Dynamics of swimming bacteria: transition to directional order at high concentration

Exploring sperm cell rheotaxis in microfluidic channel: the role of flow and viscosity

Rheotaxis is a fundamental mechanism of sperm cells that guides them in navigating towards the oocyte. The present study investigates the phenomenon of sperm rheotaxis in Newtonian and non-Newtonian fluid media, which for the first time explores a viscosity range equivalent to that of the oviductal fluid of the female reproductive tract in rectilinear microfluidic channels. Three parameters, the progressive velocity while performing rheotaxis, the radius of rotation during rheotaxis, and the percentage of rheotactic sperm cells in the bulk and near-wall regions of the microfluidic channel were measured. Numerical simulations of the flow were conducted to estimate the shear rate, flow velocity, and the drag force acting on the sperm head at specific locations where the sperms undergo rheotaxis. Increasing the flow velocity resulted in a change in the position of rheotactic sperm from the bulk center to the near wall region, an increase and subsequent decrease in the sperm's upstream progressive velocity, and a decrease in the radius of rotation. We observed that with an increase in viscosity, rheotactic sperms migrate to the near wall regions at lower flow rates, the upstream progressive velocity of the sperm decreases for Newtonian and increases for non-Newtonian media, and the radius of rotation increases for Newtonian and decreases for non-Newtonian media. These results quantify the effects of fluid properties such as viscosity and flow rate on sperm rheotaxis and navigation, thereby paving the way for manipulating sperm behavior in microfluidic devices, potentially leading to advancements in assisted reproduction techniques.

Diverse morphology and motility induced emergent order in bacterial collectives

Microbial communities exhibit complex behaviors driven by species interactions and individual characteristics. In this study, we delve into the dynamics of a mixed bacterial population comprising two distinct species with different morphology and motility aspects. Employing agent-based modeling and computer simulations, we analyze the impacts of size ratios and packing fractions on dispersal patterns, aggregate formation, clustering, and spatial ordering. Notably, we find that motility and anisotropy of elongated bacteria significantly influence the distribution and spatial organization of nonmotile spherical species. Passive spherical cells display a superdiffusive behavior, particularly at larger size ratios in the ballistic regime. As the size ratio increases, clustering of passive cells is observed, accompanied by enhanced alignment and closer packing of active cells in the presence of higher passive cell area fractions. In addition, we identify the pivotal role of passive cell area fraction in influencing the response of active cells toward nematicity, with its dependence on size ratio. These findings shed light on the significance of morphology and motility in shaping the collective behavior of microbial communities, providing valuable insights into complex microbial behaviors with implications for ecology, biotechnology, and bioengineering.

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.

Nonlinear Phototaxis and Instabilities in Suspensions of Light-Seeking Algae

The mechanism by which living organisms seek optimal light conditions-phototaxis-is a fundamental process for motile photosynthetic microbes. It is involved in a broad array of natural processes and applications from bloom formation to the production of high-value chemicals in photobioreactors. Here, we show that a population of the model alga Chlamydomonas reinhardtii exhibits a highly sensitive nonlinear response to light and demonstrate that the self-organization of cells in a heterogeneous environment becomes unstable as the result of a coupling between bioconvective flows and phototaxis.

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.

Gold-Nanoparticle-Mediated Assembly of High-Order DNA Nano-Architectures

Constructing high-order DNA nano-architectures in large sizes is of critical significance for the application of DNA nanotechnology. Robust and flexible design strategies together with easy protocols to construct high-order large-size DNA nano-architectures remain highly desirable. In this work, the authors report a simple and versatile one-pot strategy to fabricate DNA architectures with the assistance of spherical gold nanoparticles modified with thiolated oligonucleotide strands (SH-DNA-AuNPs), which serve as "power strips" to connect various DNA nanostructures carrying complementary ssDNA strands as "plugs". By modulating the plug numbers and positions on each DNA nanostructure and the ratios between DNA nanostructures and AuNPs, the desired architectures are formed via the stochastic co-assembly of different modules. This SH-DNA-AuNP-mediated plug-in assembly (SAMPA) strategy offers new opportunities to drive macroscopic self-assembly to meet the demand of the fabrication of well-defined nanomaterials and nanodevices.

Aggregation of self-propelled particles with sensitivity to local order

We study a system of self-propelled particles (SPPs) in which individual particles are allowed to switch between a fast aligning and a slow nonaligning state depending upon the degree of the alignment in the neighborhood. The switching is modeled using a threshold for the local order parameter. This additional attribute gives rise to a mixed phase, in contrast to the ordered phases found in clean SPP systems. As the threshold is increased from zero, we find the sudden appearance of clusters of nonaligners. Clusters of nonaligners coexist with moving clusters of aligners with continual coalescence and fragmentation. The behavior of the system with respect to the clustering of nonaligners appears to be very different for values of low and high global densities. In the low density regime, for an optimal value of the threshold, the largest cluster of nonaligners grows in size up to a maximum that varies logarithmically with the total number of particles. However, on further increasing the threshold the size decreases. In contrast, for the high density regime, an initial abrupt rise is followed by the appearance of a giant cluster of nonaligners. The latter growth can be characterized as a continuous percolation transition. In addition, we find that the speed differences between aligners and nonaligners is necessary for the segregation of aligners and nonaligners.

Collective motion of cells modeled as ring polymers

In this article, we use a coarse-grained model of disjoint semi-flexible ring polymers to investigate computationally the spatiotemporal collective behavior of cell colonies. A ring polymer in this model is self-propelled by a motility force along the cell's polarity, which depends on its historical kinetics. Despite the repulsive interaction between the cells, a collective behavior sets in as a result of cells pushing against each other. This cooperative motion emerges as the amplitude of the motility force is increased and/or their areal density is increased. The degree of collectivity, characterized by the average cluster size, the velocity field order parameter, and the polarity field nematic order parameter, is found to increase with increasing the amplitude of the motility force and area coverage of the cells. Furthermore, the degree of alignment exhibited by the cell velocity field within a cluster is found to be stronger than that exhibited by the cell polarity. Comparison between the collective behavior of elongated cells and that of circular cells, at the same area coverage and motility force, shows that elongated cells exhibit a stronger collective behavior than circular cells, in agreement with earlier studies of self-propelled anisotropic particles. An investigation of two-cell collisions shows that while two clustered cells move in tandem, their polarities are misaligned. As such the cells push against each other while moving coherently.

Density fluctuations and energy spectra of 3D bacterial suspensions

Giant number fluctuations are often considered as a hallmark of the emergent nonequilibrium dynamics of active fluids. However, these anomalous density fluctuations have only been reported experimentally in two-dimensional dry active systems heretofore. Here, we investigate density fluctuations of bulk Escherichia coli suspensions, a paradigm of three-dimensional (3D) wet active fluids. Our experiments demonstrate the existence and quantify the scaling relation of giant number fluctuations in 3D bacterial suspensions. Surprisingly, the anomalous scaling persists at small scales in low-concentration suspensions well before the transition to active turbulence, reflecting the long-range nature of hydrodynamic interactions of 3D wet active fluids. To illustrate the origin of the density fluctuations, we measure the energy spectra of suspension flows and explore the density-energy coupling in both the steady and transient states of active turbulence. A scale-invariant density-independent correlation between density fluctuations and energy spectra is uncovered across a wide range of length scales. In addition, our experiments show that the energy spectra of bacterial turbulence exhibit the scaling of 3D active nematic fluids, challenging the common view of dense bacterial suspensions as active polar fluids.

Surveying a Swarm: Experimental Techniques to Establish and Examine Bacterial Collective Motion

The survival and successful spread of many bacterial species hinges on their mode of motility. One of the most distinct of these is swarming, a collective form of motility where a dense consortium of bacteria employ flagella to propel themselves across a solid surface. Surface environments pose unique challenges, derived from higher surface friction/tension and insufficient hydration. Bacteria have adapted by deploying an array of mechanisms to overcome these challenges. Beyond allowing bacteria to colonize new terrain in the absence of bulk liquid, swarming also bestows faster speeds and enhanced antibiotic resistance to the collective. These crucial attributes contribute to the dissemination, and in some cases pathogenicity, of an array of bacteria. This mini-review highlights; 1) aspects of swarming motility that differentiates it from other methods of bacterial locomotion. 2) Facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges. 3) The (often difficult) approaches required to cultivate genuine swarmers. 4) The methods available to observe and assess the various facets of this collective motion, as well as the features exhibited by the population as a whole.

Polar swimmers induce several phases in active nematics

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

Pattern formation and polarity sorting of driven actin filaments on lipid membranes

Pattern formation processes in active systems give rise to a plethora of collective structures. Predicting how the emergent structures depend on the microscopic interactions between the moving agents remains a challenge. By introducing a high-density actin gliding assay on a fluid membrane, we demonstrate the emergence of polar structures in a regime of nematic binary interactions dominated by steric repulsion. The transition from a microscopic nematic symmetry to a macroscopic polar structure is linked to microscopic polarity sorting mechanisms, including accumulation in wedge-like topological defects. Our results should be instrumental for a better understanding of pattern formation and polarity sorting processes in active matter.

Collective motion of active matter is ubiquitously observed, ranging from propelled colloids to flocks of bird, and often features the formation of complex structures composed of agents moving coherently. However, it remains extremely challenging to predict emergent patterns from the binary interaction between agents, especially as only a limited number of interaction regimes have been experimentally observed so far. Here, we introduce an actin gliding assay coupled to a supported lipid bilayer, whose fluidity forces the interaction between self-propelled filaments to be dominated by steric repulsion. This results in filaments stopping upon binary collisions and eventually aligning nematically. Such a binary interaction rule results at high densities in the emergence of dynamic collectively moving structures including clusters, vortices, and streams of filaments. Despite the microscopic interaction having a nematic symmetry, the emergent structures are found to be polar, with filaments collectively moving in the same direction. This is due to polar biases introduced by the stopping upon collision, both on the individual filaments scale as well as on the scale of collective structures. In this context, positive half-charged topological defects turn out to be a most efficient trapping and polarity sorting conformation.

Design of nematic liquid crystals to control microscale dynamics

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

Imaging the emergence of bacterial turbulence: Phase diagram and transition kinetics

We experimentally study the emergence of collective bacterial swimming, a phenomenon often referred to as bacterial turbulence. A phase diagram of the flow of 3D Escherichia coli suspensions spanned by bacterial concentration, the swimming speed of bacteria, and the number fraction of active swimmers is systematically mapped, which shows quantitative agreement with kinetic theories and demonstrates the dominant role of hydrodynamic interactions in bacterial collective swimming. We trigger bacterial turbulence by suddenly increasing the swimming speed of light-powered bacteria and image the transition to the turbulence in real time. Our experiments identify two unusual kinetic pathways, i.e., the one-step transition with long incubation periods near the phase boundary and the two-step transition driven by long-wavelength instabilities deep inside the turbulent phase. Our study provides not only a quantitative verification of existing theories but also insights into interparticle interactions and transition kinetics of bacterial turbulence.

Active nematics with quenched disorder

We introduce a two-dimensional active nematic with quenched disorder. We write the coarse-grained hydrodynamic equations of motion for slow variables, viz. density and orientation. Disorder strength is tuned from zero to large values. Results from the numerical solution of equations of motion as well as the calculation of two-point orientation correlation function using linear approximation shows that the ordered steady state follows a disorder dependent crossover from quasi-long-range order to short-range order. Such crossover is due to the pinning of ±1/2 topological defects in the presence of finite disorder, which breaks the system in uncorrelated domains. Finite disorder slows the dynamics of +1/2 defect, and it leads to slower growth dynamics. The two-point correlation functions for the density and orientation fields show good dynamic scaling but no static scaling for the different disorder strengths. Our findings can motivate experimentalists to verify the results and find applications in living and artificial apolar systems in the presence of a quenched disorder.

Lipid Dynamics in Membranes Slowed Down by Transmembrane Proteins

Lipids and proteins, as essential components of biological cell membranes, exhibit a significant degree of freedom for different kinds of motions including lateral long-range mobility. Due to their interactions, they not only preserve the cellular membrane but also contribute to many important cellular functions as e.g., signal transport or molecular exchange of the cell with its surrounding. Many of these processes take place on a short time (up to some nanoseconds) and length scale (up to some nanometers) which is perfectly accessible by quasielastic neutron scattering (QENS) experiments and molecular dynamics (MD) simulations. In order to probe the influence of a peptide, a transmembrane sequence of the transferrin receptor (TFRC) protein, on the dynamics of 1,2-dimyristoyl-sn-glycero-3-phosphocholine (DMPC) large unilamellar vesicles (LUVs) on a nanosecond time scale, high-resolution QENS experiments and complementary MD simulations have been utilized. By using different scattering contrasts in the experiment (chain-deuterated lipids and protonated lipids, respectively), a model could be developed which allows to examine the lipid and peptide dynamics separately. The experimental results revealed a restricted lipid lateral mobility in the presence of the TFRC transmembrane peptides. Also the apparent self-diffusion coefficient of the lateral movement of the peptide molecules could be determined quantitatively for the probed short-time regime. The findings could be confirmed very precisely by MD simulations. Furthermore, the article presents an estimation for the radius of influence of the peptides on the lipid long-range dynamics which could be determined by consistently combining results from experiment and simulation.

Active droplet driven by a collective motion of enclosed microswimmers

Active fluids containing self-propelled particles are relevant for applications such as self-mixing, micropumping, and targeted drug delivery. With a confined boundary, active fluids can generate bulk flow inside the system, which has the potential to create self-propelled active matter. In this study, we propose that an active droplet is driven by a collective motion of enclosed microswimmers. We show that the droplet migrates via the flow field generated by the enclosed microswimmers; moreover, the locomotion direction depends on the swimming mode of these internal particles. The locomotion mechanism of the droplet can be well explained by interfacial velocity, and the locomotion velocity shows good agreement with the Lighthill-Blake theory. These findings are essential to understand the interplay between the motion of self-propelled particles and the bulk motion response of active matter.

Motile Bacteria at Oil-Water Interfaces: Pseudomonas aeruginosa

Bacteria are important examples of active or self-propelled colloids. Because of their directed motion, they accumulate near interfaces. There, they can become trapped and swim adjacent to the interface via hydrodynamic interactions, or they can adsorb directly and swim in an adhered state with complex trajectories that differ from those in bulk in both form and spatiotemporal implications. We have adopted the monotrichous bacterium Pseudomonas aeruginosa PA01 as a model species and have studied its motion at oil-aqueous interfaces. We have identified conditions in which bacteria swim persistently without restructuring the interface, allowing detailed and prolonged study of their motion. In addition to characterizing the ensemble behavior of the bacteria, we have observed a gallery of distinct trajectories of individual swimmers on and near fluid interfaces. We attribute these diverse swimming behaviors to differing trapped states for the bacteria in the fluid interface. These trajectory types include Brownian diffusive paths for passive adsorbed bacteria, curvilinear trajectories including curly paths with radii of curvature larger than the cell body length, and rapid pirouette motions with radii of curvature comparable to the cell body length. Finally, we see interfacial visitors that come and go from the interfacial plane. We characterize these individual swimmer motions. This work may impact nutrient cycles for bacteria on or near interfaces in nature. This work will also have implications in microrobotics, as active colloids in general and bacteria in particular are used to carry cargo in this burgeoning field. Finally, these results have implications in engineering of active surfaces that exploit interfacially trapped self-propelled colloids.

Speed inhomogeneity accelerates information transfer in polar flock

A collection of self-propelled particles (SPPs) shows coherent motion and exhibits a true long-range-ordered state in two dimensions. Various studies show that the presence of spatial inhomogeneities can destroy the usual long-range ordering in the system. However, the effects of inhomogeneity due to the intrinsic properties of the particles are barely addressed. In this paper we consider a collection of polar SPPs moving at inhomogeneous speed (IS) on a two-dimensional substrate, which can arise due to varying physical strengths of the individual particles. To our surprise, the IS not only preserves the usual long-range ordering present in homogeneous speed models but also induces faster ordering in the system. Furthermore, the response of the flock to an external perturbation is also faster, compared to the Vicsek-like model systems, due to the frequent update of neighbors of each SPP in the presence of the IS. Therefore, our study shows that an IS can promote information transfer in a moving flock.

Dynamics-dependent density distribution in active suspensions

Self-propelled colloids constitute an important class of intrinsically non-equilibrium matter. Typically, such a particle moves ballistically at short times, but eventually changes its orientation, and displays random-walk behaviour in the long-time limit. Theory predicts that if the velocity of non-interacting swimmers varies spatially in 1D, v(x), then their density ρ(x) satisfies ρ(x) = ρ(0)v(0)/v(x), where x = 0 is an arbitrary reference point. Such a dependence of steady-state ρ(x) on the particle dynamics, which was the qualitative basis of recent work demonstrating how to 'paint' with bacteria, is forbidden in thermal equilibrium. Here we verify this prediction quantitatively by constructing bacteria that swim with an intensity-dependent speed when illuminated and implementing spatially-resolved differential dynamic microscopy (sDDM) for quantitative analysis over millimeter length scales. Applying a spatial light pattern therefore creates a speed profile, along which we find that, indeed, ρ(x)v(x) = constant, provided that steady state is reached.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Reaction processes among self-propelled particles

We study a system of self-propelled disks that perform run-and-tumble motion, where particles can adopt more than one internal state. One of those internal states can be transmitted to other particle if the particle carrying this state maintains physical contact with another particle for a finite period of time. We refer to this process as a reaction process and to the different internal states as particle species, making an analogy to chemical reactions. The studied system may fall into an absorbing phase, where due to the disappearance of one of the particle species no further reaction can occur, or may remain in an active phase where particles constantly react. By combining individual-based simulations and mean-field arguments, we study the dependency of the equilibrium densities of particle species on motility parameters, specifically the active speed v₀ and tumbling frequency λ. We find that the equilibrium densities of particle species exhibit two very distinct, non-trivial scaling regimes, with v₀ and λ depending on whether the system is in the so-called ballistic or diffusive regime. Our mean-field estimates lead to an effective renormalization of reaction rates that allow building the phase-diagram v₀-λ that separates the absorbing and active phases. We find an excellent agreement between numerical simulations and mean-field estimates. This study is a necessary step towards an understanding of phase transitions into absorbing states in active systems and sheds light on the spreading of information/signaling among moving elements.

A statistical physics view of swarming bacteria

Bacterial swarming is a collective mode of motion in which cells migrate rapidly over surfaces, forming dynamic patterns of whirls and jets. This review presents a physical point of view of swarming bacteria, with an emphasis on the statistical properties of the swarm dynamics as observed in experiments. The basic physical principles underlying the swarm and their relation to contemporary theories of collective motion and active matter are reviewed and discussed in the context of the biological properties of swarming cells. We suggest a paradigm according to which bacteria have optimized some of their physical properties as a strategy for rapid surface translocation. In other words, cells take advantage of favorable physics, enabling efficient expansion that enhances survival under harsh conditions.

The 3D architecture of a bacterial swarm has implications for antibiotic tolerance

Swarming bacteria are an example of a complex, active biological system, where high cell density and super-diffusive cell mobility confer survival advantages to the group as a whole. Previous studies on the dynamics of the swarm have been limited to easily observable regions at the advancing edge of the swarm where cells are restricted to a plane. In this study, using defocused epifluorescence video imaging, we have tracked the motion of fluorescently labeled individuals within the interior of a densely packed three-dimensional (3D) region of a swarm. Our analysis reveals a novel 3D architecture, where bacteria are constrained by inter-particle interactions, sandwiched between two distinct boundary conditions. We find that secreted biosurfactants keep bacteria away from the swarm-air upper boundary, and added antibiotics at the lower swarm-surface boundary lead to their migration away from this boundary. Formation of the antibiotic-avoidance zone is dependent on a functional chemotaxis signaling system, in the absence of which the swarm loses its high tolerance to the antibiotics.

Cargo carrying bacteria at interfaces

The displacements of ensembles of colloids at the interface between oil and suspensions of the bacterium Pseudomonas aeruginosa PA14ΔpelA indicate enhanced colloid mobilities and apparently diffusive motion driven by interactions with the bacteria. However, inspection of individual trajectories of ∼500 particles reveals prolonged, directed displacements inconsistent with purely hydrodynamic interactions between swimming bacteria and colloids. Analysis of the properties of colloid paths indicates trajectories can be sorted into four distinct categories, including diffusive, persistent, curly, and mixed trajectory types. Non-diffusive trajectories are the norm, comprising 2/3 of the observed trajectories. Imaging of colloids in the interface reveals anisotropic assemblies formed by colloids decorated with one or more adhered bacteria that drive the colloids along these paths. The trajectories and enhanced transport result from individual colloids being moved as cargo by these adhered bacteria. The implications of these structures and open questions for interfacial transport are discussed and related to the active colloid literature.

Films of bacteria at interfaces

Bacteria are often discussed as active colloids, self-propelled organisms whose collective motion can be studied in the context of non-equilibrium statistical mechanics. In such studies, the behavior of bacteria confined to interfaces or in the proximity of an interface plays an important role. For instance, many studies have probed collective behavior of bacteria in quasi two-dimensional systems such as soap films. Since fluid interfaces can adsorb surfactants and other materials, the stress and velocity boundary conditions at interfaces can alter bacteria motion; hydrodynamic studies of interfaces with differing boundary conditions are reviewed. Also, bacteria in bulk can become trapped at or near fluid interfaces, where they colonize and form structures comprising secretions like exopolysaccharides, surfactants, living and dead bacteria, thereby creating Films of Bacteria at Interfaces (FBI). The formation of FBI is discussed at air-water, oil-water, and water-water interfaces, with an emphasis on film mechanics, and with some allusion to genetic functions guiding bacteria to restructure fluid interfaces. At air-water interfaces, bacteria form pellicles or interfacial biofilms. Studies are reviewed that reveal that pellicle material properties differ for different strains of bacteria, and that pellicle physicochemistry can act as a feedback mechanism to regulate film formation. At oil-water interfaces, a range of FBI form, depending on bacteria strain. Some bacteria-laden interfaces age from an initial active film, with dynamics dominated by motile bacteria, through viscoelastic states, to form an elastic film. Others remain active with no evidence of elastic film formation even at significant interface ages. Finally, bacteria can adhere to and colonize ultra-low surface tension interfaces such as aqueous-aqueous systems common in food industries. Relevant literature is reviewed, and areas of interest for potential application are discussed, ranging from health to bioremediation.

Role of tumbling in bacterial swarming

Typical wild-type bacteria swimming in sparse suspensions exhibit a movement pattern called "run and tumble," characterized by straight trajectories (runs) interspersed by shorter, random reorientation (tumbles). This is achieved by rotating their flagella counterclockwise, or clockwise, respectively. The chemotaxis signaling network operates in controlling the frequency of tumbles, enabling navigation toward or away from desired regions in the medium. In contrast, while in dense populations, flagellated bacteria exhibit collective motion and form large dynamic clusters, whirls, and jets, with intricate dynamics that is fundamentally different than trajectories of sparsely swimming cells. Although collectively swarming cells do change direction at the level of the individual cell, often exhibiting reversals, it has been suggested that chemotaxis does not play a role in multicellular colony expansion, but the change in direction stems from clockwise flagellar rotation. In this paper, the effects of cell rotor switching (i.e., the ability to tumble) and chemotaxis on the collective statistics of swarming bacteria are studied experimentally in wild-type Bacillus subtilis and two mutants-one that does not tumble and one that tumbles independently of the chemotaxis system. We show that while several of the parameters examined are similar between the strains, other collective and individual characteristics are significantly different. The results demonstrate that tumbling and/or flagellar directional rotor switching has an important role on the dynamics of swarming, and imply that swarming models of self-propelled rods that do not take tumbling and/or rotor switching into account may be oversimplified.

Noncontact Cohesive Swimming of Bacteria in Two-Dimensional Liquid Films

Bacterial swimming in confined two-dimensional environments is ubiquitous in nature and in clinical settings. Characterizing individual interactions between swimming bacteria in 2D confinement will help to understand diverse microbial processes, such as bacterial swarming and biofilm formation. Here we report a novel motion pattern displayed by flagellated bacteria in 2D confinement: When two nearby cells align their moving directions, they tend to engage in cohesive swimming without direct cell body contact, as a result of hydrodynamic interaction but not flagellar intertwining. We further found that cells in cohesive swimming move with higher directional persistence, which can increase the effective diffusivity of cells by ∼3 times as predicted by computational modeling. As a conserved behavior for peritrichously flagellated bacteria, cohesive swimming in 2D confinement may be key to collective motion and self-organization in bacterial swarms; it may also promote bacterial dispersal in unsaturated soils and in interstitial space during infections.

Effect of Cell Aspect Ratio on Swarming Bacteria

Swarming bacteria collectively migrate on surfaces using flagella, forming dynamic whirls and jets that consist of millions of individuals. Because some swarming bacteria elongate prior to actual motion, cell aspect ratio may play a significant role in the collective dynamics. Extensive research on self-propelled rodlike particles confirms that elongation promotes alignment, strongly affecting the dynamics. Here, we study experimentally the collective dynamics of variants of swarming Bacillus subtilis that differ in length. We show that the swarming statistics depends on the aspect ratio in a critical, fundamental fashion not predicted by theory. The fastest motion was obtained for the wild-type and variants that are similar in length. However, shorter and longer cells exhibit anomalous, non-Gaussian statistics and nonexponential decay of the autocorrelation function, indicating lower collective motility. These results suggest that the robust mechanisms to maintain aspect ratios may be important for efficient swarming motility. Wild-type cells are optimal in this sense.

A 2D suspension of active agents: the role of fluid mediated interactions

Taking into account both the Vicsek short-range ordering and the far-field hydrodynamic interactions mediated by the ambient fluid, we investigate the role of long-range interactions in the ordering phenomena in a quasi 2-dimensional active suspension. By studying the number fluctuations, the velocity correlation functions and cluster size distribution function, we show that depending on the number density of swimmers and the strength of noise, the hydrodynamic interactions can have significant effects in a suspension. For a fixed value of noise, at larger density of particles, long-range interactions enhance the particle pairing and cluster formation in the system.

Geometric control of active collective motion

Recent experimental studies have shown that confinement can profoundly affect self-organization in semi-dilute active suspensions, leading to striking features such as the formation of steady and spontaneous vortices in circular domains and the emergence of unidirectional pumping motions in periodic racetrack geometries. Motivated by these findings, we analyze the two-dimensional dynamics in confined suspensions of active self-propelled swimmers using a mean-field kinetic theory where conservation equations for the particle configurations are coupled to the forced Navier-Stokes equations for the self-generated fluid flow. In circular domains, a systematic exploration of the parameter space casts light on three distinct states: equilibrium with no flow, stable vortex, and chaotic motion, and the transitions between these are explained and predicted quantitatively using a linearized theory. In periodic racetracks, similar transitions from equilibrium to net pumping to traveling waves to chaos are observed in agreement with experimental observations and are also explained theoretically. Our results underscore the subtle effects of geometry on the morphology and dynamics of emerging patterns in active suspensions and pave the way for the control of active collective motion in microfluidic devices.

Generalized Swift-Hohenberg models for dense active suspensions

In describing the physics of living organisms, a mathematical theory that captures the generic ordering principles of intracellular and multicellular dynamics is essential for distinguishing between universal and system-specific features. Here, we compare two recently proposed nonlinear high-order continuum models for active polar and nematic suspensions, which aim to describe collective migration in dense cell assemblies and the ordering processes in ATP-driven microtubule-kinesin networks, respectively. We discuss the phase diagrams of the two models and relate their predictions to recent experiments. The satisfactory agreement with existing experimental data lends support to the hypothesis that non-equilibrium pattern formation phenomena in a wide range of active systems can be described within the same class of higher-order partial differential equations.

Classical Nucleation Theory Description of Active Colloid Assembly

Nonaligning self-propelled particles with purely repulsive excluded volume interactions undergo athermal motility-induced phase separation into a dilute gas and a dense cluster phase. Here, we use enhanced sampling computational methods and analytic theory to examine the kinetics of formation of the dense phase. Despite the intrinsically nonequilibrium nature of the phase transition, we show that the kinetics can be described using an approach analogous to equilibrium classical nucleation theory, governed by an effective free energy of cluster formation with identifiable bulk and surface terms. The theory captures the location of the binodal, nucleation rates as a function of supersaturation, and the cluster size distributions below the binodal, while discrepancies in the metastable region reveal additional physics about the early stages of active crystal formation. The success of the theory shows that a framework similar to equilibrium thermodynamics can be obtained directly from the microdynamics of an active system, and can be used to describe the kinetics of evolution toward nonequilibrium steady states.

Collective Motion of Microorganisms in a Viscoelastic Fluid

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Stability and dynamics of anisotropically tumbling chemotactic swimmers

Microswimmers such as bacteria perform random walks known as run-and-tumbles to move up chemoattractant gradients and as a result aggregate with others. It is also known that such micro-swimmers can self-organize into macroscopic patterns due to interactions with neighboring cells through the fluidic environment they live in. While the pattern formation resulting from chemotactic and hydrodynamic interactions separately and together have been previously investigated, the effect of the anisotropy in the tumbles of microswimmers has been unexplored. Here we show through linear analysis and full nonlinear simulations that the slight anisotropy in the individual swimmer tumbles can alter the collective pattern formation in nontrivial ways. We show that tumbling anisotropy diminishes the magnitude of the chemotactic aggregates but may result in more such aggregation peaks.

Vortex with fourfold defect lines in a simple model of self-propelled particles

We study the formation of a vortex with fourfold symmetry in a minimal model of self-propelled particles, confined inside a squared box, using computer simulations and also theoretical analysis. In addition to the vortex pattern, we observe five other regimes in the system: a homogeneous gaseous phase, band structures, moving clumps, moving clusters, and vibrating rings. All six regimes emerge from controlling the strength of noise and from the contribution of repulsion and alignment interactions. We study the shape of the vortex and its symmetry in detail. The pattern shows exponential defect lines where incoming and outgoing flows of particles collide. We show that alignment and repulsion interactions between particles are necessary to form such patterns. We derive hydrodynamical equations with an introduction of the "small deviation" technique to describe the vortex phase. The method is applicable to other systems as well. Finally, we compare the theory with the results of both computer simulations and an experiment using Quincke rotors. A good agreement between the three is observed.

Effective Rheological Properties in Semi-dilute Bacterial Suspensions

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally, we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.

Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods

Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.

Flexibility of bacterial flagella in external shear results in complex swimming trajectories

Many bacteria use rotating helical flagella in swimming motility. In the search for food or migration towards a new habitat, bacteria occasionally unbundle their flagellar filaments and tumble, leading to an abrupt change in direction. Flexible flagella can also be easily deformed by external shear flow, leading to complex bacterial trajectories. Here, we examine the effects of flagella flexibility on the navigation of bacteria in two fundamental shear flows: planar shear and Poiseuille flow realized in long channels. On the basis of slender body elastodynamics and numerical analysis, we discovered a variety of non-trivial effects stemming from the interplay of self-propulsion, elasticity and shear-induced flagellar bending. We show that in planar shear flow the bacteria execute periodic motion, whereas in Poiseuille flow, they migrate towards the centre of the channel or converge towards a limit cycle. We also find that even a small amount of random reorientation can induce a strong response of bacteria, leading to overall non-periodic trajectories. Our findings exemplify the sensitive role of flagellar flexibility and shed new light on the navigation of bacteria in complex shear flows.

Physics of microswimmers--single particle motion and collective behavior: a review

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.

Individual behavior and pairwise interactions between microswimmers in anisotropic liquid

A motile bacterium swims by generating flow in its surrounding liquid. Anisotropy of the suspending liquid significantly modifies the swimming dynamics and corresponding flow signatures of an individual bacterium and impacts collective behavior. We study the interactions between swimming bacteria in an anisotropic environment exemplified by lyotropic chromonic liquid crystal. Our analysis reveals a significant localization of the bacteria-induced flow along a line coaxial with the bacterial body, which is due to strong viscosity anisotropy of the liquid crystal. Despite the fact that the average viscosity of the liquid crystal is two to three orders of magnitude higher than the viscosity of pure water, the speed of bacteria in the liquid crystal is of the same order of magnitude as in water. We show that bacteria can transport a cargo (a fluorescent particle) along a predetermined trajectory defined by the direction of molecular orientation of the liquid crystal. We demonstrate that while the hydrodynamic interaction between flagella of two close-by bacteria is negligible, the observed convergence of the swimming speeds as well as flagella waves' phase velocities may occur due to viscoelastic interaction between the bacterial bodies.

Large-scale chaos and fluctuations in active nematics

We show that dry active nematics, e.g., collections of shaken elongated granular particles, exhibit large-scale spatiotemporal chaos made of interacting dense, ordered, bandlike structures in a parameter region including the linear onset of nematic order. These results are obtained from the study of both the well-known (deterministic) hydrodynamic equations describing these systems and of the self-propelled particle model they were derived from. We prove, in particular, that the chaos stems from the generic instability of the band solution of the hydrodynamic equations. Revisiting the status of the strong fluctuations and long-range correlations in the particle model, we show that the giant number fluctuations observed in the chaotic phase are a trivial consequence of density segregation. However anomalous, curvature-driven number fluctuations are present in the homogeneous quasiordered nematic phase and characterized by a nontrivial scaling exponent.

Gait synchronization in Caenorhabditis elegans

Collective motion is observed in swarms of swimmers of various sizes, ranging from self-propelled nanoparticles to fish. The mechanisms that govern interactions among individuals are debated, and vary from one species to another. Although the interactions among relatively large animals, such as fish, are controlled by their nervous systems, the interactions among microorganisms, which lack nervous systems, are controlled through physical and chemical pathways. Little is known, however, regarding the mechanism of collective movements in microscopic organisms with nervous systems. To attempt to remedy this, we studied collective swimming behavior in the nematode Caenorhabditis elegans, a microorganism with a compact nervous system. We evaluated the contributions of hydrodynamic forces, contact forces, and mechanosensory input to the interactions among individuals. We devised an experiment to examine pair interactions as a function of the distance between the animals and observed that gait synchronization occurred only when the animals were in close proximity, independent of genes required for mechanosensation. Our measurements and simulations indicate that steric hindrance is the dominant factor responsible for motion synchronization in C. elegans, and that hydrodynamic interactions and genotype do not play a significant role. We infer that a similar mechanism may apply to other microscopic swimming organisms and self-propelled particles.

Collective surfing of chemically active particles

We study theoretically the collective dynamics of immotile particles bound to a 2D surface atop a 3D fluid layer. These particles are chemically active and produce a chemical concentration field that creates surface-tension gradients along the surface. The resultant Marangoni stresses create flows that carry the particles, possibly concentrating them. For a 3D diffusion-dominated concentration field and Stokesian fluid we show that the surface dynamics of active particle density can be determined using nonlocal 2D surface operators. Remarkably, we also show that for both deep or shallow fluid layers this surface dynamics reduces to the 2D Keller-Segel model for the collective chemotactic aggregation of slime mold colonies. Mathematical analysis has established that the Keller-Segel model can yield finite-time, finite-mass concentration singularities. We show that such singular behavior occurs in our finite-depth system, and study the associated 3D flow structures.

Globally aligned states and hydrodynamic traffic jams in confined suspensions of active asymmetric particles

Strongly confined active liquids are subject to unique hydrodynamic interactions due to momentum screening and lubricated friction by the confining walls. Using numerical simulations, we demonstrate that two-dimensional dilute suspensions of fore-aft asymmetric polar swimmers in a Hele-Shaw geometry can exhibit a rich variety of novel phase behaviors depending on particle shape, including coherent polarized density waves with global alignment, persistent counterrotating vortices, density shocks and rarefaction waves. We also explain these phenomena using a linear stability analysis and a nonlinear traffic flow model, both derived from a mean-field kinetic theory.