal control of structure and dynamics in a polar active fluid

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.

Scaling Transition of Active Turbulence from Two to Three Dimensions

Turbulent flows are observed in low-Reynolds active fluids, which display similar phenomenology to the classical inertial turbulence but are of a different nature. Understanding the dependence of this new type of turbulence on dimensionality is a fundamental challenge in non-equilibrium physics. Real-space structures and kinetic energy spectra of bacterial turbulence are experimentally measured from two to three dimensions. The turbulence shows three regimes separated by two critical confinement heights, resulting from the competition of bacterial length, vortex size and confinement height. Meanwhile, the kinetic energy spectra display distinct universal scaling laws in quasi-2D and 3D regimes, independent of bacterial activity, length, and confinement height, whereas scaling exponents transition in two steps around the critical heights. The scaling behaviors are well captured by the hydrodynamic model we develop, which employs image systems to represent the effects of confining boundaries. The study suggests a framework for investigating the effect of dimensionality on non-equilibrium self-organized systems.

Model of Active Solids: Rigid Body Motion and Shape-Changing Mechanisms

Active solids such as cell collectives, colloidal clusters, and active metamaterials exhibit diverse collective phenomena, ranging from rigid body motion to shape-changing mechanisms. The nonlinear dynamics of such active materials remains, however, poorly understood when they host zero-energy deformation modes and when noise is present. Here, we show that stress propagation in a model of active solids induces the spontaneous actuation of multiple soft floppy modes, even without exciting vibrational modes. By introducing an adiabatic approximation, we map the dynamics onto an effective Landau free energy, predicting mode selection and the onset of collective dynamics. These results open new ways to study and design living and robotic materials with multiple modes of locomotion and shape change.

Active Darcy's Law

While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.

United under stress: High-speed transport network emerging at bacterial living edge

Individuals tend to move freely when there is enough room but would act collectively for their survival under external stress. In the case of living cells, for instance, when a drop of low-density flagellated bacterial solution is transferred onto the agar surface, the initially disordered movement of individual bacteria would be replaced with coordinated cell swarming after a lag phase of a few hours. Here, we study how such cooperation is established while overcoming the disorder at the onset of the lag phase with single nanoparticle tracking. Upon the spreading of the droplet, the bacteria in the solution cluster and align near the almost immobilized contact line confining the drop, forming a narrow ring of cells. As individual cells move in and out of the ring continuously, certain flow patterns emerge in the inter-bacterial fluid. We reveal high-speed long-distance unidirectional flows with definite chirality along the outside of the ring, along the inside of the ring and across the ring. We speculate that these flows enable the fast and efficient transport, facilitating the communication and unification of the bacterial community.

Agent-based modeling of stress anisotropy driven nematic ordering in growing biofilms

Living active collectives have evolved with remarkable self-patterning capabilities to adapt to the physical and biological constraints crucial for their growth and survival. However, the intricate process by which complex multicellular patterns emerge from a single founder cell remains elusive. In this study, we utilize an agent-based model, validated through single-cell microscopy imaging, to track the three-dimensional (3D) morphodynamics of cells within growing bacterial biofilms encased by agarose gels. The confined growth conditions give rise to a spatiotemporally heterogeneous stress landscape within the biofilm. In the core of the biofilm, where high hydrostatic and low shear stresses prevail, cell packing appears disordered. In contrast, near the gel-cell interface, a state of high shear stress and low hydrostatic stress emerges, driving nematic ordering, albeit with a time delay inherent to shear stress relaxation. Strikingly, we observe a robust spatiotemporal correlation between stress anisotropy and nematic ordering within these confined biofilms. This correlation suggests a mechanism whereby stress anisotropy plays a pivotal role in governing the spatial organization of cells. The reciprocity between stress anisotropy and cell ordering in confined biofilms opens new avenues for innovative 3D mechanically guided patterning techniques for living active collectives, which hold significant promise for a wide array of environmental and biomedical applications.

Vortex Pattern Stabilization in Thin Films Resulting from Shear Thickening of Active Suspensions

The need for structuring on micrometer scales is abundant, for example, in view of phononic applications. We here outline a novel approach based on the phenomenon of active turbulence on the mesoscale. As we demonstrate, a shear-thickening carrier fluid of active microswimmers intrinsically stabilizes regular vortex patterns of otherwise turbulent active suspensions. The fluid self-organizes into a periodically structured nonequilibrium state. Introducing additional passive particles of intermediate size leads to regular spatial organization of these objects. Our approach opens a new path toward functionalization through patterning of thin films and membranes.

Self-enhanced mobility enables vortex pattern formation in living matter

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Purely elastic turbulence in pressure-driven channel flows

Solutions of long, flexible polymer molecules are complex fluids that simultaneously exhibit fluid-like and solid-like behavior. When subjected to an external flow, dilute polymer solutions exhibit elastic turbulence-a unique, chaotic flow state absent in Newtonian fluids, like water. Unlike its Newtonian counterpart, elastic turbulence is caused by polymer molecules stretching and aligning in the flow, and can occur at vanishing inertia. While experimental realizations of elastic turbulence are well-documented, there is currently no understanding of its mechanism. Here, we present large-scale direct numerical simulations of elastic turbulence in pressure-driven flows through straight channels. We demonstrate that the transition to elastic turbulence is sub-critical, giving rise to spot-like flow structures that, further away from the transition, eventually spread throughout the domain. We provide evidence that elastic turbulence is organized around unstable coherent states that are localized close to the channel midplane.

Noise-induced collective actuation in active solids

Collective actuation describes the spontaneous synchronized oscillations taking place in active solids when the elasto-active feedback, which generically couples the reorientation of the active forces and the elastic stress, is large enough. In the absence of noise, collective actuation takes the form of a strong condensation of the dynamics on a specific pair of modes and their generalized harmonics. Here we report experiments conducted with centimetric active elastic structures, where collective oscillation takes place along the single lowest energy mode of the system, gapped from the other modes because of the system's geometry. Combining the numerical and theoretical analysis of an agent-based model, we demonstrate that this form of collective actuation is noise-induced. The effect of the noise is first analyzed in a single-particle toy model that reveals the interplay between the noise and the specific structure of the phase space. We then show that in the continuous limit, any finite amount of noise turns this new form of transition to collective actuation into a bona fide supercritical Hopf bifurcation.

Viscoelastic confinement induces periodic flow reversals in active nematics

We use linear stability analysis and hybrid lattice Boltzmann simulations to study the dynamical behavior of an active nematic confined in a channel made of viscoelastic material. We find that the quiescent, ordered active nematic is unstable above a critical activity. The transition is to a steady flow state for high elasticity of the channel surroundings. However, below a threshold elastic modulus, the system produces spontaneous oscillations with periodic flow reversals. We provide a phase diagram that highlights the region where time-periodic oscillations are observed and explain how they are produced by the interplay of activity and viscoelasticity. Our results suggest experiments to study the role of viscoelastic confinement in the spatiotemporal organization and control of active matter.

Bioinspired self-assembled colloidal collectives drifting in three dimensions underwater

Active matter systems feature a series of unique behaviors, including the emergence of collective self-assembly structures and collective migration. However, realizing collective entities formed by synthetic active matter in spaces without wall-bounded support makes it challenging to perform three-dimensional (3D) locomotion without dispersion. Inspired by the migration mechanism of plankton, we propose a bimodal actuation strategy in the artificial colloidal systems, i.e., combining magnetic and optical fields. The magnetic field triggers the self-assembly of magnetic colloidal particles to form a colloidal collective, maintaining numerous colloids as a dynamically stable entity. The optical field allows the colloidal collectives to generate convective flow through the photothermal effect, enabling them to use fluidic currents for 3D drifting. The collectives can perform 3D locomotion underwater, transit between the water-air interface, and have a controlled motion on the water surface. Our study provides insights into designing smart devices and materials, offering strategies for developing synthetic active matter capable of controllable collective movement in 3D space.

50-year history and perspective on biomechanics of swimming microorganisms: Part II. Collective behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years. Parts I and II are divided not by the period covered, but by the content of the research: Part I explains the behaviours of individual microorganisms, and Part II explains collective behaviour. In the 1990s, the description of microbial suspensions as a continuum progressed, and macroscopic flow structures such as bioconvection were analysed. The continuum model was later extended to analyse various phenomena such as flow induced trapping of microorganisms and accumulation of cells at interfaces. In the 2000s, the collective behaviour of swimming microorganisms came into the limelight, and physicists as well as biomechanics researchers carried out many studies probing microorganism collectivity. In particular, research on the turbulence-like flow structure of dense bacterial suspensions has led to dramatic developments in the field of microbial biomechanics. Efforts to bridge the cellular scale to the macroscopic scale by extracting macroscopic physical quantities from the microstructure of cell suspensions are also underway. This Part II reviews these collective behaviours of swimming microorganisms and discusses future prospects of the field.

Hydrodynamic Anisotropy of Depletion in Nonequilibrium

Active colloids in a bath of inert particles of smaller size cause anisotropic depletion. The active hydrodynamics of this nonequilibrium phenomenon, which is fundamentally different from its equilibrium counterpart and passive particles in an active bath, remains scarcely understood. Here we combine mesoscale hydrodynamic simulation as well as theoretical analysis to examine the physical origin for the active depletion around a self-propelled noninteractive colloid. Our results elucidate that the variable hydrodynamic effect critically governs the microstructure of the depletion zone. Three characteristic states of anisotropic depletion are identified, depending on the strength and stress of activity. This yields a state diagram of depletion in the two-parameter space, captured by developing a theoretical model with the continuum kinetic theory and leading to a mechanistic interpretation of the hydrodynamic anisotropy of depletion. Furthermore, we demonstrate that such depletion in nonequilibrium results in various clusters with ordered organization of squirmers, which follows a distinct principle contrary to that of the entropy scenario of depletion in equilibrium. The findings might be of immediate interest to tune the hydrodynamics-mediated anisotropic interactions and active nonequilibrium organizations in the self-propulsion systems.

Viscoelasticity enhances collective motion of bacteria

Bacteria form human and animal microbiota. They are the leading causes of many infections and constitute an important class of active matter. Concentrated bacterial suspensions exhibit large-scale turbulent-like locomotion and swarming. While the collective behavior of bacteria in Newtonian fluids is relatively well understood, many fundamental questions remain open for complex fluids. Here, we report on the collective bacterial motion in a representative biological non-Newtonian viscoelastic environment exemplified by mucus. Experiments are performed with synthetic porcine gastric mucus, natural cow cervical mucus, and a Newtonian-like polymer solution. We have found that an increase in mucin concentration and, correspondingly, an increase in the suspension's elasticity monotonously increases the length scale of collective bacterial locomotion. On the contrary, this length remains practically unchanged in Newtonian polymer solution in a wide range of concentrations. The experimental observations are supported by computational modeling. Our results provide insight into how viscoelasticity affects the spatiotemporal organization of bacterial active matter. They also expand our understanding of bacterial colonization of mucosal surfaces and the onset of antibiotic resistance due to swarming.

Geometrical control of interface patterning underlies active matter invasion

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

Horizontal and Vertical Coalescent Microrobotic Collectives Using Ferrofluid Droplets

Many artificial miniature robotic collectives have been developed to overcome the inherent limitations of inadequate individual capabilities. However, the basic building blocks of the reported collectives are mainly in the solid state, where the morphological boundaries of internal individuals are clear and cannot genuinely merge. Miniature robotic collectives based on liquid units still need to be explored; such on-demand mergeable swarm systems are advantageous for adapting to the changing external environment. Here, a strategy to achieve a coalescent collective system we presented that exploits the ferrofluid droplets' splitting and coalescence properties to trigger the formation of horizontal multimodal and vertical gravity-resistant collectives and unveil pattern-enabled robotic functionalities. When subjected to a time-varying magnetic field, the droplet swarm exhibits a variety of morphologies ranging from horizontal collectives, including vortex-like, chain-like, and crystal-like patterns to vertical layer-upon-layer patterns. Using experiments and simulations, the formation and transformation of different morphological collectives are shown and their robust environmental adaptability are demonstrated. Potential applications of the multimodal droplet collectives are presented, including exploring an unknown environment, targeted object delivery, and fluid flow filtration in a lab-on-a-chip. This work may facilitate the design of microrobotic swarm systems and expand the range of materials for miniature robots.

Decoding the hydrodynamic properties of microscale helical propellers from Brownian fluctuations

The complex motility of bacteria, ranging from single-swimmer behaviors such as chemotaxis to collective dynamics, including biofilm formation and active matter phenomena, is driven by their microscale propellers. Despite extensive study of swimming flagellated bacteria, the hydrodynamic properties of their helical-shaped propellers have never been directly measured. The primary challenges to directly studying microscale propellers are 1) their small size and fast, correlated motion, 2) the necessity of controlling fluid flow at the microscale, and 3) isolating the influence of a single propeller from a propeller bundle. To solve the outstanding problem of characterizing the hydrodynamic properties of these propellers, we adopt a dual statistical viewpoint that connects to the hydrodynamics through the fluctuation-dissipation theorem (FDT). We regard the propellers as colloidal particles and characterize their Brownian fluctuations, described by 21 diffusion coefficients for translation, rotation, and correlated translation-rotation in a static fluid. To perform this measurement, we applied recent advances in high-resolution oblique plane microscopy to generate high-speed volumetric movies of fluorophore-labeled, freely diffusing Escherichia coli flagella. Analyzing these movies with a bespoke helical single-particle tracking algorithm, we extracted trajectories, calculated the full set of diffusion coefficients, and inferred the average propulsion matrix using a generalized Einstein relation. Our results provide a direct measurement of a microhelix's propulsion matrix and validate proposals that the flagella are highly inefficient propellers, with a maximum propulsion efficiency of less than 3%. Our approach opens broad avenues for studying the motility of particles in complex environments where direct hydrodynamic approaches are not feasible.

The analytical solution to the migration of an epithelial monolayer with a circular spreading front and its implications in the gap closure process

The coordinated behaviors of epithelial cells are widely observed in tissue development, such as re-epithelialization, tumor growth, and morphogenesis. In these processes, cells either migrate collectively or organize themselves into specific structures to serve certain purposes. In this work, we study a spreading epithelial monolayer whose migrating front encloses a circular gap in the monolayer center. Such tissue is usually used to mimic the wound healing process in vitro. We model the epithelial sheet as a layer of active viscous polar fluid. With an axisymmetric assumption, the model can be analytically solved under two special conditions, suggesting two possible spreading modes for the epithelial monolayer. Based on these two sets of analytical solutions, we assess the velocity of the spreading front affected by the gap size, the active intercellular contractility, and the purse-string contraction acting on the spreading edge. Several critical values exist in the model parameters for the initiation of the gap closure process, and the purse-string contraction plays a vital role in governing the gap closure kinetics. Finally, the instability of the morphology of the spreading front was studied. Numerical calculations show how the perturbated velocities and the growth rates vary with respect to different model parameters.

Three-Dimensionally Complex Phase Behavior and Collective Phenomena in Mixtures of Acoustically Powered Chiral Microspinners

The process of dynamic self-organization of small building blocks is fundamental to the emergent function of living systems and is characteristic of their out-of-equilibrium homeostasis. The ability to control the interactions of synthetic particles in large groups could lead to the realization of analogous macroscopic robotic systems with microscopic complexity. Rotationally induced self-organization has been observed in biological systems and modeled theoretically, but studies of fast, autonomously moving synthetic rotors remain rare. Here, we report switchable, out-of-equilibrium hydrodynamic assembly and phase separation in suspensions of acoustically powered chiral microspinners. Semiquantitative modeling suggests that three-dimensionally (3D) complex spinners interact through viscous and weakly inertial (streaming) flows. The interactions between spinners were studied over a range of densities to construct a phase diagram, which included gaseous dimer pairing at low density, collective rotation and multiphase separation at intermediate densities, and ultimately jamming at high density. The 3D chirality of the spinners leads to self-organization in parallel planes, forming a three-dimensionally hierarchical system that goes beyond the 2D systems that have so far been modeled computationally. Dense mixtures of spinners and passive tracer particles also show active-passive phase separation. These observations are consistent with recent theoretical predictions of the hydrodynamic coupling between rotlets generated by autonomous spinners and provide an exciting experimental window to the study of colloidal active matter and microrobotic systems.

Spontaneous symmetry-breaking of the active cluster drives the directed movement and self-sustained oscillation of symmetric rod-like passive particles

Active particles without detailed balance can rectify their random motions to drive the directed movement or rotation of asymmetric passive obstacles. However, whether they can drive the directed movement of symmetric passive obstacles is still unclear. Here, we show that a rod-like passive particle which is fixed to move along the x-axis in an active bath can keep long-lived directed movement at nearly constant speed due to the spontaneous symmetry breaking of the neighboring active particle cluster. If the passive particle is further confined by a harmonic potential, it may undergo self-sustained periodic oscillation for an appropriate length of the passive particle and self-propelled velocity of active particles. The restoring force from the harmonic potential will trigger the velocity jump-off and thus lead to self-sustained periodic oscillation. Remarkably, the relationship between the velocity of the passive particle and the external force shows that the effective viscosity of the active bath may become negative in some regime. Finally, we develop a minimum 1D theoretical model to further probe the mechanism underlying the directed movement and self-sustained oscillation of the passive particle. Our findings reveal the effect of the moving boundary on the active bath and demonstrate a novel method to extract practical mechanical work from the active bath to propel microdevices.

Flocking without Alignment Interactions in Attractive Active Brownian Particles

Within a simple model of attractive active Brownian particles, we predict flocking behavior and challenge the widespread idea that alignment interactions are necessary to observe this collective phenomenon. Here, we show that even nonaligning attractive interactions can lead to a flocking state. Monitoring the velocity polarization as the order parameter, we reveal the onset of a first-order transition from a disordered phase, characterized by several small clusters, to a flocking phase, where a single flocking cluster is emerging. The scenario is confirmed by studying the spatial connected correlation function of particle velocities, which reveals scale-free behavior in flocking states and exponential-like decay for nonflocking configurations. Our predictions can be tested in microscopic and macroscopic experiments showing flocking, such as animals, migrating cells, and active colloids.

Collective behavior of chiral active particles with anisotropic interactions in a confined space

Extensive studies so far have indicated that chirality, anisotropic interactions and spatial confinement play important roles in collective dynamics in active matter systems. However, how the overall interplay of these crucial factors affects the novel phases and macroscopic properties remains less explored. Here, using Langevin dynamics simulations, we investigate the self-organization of a chiral active system composed of amphiphilic Janus particles, where the embedded anisotropic interaction orientation is assumed to be either the same or just opposite to the direction of active force. A wealth of dynamic phases are observed including formation of phase separation, clustering state, homogeneous state, spiral vortex flow, swarm and spatiotemporal oscillation. By tuning self-propelled angular speed and anisotropic interaction strength, we identify the non-equilibrium phase diagrams, and reveal the very non-trivial modulation of both vortex and swarm patterns. Intriguingly, we find that strong chirality-alignment-confinement coupling yields a self-driven spatial and temporal organization periodically oscillating between a counterclockwise vortex and a clockwise one. Our work provides a new understanding of the novel self-assembly arising in such a confined system and enables new strategies for achieving ordered dynamic structures.

Simulating structured fluids with tensorial viscoelasticity

We consider an immersed elastic body that is actively driven through a structured fluid by a motor or an external force. The behavior of such a system generally cannot be solved analytically, necessitating the use of numerical methods. However, current numerical methods omit important details of the microscopic structure and dynamics of the fluid, which can modulate the magnitudes and directions of viscoelastic restoring forces. To address this issue, we develop a simulation platform for modeling viscoelastic media with tensorial elasticity. We build on the lattice Boltzmann algorithm and incorporate viscoelastic forces, elastic immersed objects, a microscopic orientation field, and coupling between viscoelasticity and the orientation field. We demonstrate our method by characterizing how the viscoelastic restoring force on a driven immersed object depends on various key parameters as well as the tensorial character of the elastic response. We find that the restoring force depends non-monotonically on the rate of diffusion of the stress and the size of the object. We further show how the restoring force depends on the relative orientation of the microscopic structure and the pulling direction. These results imply that accounting for previously neglected physical features, such as stress diffusion and the microscopic orientation field, can improve the realism of viscoelastic simulations. We discuss possible applications and extensions to the method.

Collective Behaviors of Active Matter Learning from Natural Taxes Across Scales

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

Collective vortical motion and vorticity reversals of self-propelled particles on circularly patterned substrates

The collective behavior of self-propelled particles (SPPs) under the combined effects of a circularly patterned substrate and circular confinement is investigated through coarse-grained molecular dynamics simulations of polarized and disjoint ring polymers. The study is performed over a wide range of values of the SPPs packing fraction ϕ[over ¯], motility force F_{D}, and area fraction of the patterned region. At low packing fractions, the SPPs are excluded from the system's center and exhibit a vortical motion that is dominated by the substrate at intermediate values of F_{D}. This exclusion zone is due to the coupling between the driving force and torque induced by the substrate, which induces an outward spiral motion of the SPPs. For high values of F_{D}, the SPPs exclusion from the center is dominated by the confining boundary. At high values of ϕ[over ¯], the substrate pattern leads to reversals in the vorticity, which become quasiperiodic with increasing ϕ[over ¯]. We also found that the substrate pattern is able to separate SPPs based on their motilities.

Discontinuous Tension-Controlled Transition between Collective Actuations in Active Solids

The recent finding of collective actuation in active solids-solids embedded with active units-is a new promise for the design of multifunctional materials with genuine autonomy, and a better understanding of dense biological systems. Here, we combine the experimental study of centimetric model active solids, the numerical study of an agent-based model, and theoretical arguments to reveal a new form of collective actuation and how mechanical tension can serve as a general mechanism for transitioning between different collective actuation regimes. The presence of hysteresis when varying tension back and forth highlights the nontrivial selectivity of collective actuations.

Active particles crossing sharp viscosity gradients

Active particles (living or synthetic) often move through inhomogeneous environments, such as gradients in light, heat or nutrient concentration, that can lead to directed motion (or taxis). Recent research has explored inhomogeneity in the rheological properties of a suspending fluid, in particular viscosity, as a mechanical (rather than biological) mechanism for taxis. Theoretical and experimental studies have shown that gradients in viscosity can lead to reorientation due to asymmetric viscous forces. In particular, recent experiments with Chlamydomonas Reinhardtii algae swimming across sharp viscosity gradients have observed that the microorganisms are redirected and scattered due to the viscosity change. Here we develop a simple theoretical model to explain these experiments. We model the swimmers as spherical squirmers and focus on small, but sharp, viscosity changes. We derive a law, analogous to Snell's law of refraction, that governs the orientation of active particles in the presence of a viscosity interface. Theoretical predictions show good agreement with experiments and provide a mechanistic understanding of the observed reorientation process.

Real-time in-situ optical detection of fluid viscosity based on the Beer-Lambert law and machine learning

As an important physical quantity to describe the resistance of fluid to flow, viscosity is an essential property of fluids in fluid mechanics, chemistry, medicine, as well as hydraulic engineering. While traditional measurement methods, including the rotating-cylinder method, capillary tube method and falling sphere method, have significant drawbacks especially in terms of accuracy, response time and the sample must be made to move. In this work, a novel Beer-Lambert law-based method was proposed for the viscosity measurement. Specifically, this work demonstrates that viscosity can be quantitatively reflected by spectral line intensity, and castor oil was selected due to its viscous temperature properties (viscosity has been accurately measured under different temperature), and its transmission spectrum at different temperatures ranging from 10 to 50°C was detected firstly. Then, the principal component analysis (PCA) was employed to obtain the intrinsic features of the transmission spectrum. Finally, the processed data was utilized to train and verify the radial basis function (RBF) neural network. As a result, the accuracy of the predictions conducted by means of the RBF reached 98.45%, which indicates the complicated and non-linear relationships between spectra formation and viscosity can be depicted well by RBF. The results show that the real-time in-situ optical detection method adopted in this work represents a great leap forward in the viscosity measurement, which fundamentally reforms the traditional viscosity measurement methods.

Giant vortex dynamics in confined bacterial turbulence

We report the numerical evidence of a new state of bacterial turbulence in confined domains. By means of extensive numerical simulations of the Toner-Tu-Swift-Hohenberg model for dense bacterial suspensions in circular geometry, we discover the formation a stable, ordered state in which the angular momentum symmetry is broken. This is achieved by self-organization of a turbulent-like flow into a single, giant vortex of the size of the domain. The giant vortex is surrounded by an annular region close to the boundary, characterized by small-scale, radial vorticity streaks. The average radial velocity profile of the vortex is found to be in agreement with a simple analytical prediction. We also provide an estimate of the temporal and spatial scales of a suitable experimental setup comparable with our numerical findings.

Competing instabilities reveal how to rationally design and control active crosslinked gels

How active stresses generated by molecular motors set the large-scale mechanics of the cell cytoskeleton remains poorly understood. Here, we combine experiments and theory to demonstrate how the emergent properties of a biomimetic active crosslinked gel depend on the properties of its microscopic constituents. We show that an extensile nematic elastomer exhibits two distinct activity-driven instabilities, spontaneously bending in-plane or buckling out-of-plane depending on its composition. Molecular motors play a dual antagonistic role, fluidizing or stiffening the gel depending on the ATP concentration. We demonstrate how active and elastic stresses are set by each component, providing estimates for the active gel theory parameters. Finally, activity and elasticity were manipulated in situ with light-activable motor proteins, controlling the direction of the instability optically. These results highlight how cytoskeletal stresses regulate the self-organization of living matter and set the foundations for the rational design and optogenetic control of active materials.

A one-dimensional three-state run-and-tumble model with a 'cell cycle'

We study a one-dimensional three-state run-and-tumble model motivated by the bacterium Caulobacter crescentus which displays a cell cycle between two non-proliferating mobile phases and a proliferating sedentary phase. Our model implements kinetic transitions between the two mobile and one sedentary states described in terms of their number densities, where mobility is allowed with different running speeds in forward and backward direction. We start by analyzing the stationary states of the system and compute the mean and squared-displacements for the distribution of all cells, as well as for the number density of settled cells. The latter displays a surprising super-ballistic scaling [Formula: see text] at early times. Including repulsive and attractive interactions between the mobile cell populations and the settled cells, we explore the stability of the system and employ numerical methods to study structure formation in the fully nonlinear system. We find traveling waves of bacteria, whose occurrence is quantified in a non-equilibrium state diagram.

Self-organized canals enable long-range directed material transport in bacterial communities

Long-range material transport is essential to maintain the physiological functions of multicellular organisms such as animals and plants. By contrast, material transport in bacteria is often short-ranged and limited by diffusion. Here, we report a unique form of actively regulated long-range directed material transport in structured bacterial communities. Using Pseudomonas aeruginosa colonies as a model system, we discover that a large-scale and temporally evolving open-channel system spontaneously develops in the colony via shear-induced banding. Fluid flows in the open channels support high-speed (up to 450 µm/s) transport of cells and outer membrane vesicles over centimeters, and help to eradicate colonies of a competing species Staphylococcus aureus. The open channels are reminiscent of human-made canals for cargo transport, and the channel flows are driven by interfacial tension mediated by cell-secreted biosurfactants. The spatial-temporal dynamics of fluid flows in the open channels are qualitatively described by flow profile measurement and mathematical modeling. Our findings demonstrate that mechanochemical coupling between interfacial force and biosurfactant kinetics can coordinate large-scale material transport in primitive life forms, suggesting a new principle to engineer self-organized microbial communities.

Response of vesicle shapes to dense inner active matter

We consider experimentally the Takatori-Sahu model of vesicle shape fluctuations induced by enclosed active matter, a model till present tested only in the absence of collective motion because few enclosed bacteria were used to generate the desired active motion (S. C. Takatori and A. Sahu, Phys. Rev. Lett., 2020, 124, 158102). Using deformable giant unilamellar vesicles (GUVs) and phase contrast microscopy, we extract the mode-dependence of GUV shape fluctuations when hundreds of E. coli bacteria are contained within each GUV. In the microscope focal plane, patterns of collective bacteria flow include vortex flow, dipolar flow, and chaotic motion, all of which influence the GUV shapes. The Takatori-Sahu model generalizes well to this situation if one considers the moving element to be the experimentally-determined size of the collecively-moving flock.

Spontaneous population oscillation of confined active granular particles

Spontaneous collective oscillation may emerge from seemingly irregular active matter systems. Here, we experimentally demonstrate a spontaneous population oscillation of active granular particles confined in two chambers connected by a narrow channel, and verify the intriguing behavior predicted in simulation [M. Paoluzzi, R. Di Leonardo and L. Angelani, Self-sustained density oscillations of swimming bacteria confined in microchambers, Phys. Rev. Lett., 2015, 115(18), 188303]. During the oscillation, the two chambers are alternately (nearly) filled up and emptied by the self-propelled particles in a periodic manner. We show that the stable unidirectional flow induced due to the confined channel and its periodic reversal triggered by the particle concentration difference between two chambers jointly give rise to the oscillatory collective behavior. Furthermore, we propose a minimal theoretical model that properly reproduces the experimental results without free parameters. This self-sustained collective oscillation could serve as a robust active granular clock, capable of providing rhythmic signals.

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Active depletion torque between two passive rods

The active depletion torque experienced by two anisotropic objects in an active bath is a conceptional generalization of the equilibrium entropic torque. Using Brownian dynamics simulations, we compute the active depletion torque suffered by two passive rods immersed in an ensemble of active Brownian particles. Our results demonstrate that the active depletion torque is qualitatively different from its passive counterpart. Interestingly, we find that the active depletion torque can be greatly affected by the external constraint applied on the rotational degree of freedom of the rods, and even the direction may be changed with the orientational constraint, which is in contrast to the equilibrium depletion torque. The main reason for the remarkable features of the active depletion torque is that the active particles can significantly accumulate in the vicinity of the rods due to persistent self-propulsion, which is sensitively dependent on the constraint strength and the rod configurations. Our findings could be relevant for understanding the self-assembly and dynamics of anisotropic macromolecules in living environments.

Active Brownian motion with memory delay induced by a viscoelastic medium

By now active Brownian motion is a well-established model to describe the motion of mesoscopic self-propelled particles in a Newtonian fluid. On the basis of the generalized Langevin equation, we present an analytic framework for active Brownian motion with memory delay assuming time-dependent friction kernels for both translational and orientational degrees of freedom to account for the time-delayed response of a viscoelastic medium. Analytical results are obtained for the orientational correlation function, mean displacement, and mean-square displacement which we evaluate in particular for a Maxwell fluid characterized by a kernel which decays exponentially in time. Further, we identify a memory-induced delay between the effective self-propulsion force and the particle orientation which we quantify in terms of a special dynamical correlation function. In principle, our predictions can be verified for an active colloidal particle in various viscoelastic environments such as a polymer solution.

Active elastocapillarity in soft solids with negative surface tension

Active solids consume energy to allow for actuation, shape change, and wave propagation not possible in equilibrium. Whereas active interfaces have been realized across many experimental systems, control of three-dimensional (3D) bulk materials remains a challenge. Here, we develop continuum theory and microscopic simulations that describe a 3D soft solid whose boundary experiences active surface stresses. The competition between active boundary and elastic bulk yields a broad range of previously unexplored phenomena, which are demonstrations of so-called active elastocapillarity. In contrast to thin shells and vesicles, we discover that bulk 3D elasticity controls snap-through transitions between different anisotropic shapes. These transitions meet at a critical point, allowing a universal classification via Landau theory. In addition, the active surface modifies elastic wave propagation to allow zero, or even negative, group velocities. These phenomena offer robust principles for programming shape change and functionality into active solids, from robotic metamaterials down to shape-shifting nanoparticles.

Oscillative Trapping of a Droplet in a Converging Channel Induced by Elastic Instability

Permanent trapping of an oscillating, nonwetting droplet is observed in a converging-diverging microchannel when aqueous, viscoelastic fluids are injected. Classical theories based on the balance between capillary and viscous forces suggest that the droplet size should decrease with increasing flow rates of a displacing Newtonian fluid, and the droplet should be completely displaced at high injection rates. However, droplets in viscoelastic fluids cannot be removed by increasing flow rates due to the oscillation. The oscillation amplitude linearly increases with the Deborah number (De), which further inhibits the droplet's passing through the constriction, "permanently." Our microfluidic experiments show that the onset of oscillation is determined by a critical De, which is near 1. We derive a linear relationship for the trapped droplet length with Ec^{1/3}, where Ec is the elastocapillary number, by introducing the elastic force into the force balance in addition to the capillary and viscous forces.

Extensile to contractile transition in active microtubule-actin composites generates layered asters with programmable lifetimes

We study a reconstituted composite system consisting of an active microtubule network interdigitated with a passive network of entangled F-actin filaments. Increasing the concentration of filamentous actin controls the emergent dynamics, inducing a transition from turbulent-like flows to bulk contractions. At intermediate concentrations, where the active stresses change their symmetry from anisotropic extensile to isotropic contracting, the composite separates into layered asters that coexist with the background turbulent fluid. Contracted onion-like asters have a radially extending microtubule-rich cortex that envelops alternating layers of microtubules and F-actin. These self-regulating structures undergo internal reorganization, which appears to minimize the surface area and maintain the ordered layering, even when undergoing aster merging events. Finally, the layered asters are metastable structures. Their lifetime, which ranges from minutes to hours, is encoded in the material properties of the composite. These results challenge the current models of active matter. They demonstrate self-organized dynamical states and patterns evocative of those observed in the cytoskeleton do not require precise biochemical regulation, but can arise from purely mechanical interactions of actively driven filamentous materials.

Exploring order in active turbulence: Geometric rule and pairing order transition in confined bacterial vortices

Ordered collective motion emerges in a group of autonomously motile elements (known as active matter) as their density increases. Microswimmers, such as swimming bacteria, have been extensively studied in physics and biology. A dense suspension of bacteria forms seemingly chaotic turbulence in viscous fluids. Interestingly, this active turbulence driven by bacteria can form a hidden ensemble of many vortices. Understanding the active turbulence in a bacterial suspension can provide physical principles for pattern formation and insight into the instability underlying biological phenomena. This review presents recent findings regarding ordered structures causing active turbulence and discusses a physical approach for controlling active turbulence via geometric confinement. When the active matter is confined in a compartment with a size comparable to the correlation length of the collective motion, vortex-like rotation appears, and the vortex pairing order is indicated by the patterns of interacting vortices. Additionally, we outline the design principle for controlling collective motions via the geometric rule of the vortex pairing, which may advance engineering microdevices driven by a group of active matter. This article is an extended version of the Japanese article, Ordered Structure and Geometric Control of Active Matter in Dense Bacterial Suspensions, published in SEIBUTSU BUTSURI Vol. 60, p. 13–18 (2020).

Mechanical forces drive a reorientation cascade leading to biofilm self-patterning

In growing active matter systems, a large collection of engineered or living autonomous units metabolize free energy and create order at different length scales as they proliferate and migrate collectively. One such example is bacterial biofilms, surface-attached aggregates of bacterial cells embedded in an extracellular matrix that can exhibit community-scale orientational order. However, how bacterial growth coordinates with cell-surface interactions to create distinctive, long-range order during biofilm development remains elusive. Here we report a collective cell reorientation cascade in growing Vibrio cholerae biofilms that leads to a differentially ordered, spatiotemporally coupled core-rim structure reminiscent of a blooming aster. Cell verticalization in the core leads to a pattern of differential growth that drives radial alignment of the cells in the rim, while the growing rim generates compressive stresses that expand the verticalized core. Such self-patterning disappears in nonadherent mutants but can be restored through opto-manipulation of growth. Agent-based simulations and two-phase active nematic modeling jointly reveal the strong interdependence of the driving forces underlying the differential ordering. Our findings offer insight into the developmental processes that shape bacterial communities and provide ways to engineer phenotypes and functions in living active matter.

Morphologies and dynamics of the interfaces between active and passive phases

Active matters exhibit interesting collective behaviors and novel phases, which provide an important platform for the study of nonequilibrium physics. Mixtures of active and passive particles have been intensively studied in motility-induced phase separation, but the morphology of the active-passive interface has been poorly explored. In this work, we investigate the interface morphology in two-dimensional mixtures of active and passive particles using Brownian dynamics simulations. By systematically changing the Péclet number (Pe) and area fraction (ρ), we obtain the phase diagram of the active-passive interface, including rough sharp, rough invasive and flat interdiffusive interfaces. For a sharp interface, dynamic scaling analysis in the propagation stage shows that the roughness exponent α, the growth exponent β, the time exponent κ, and the dynamic exponent z satisfy z = α/(β - κ). Such anomalous scaling indicates that the roughening behavior does not belong to the conventional universality classes with Family-Vicsek scaling for the growth of passive interfaces. On the other hand, the interface in the middle-wavelength regime during the morphology relaxation stage can be described by capillary wave theory. The mean interface position propagates with time as t^1/2, which is robust at different ρ and Pe values in the propagation stage and exhibits superdiffusion in the morphology relaxation stage. These similarities and differences between the active-inactive interfaces and passive interfaces cast light on the interfacial growth of active matter.

Edge current and pairing order transition in chiral bacterial vortices

Bacterial suspensions show turbulence-like spatiotemporal dynamics and vortices moving irregularly inside the suspensions. Understanding these ordered vortices is an ongoing challenge in active matter physics, and their application to the control of autonomous material transport will provide significant development in microfluidics. Despite the extensive studies, one of the key aspects of bacterial propulsion has remained elusive: The motion of bacteria is chiral, i.e., it breaks mirror symmetry. Therefore, the mechanism of control of macroscopic active turbulence by microscopic chirality is still poorly understood. Here, we report the selective stabilization of chiral rotational direction of bacterial vortices in achiral circular microwells sealed by an oil/water interface. The intrinsic chirality of bacterial swimming near the top and bottom interfaces generates chiral collective motions of bacteria at the lateral boundary of the microwell that are opposite in directions. These edge currents grow stronger as bacterial density increases, and, within different top and bottom interfaces, their competition leads to a global rotation of the bacterial suspension in a favored direction, breaking the mirror symmetry of the system. We further demonstrate that chiral edge current favors corotational configurations of interacting vortices, enhancing their ordering. The intrinsic chirality of bacteria is a key feature of the pairing order transition from active turbulence, and the geometric rule of pairing order transition may shed light on the strategy for designing chiral active matter.

Collective effects in confined active Brownian particles

We investigate a two-dimensional system of active particles confined to a narrow annular domain. Despite the absence of explicit interactions among the velocities or the active forces of different particles, the system displays a transition from a disordered and stuck state to an ordered state of global collective motion where the particles rotate persistently clockwise or anticlockwise. We describe this behavior by introducing a suitable order parameter, the velocity polarization, measuring the global alignment of the particles' velocities along the tangential direction of the ring. We also measure the spatial velocity correlation function and its correlation length to characterize the two states. In the rotating phase, the velocity correlation displays an algebraic decay that is analytically predicted together with its correlation length, while in the stuck regime, the velocity correlation decays exponentially with a correlation length that increases with the persistence time. In the first case, the correlation (and, in particular, its correlation length) does not depend on the active force but the system size only. The global collective motion, an effect caused by the interplay between finite-size, periodicity, and persistent active forces, disappears as the size of the ring becomes infinite, suggesting that this phenomenon does not correspond to a phase transition in the usual thermodynamic sense.