Collective dynamics of model microorganisms with chemotactic signaling

Chemotactic self-caging in active emulsions

The out-of-equilibrium dynamics of chemotactic active matter—be it animate or inanimate—is closely coupled to the environment, a chemical landscape shaped by secretions from the motile agents, fuel uptake, or autochemotactic signaling. This gives rise to complex collective effects, which can be exploited by the agents for colony migration strategies or pattern formation. We study such effects using an idealized experimental system: self-propelled microdroplets that communicate via chemorepulsive trails. We present a comprehensive experimental analysis that involves direct probing of the diffusing chemical trails and the trail–droplet interactions and use it to construct a generic theoretical model. We connect these repulsive autochemotactic interactions to the collective dynamics in emulsions, demonstrating a state of dynamical arrest: chemotactic self-caging.

A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent–trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other’s trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.

Interactions in active colloids

The past two decades have seen a remarkable progress in the development of synthetic colloidal agents which are capable of creating directed motion in an unbiased environment at the microscale. These self-propelling particles are often praised for their enormous potential to self-organize into dynamic nonequilibrium structures such as living clusters, synchronized super-rotor structures or self-propelling molecules featuring a complexity which is rarely found outside of the living world. However, the precise mechanisms underlying the formation and dynamics of many of these structures are still barely understood, which is likely to hinge on the gaps in our understanding of how active colloids interact. In particular, besides showing comparatively short-ranged interactions which are well known from passive colloids (Van der Waals, electrostatic etc), active colloids show novel hydrodynamic interactions as well as phoretic and substrate-mediated 'osmotic' cross-interactions which hinge on the action of the phoretic field gradients which are induced by the colloids on other colloids in the system. The present article discusses the complexity and the intriguing properties of these interactions which in general are long-ranged, non-instantaneous, non-pairwise and non-reciprocal and which may serve as key ingredients for the design of future nonequilibrium colloidal materials. Besides providing a brief overview on the state of the art of our understanding of these interactions a key aim of this review is to emphasize open key questions and corresponding open challenges.

Optimal Non-Markovian Search Strategies with n-Step Memory

Stochastic search processes are ubiquitous in nature and are expected to become more efficient when equipped with a memory, where the searcher has been before. A natural realization of a search process with long-lasting memory is a migrating cell that is repelled from the diffusive chemotactic signal that it secretes on its way, denoted as an autochemotactic searcher. To analyze the efficiency of this class of non-Markovian search processes, we present a general formalism that allows one to compute the mean first-passage time (MFPT) for a given set of conditional transition probabilities for non-Markovian random walks on a lattice. We show that the optimal choice of the n-step transition probabilities decreases the MFPT systematically and substantially with an increasing number of steps. It turns out that the optimal search strategies can be reduced to simple cycles defined by a small parameter set and that mirror-asymmetric walks are more efficient. For the autochemotactic searcher, we show that an optimal coupling between the searcher and the chemical reduces the MFPT to 1/3 of the one for a Markovian random walk.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

Long-distance Transport in Bacterial Swarms Revealed by Single Nanoparticle Tracking

During swarming, high density flagella-driven bacteria migrate collectively in a swirling pattern on wet agar surfaces, immersed in a thin viscous fluid layer called "swarm fluid". Though the fluid environment has essential role in the emergence of swarming behavior, the microscopic mechanisms of it in mediating the cooperation of bacteria populations are not fully understood. Here, instead of micro-sized tracers used in previous research, we use gold nanorods as single particle tracers to probe the dynamics of the swarm fluid. This protocol includes five major parts: (1) the culture of swarming bacterial colony; (2) the preparations of gold nanorod tracers and the micro-spraying technique which are used to put the nanotracers into the upper fluid of bacterial swarms; (3) imaging and tracking; (4) other necessary control experiments; (5) data analysis and fitting of physical models. With this method, the nano-sized tracers could move long distances above motile cells without direct collisions with the bacteria bodies. In this way, the microscopic dynamics of the swarm fluid could be tracked with high spatiotemporal resolution. Moreover, the comprehensive analysis of multi-particle trajectories provides systematic visualization of the fluid dynamics. The method is promising to probe the fluid dynamics of other natural or artificial active matter systems.

Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning

We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.

Bose-Einstein-like condensation in scalar active matter with diffusivity edge

Due to their remarkable properties, systems that exhibit self-organization of their components resulting from intrinsic microscopic activity have been extensively studied in the last two decades. In a generic class of active matter, the interactions between the active components are represented via an effective density-dependent diffusivity in a mean-field single-particle description. Here, a class of scalar active matter is proposed by incorporating a diffusivity edge into the dynamics: when the local density of the system surpasses a critical threshold, the diffusivity vanishes. The effect of the diffusivity edge is studied under the influence of an external potential, which introduces the ability to control the behavior of the system by changing an effective temperature, which is defined in terms of the single-particle diffusivity and mobility. At a critical effective temperature, a system that is trapped by a harmonic potential is found to undergo a condensation transition, which manifests formal similarities to Bose-Einstein condensation.

Modeling aerotaxis band formation in Azospirillum brasilense

BACKGROUND

Bacterial chemotaxis, the ability of motile bacteria to navigate gradients of chemicals, plays key roles in the establishment of various plant-microbe associations, including those that benefit plant growth and crop productivity. The motile soil bacterium Azospirillum brasilense colonizes the rhizosphere and promotes the growth of diverse plants across a range of environments. Aerotaxis, or the ability to navigate oxygen gradients, is a widespread behavior in bacteria. It is one of the strongest behavioral responses in A. brasilense and it is essential for successful colonization of the root surface. Oxygen is one of the limiting nutrients in the rhizosphere where density and activity of organisms are greatest. The aerotaxis response of A. brasilense is also characterized by high precision with motile cells able to detect narrow regions in a gradient where the oxygen concentration is low enough to support their microaerobic lifestyle and metabolism.

RESULTS

Here, we present a mathematical model for aerotaxis band formation that captures most critical features of aerotaxis in A. brasilense. Remarkably, this model recapitulates experimental observations of the formation of a stable aerotactic band within 2 minutes of exposure to the air gradient that were not captured in previous modeling efforts. Using experimentally determined parameters, the mathematical model reproduced an aerotactic band at a distance from the meniscus and with a width that matched the experimental observation.

CONCLUSIONS

Including experimentally determined parameter values allowed us to validate a mathematical model for aerotactic band formation in spatial gradients that recapitulates the spatiotemporal stability of the band and its position in the gradient as well as its overall width. This validated model also allowed us to capture the range of oxygen concentrations the bacteria prefer during aerotaxis, and to estimate the effect of parameter values (e.g. oxygen consumption rate), both of which are difficult to obtain in experiments.

Synthetic Chemotaxis and Collective Behavior in Active Matter

The ability to navigate in chemical gradients, called chemotaxis, is crucial for the survival of microorganisms. It allows them to find food and to escape from toxins. Many microorganisms can produce the chemicals to which they respond themselves and use chemotaxis for signaling, which can be seen as a basic form of communication, allowing ensembles of microorganisms to coordinate their behavior, for example, during embryogenesis, biofilm formation, or cellular aggregation. For example, Dictyostelium cells use signaling as a survival strategy: when starving, they produce certain chemicals toward which other cells show taxis. This leads to aggregation of the cells resulting in a multicellular aggregate that can sustain long starvation periods. Remarkably, the past decade has led to the development of synthetic microswimmers, which can self-propel through a solvent, analogously to bacteria and other microorganisms. The mechanism underlying the self-propulsion of synthetic microswimmers like camphor boats, droplet swimmers, and in particular autophoretic Janus colloids involves the production of certain chemicals. As we will discuss in this Account, the same chemicals (phoretic fields) involved in the self-propulsion of a (Janus) microswimmer also act on other ones and bias their swimming direction toward (or away from) the producing microswimmer. Synthetic microswimmers therefore provide a synthetic analogue to motile microorganisms interacting by taxis toward (or away from) self-produced chemical fields. In this Account, we review recent progress in the theoretical description of synthetic chemotaxis mainly based on simulations and field theoretical descriptions. We will begin with single motile particles leaving chemical trails behind with which they interact themselves, leading to effects like self-trapping or self-avoidance. Besides these self-interactions, in ensembles of synthetic motile particles each particle also responds to the chemicals produced by other particles, inducing chemical (or phoretic) cross-interactions. When these interactions are attractive, they commonly lead to clusters, even at low particle density. These clusters may either proceed toward macrophase separation, resembling Dictyostelium aggregation, or, as shown very recently, lead to dynamic clusters of self-limited size (dynamic clustering) as seen in experiments in autophoretic Janus colloids. Besides the classical case where chemical interactions are attractive, this Account discusses, as its main focus, repulsive chemical interactions, which can create a new and less known avenue to pattern formation in active systems leading to a variety of pattern, including clusters which are surrounded by shells of chemicals, traveling waves and more complex continuously reshaping patterns. In all these cases "synthetic signalling" can crucially determine the collective behavior of synthetic microswimmer ensembles and can be used as a design principle to create patterns in motile active particles.

Modeling of active swimmer suspensions and their interactions with the environment

In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

Predicting Escherichia coli's chemotactic drift under exponential gradient

Bacterial species are known to show chemotaxis, i.e., the directed motions in the presence of certain chemicals, whereas the motion is random in the absence of those chemicals. The bacteria modulate their run time to induce chemotactic drift towards the attractant chemicals and away from the repellent chemicals. However, the existing theoretical knowledge does not exhibit a proper match with experimental validation, and hence there is a need for developing alternate models and validating experimentally. In this paper a more robust theoretical model is proposed to investigate chemotactic drift of peritrichous Escherichia coli under an exponential nutrient gradient. An exponential gradient is used to understand the steady state behavior of drift because of the logarithmic functionality of the chemosensory receptors. Our theoretical estimations are validated through the experimentation and simulation results. Thus, the developed model successfully delineates the run time, run trajectory, and drift velocity as measured from the experiments.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration.

Multicellular Self-Organization of P. aeruginosa due to Interactions with Secreted Trails

Guided movement in response to slowly diffusing polymeric trails provides a unique mechanism for self-organization of some microorganisms. To elucidate how this signaling route leads to microcolony formation, we experimentally probe the trajectory and orientation of Pseudomonas aeruginosa that propel themselves on a surface using type IV pili motility appendages, which preferentially attach to deposited exopolysaccharides. We construct a stochastic model by analyzing single-bacterium trajectories and show that the resulting theoretical prediction for the many-body behavior of the bacteria is in quantitative agreement with our experimental characterization of how cells explore the surface via a power-law strategy.

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.

Pattern formation in chemically interacting active rotors with self-propulsion

We demonstrate that active rotations in chemically signalling particles, such as autochemotactic E. coli close to walls, create a route for pattern formation based on a nonlinear yet deterministic instability mechanism. For slow rotations, we find a transient persistence of the uniform state, followed by a sudden formation of clusters contingent on locking of the average propulsion direction by chemotaxis. These clusters coarsen, which results in phase separation into a dense and a dilute region. Faster rotations arrest phase separation leading to a global travelling wave of rotors with synchronized roto-translational motion. Our results elucidate the physics resulting from the competition of two generic paradigms in active matter, chemotaxis and active rotations, and show that the latter provides a tool to design programmable self-assembly of active matter, for example to control coarsening.

Effective Dynamics of Microorganisms That Interact with Their Own Trail

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For a moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.

Quorum sensing is a language of chemical signals and plays an ecological role in algal-bacterial interactions

Algae are ubiquitous in the marine environment, and the ways in which they interact with bacteria are of particular interest in marine ecology field. The interactions between primary producers and bacteria impact the physiology of both partners, alter the chemistry of their environment, and shape microbial diversity. Although algal-bacterial interactions are well known and studied, information regarding the chemical-ecological role of this relationship remains limited, particularly with respect to quorum sensing (QS), which is a system of stimuli and response correlated to population density. In the microbial biosphere, QS is pivotal in driving community structure and regulating behavioral ecology, including biofilm formation, virulence, antibiotic resistance, swarming motility, and secondary metabolite production. Many marine habitats, such as the phycosphere, harbour diverse populations of microorganisms and various signal languages (such as QS-based autoinducers). QS-mediated interactions widely influence algal-bacterial symbiotic relationships, which in turn determine community organization, population structure, and ecosystem functioning. Understanding infochemicals-mediated ecological processes may shed light on the symbiotic interactions between algae host and associated microbes. In this review, we summarize current achievements about how QS modulates microbial behavior, affects symbiotic relationships, and regulates phytoplankton chemical ecological processes. Additionally, we present an overview of QS-modulated co-evolutionary relationships between algae and bacterioplankton, and consider the potential applications and future perspectives of QS.

Pili-Induced Clustering of N. gonorrhoeae Bacteria

Type IV pili (Tfp) are prokaryotic retractable appendages known to mediate surface attachment, motility, and subsequent clustering of cells. Tfp are the main means of motility for Neisseria gonorrhoeae, the causative agent of gonorrhea. Tfp are also involved in formation of the microcolonies, which play a crucial role in the progression of the disease. While motility of individual cells is relatively well understood, little is known about the dynamics of N. gonorrhoeae aggregation. We investigate how individual N. gonorrhoeae cells, initially uniformly dispersed on flat plastic or glass surfaces, agglomerate into spherical microcolonies within hours. We quantify the clustering process by measuring the area fraction covered by the cells, number of cell aggregates, and their average size as a function of time. We observe that the microcolonies are also able to move but their mobility rapidly vanishes as the size of the colony increases. After a certain critical size they become immobile. We propose a simple theoretical model which assumes a pili-pili interaction of cells as the main clustering mechanism. Numerical simulations of the model quantitatively reproduce the experimental data on clustering and thus suggest that the agglomeration process can be entirely explained by the Tfp-mediated interactions. In agreement with this hypothesis mutants lacking pili are not able to form colonies. Moreover, cells with deficient quorum sensing mechanism show similar aggregation as the wild-type bacteria. Therefore, our results demonstrate that pili provide an essential mechanism for colony formation, while additional chemical cues, for example quorum sensing, might be of secondary importance.

Cell-cell signalling in sexual chemotaxis: a basis for gametic differentiation, mating types and sexes

While sex requires two parents, there is no obvious need for them to be differentiated into distinct mating types or sexes. Yet this is the predominate state of nature. Here, we argue that mating types could play a decisive role because they prevent the apparent inevitability of self-stimulation during sexual signalling. We rigorously assess this hypothesis by developing a model for signaller-detector dynamics based on chemical diffusion, chemotaxis and cell movement. Our model examines the conditions under which chemotaxis improves partner finding. Varying parameter values within ranges typical of protists and their environments, we show that simultaneous secretion and detection of a single chemoattractant can cause a multifold movement impediment and severely hinder mate finding. Mutually exclusive roles result in faster pair formation, even when cells conferring the same roles cannot pair up. This arrangement also allows the separate mating types to optimize their signalling or detecting roles, which is effectively impossible for cells that are both secretors and detectors. Our findings suggest that asymmetric roles in sexual chemotaxis (and possibly other forms of sexual signalling) are crucial, even without morphological differences, and may underlie the evolution of gametic differentiation among both mating types and sexes.

Self-phoretic active particles interacting by diffusiophoresis: A numerical study of the collapsed state and dynamic clustering

Self-phoretic active colloids move and orient along self-generated chemical gradients by diffusiophoresis, a mechanism reminiscent of bacterial chemotaxis. In combination with the activity of the colloids, this creates effective repulsive and attractive interactions between particles depending on the sign of the translational and rotational diffusiophoretic parameters. A delicate balance of these interactions causes dynamic clustering and for overall strong effective attraction the particles collapse to one single cluster. Using Langevin dynamics simulations, we extend the state diagram of our earlier work (Phys. Rev. Lett. 112, 238303 (2014)) to regions with translational phoretic repulsion. With increasing repulsive strength, the collapsed cluster first starts to fluctuate strongly, then oscillates between a compact form and a colloidal cloud, and ultimately the colloidal cloud becomes static. The oscillations disappear if the phoretic interactions within compact clusters are not screened. We also study dynamic clustering at larger area fractions by exploiting cluster size distributions and mean cluster sizes. In particular, we identify the dynamic clustering 2 state as a signature of phoretic interactions. We analyze fusion and fission rate functions to quantify the kinetics of cluster formation and identify them as local signatures of phoretic interactions, since they can be measured on single clusters.

Detention Times of Microswimmers Close to Surfaces: Influence of Hydrodynamic Interactions and Noise

After colliding with a surface, microswimmers reside there during the detention time. They accumulate and may form complex structures such as biofilms. We introduce a general framework to calculate the distribution of detention times using the method of first-passage times and study how rotational noise and hydrodynamic interactions influence the escape from a surface. We compare generic swimmer models to the simple active Brownian particle. While the respective detention times of source dipoles are smaller, the ones of pullers are larger by up to several orders of magnitude, and pushers show both trends. We apply our results to the more realistic squirmer model, for which we use lubrication theory, and validate them by simulations with multiparticle collision dynamics.

Tricritical points in a Vicsek model of self-propelled particles with bounded confidence

We study the orientational ordering in systems of self-propelled particles with selective interactions. To introduce the selectivity we augment the standard Vicsek model with a bounded-confidence collision rule: a given particle only aligns to neighbors who have directions quite similar to its own. Neighbors whose directions deviate more than a fixed restriction angle α are ignored. The collective dynamics of this system is studied by agent-based simulations and kinetic mean-field theory. We demonstrate that the reduction of the restriction angle leads to a critical noise amplitude decreasing monotonically with that angle, turning into a power law with exponent 3/2 for small angles. Moreover, for small system sizes we show that upon decreasing the restriction angle, the kind of the transition to polar collective motion changes from continuous to discontinuous. Thus, an apparent tricritical point with different scaling laws is identified and calculated analytically. We investigate the shifting and vanishing of this point due to the formation of density bands as the system size is increased. Agent-based simulations in small systems with large particle velocities show excellent agreement with the kinetic theory predictions. We also find that at very small interaction angles, the polar ordered phase becomes unstable with respect to the apolar phase. We derive analytical expressions for the dependence of the threshold noise on the restriction angle. We show that the mean-field kinetic theory also permits stationary nematic states below a restriction angle of 0.681π. We calculate the critical noise, at which the disordered state bifurcates to a nematic state, and find that it is always smaller than the threshold noise for the transition from disorder to polar order. The disordered-nematic transition features two tricritical points: At low and high restriction angle, the transition is discontinuous but continuous at intermediate α. We generalize our results to systems that show fragmentation into more than two groups and obtain scaling laws for the transition lines and the corresponding tricritical points. A numerical method to evaluate the nonlinear Fredholm integral equation for the stationary distribution function is also presented. This method is shown to give excellent agreement with agent-based simulations, even in strongly ordered systems at noise values close to zero.

Nonequilibrium glassy dynamics of self-propelled hard disks

We analyze the collective dynamics of self-propelled particles in the large-density regime where passive particles undergo a kinetic arrest to an amorphous glassy state. We capture the competition between self-propulsion and crowding effects using a two-dimensional model of self-propelled hard disks, which we study using Monte Carlo simulations. Although the activity drives the system far from equilibrium, self-propelled particles undergo a kinetic arrest, which we characterize in detail and compare with its equilibrium counterpart. In particular, the critical density for dynamic arrest continuously shifts to larger densities with increasing activity, and the relaxation time is surprisingly well described by an algebraic divergence resulting from the emergence of highly collective dynamics. These results show that dense assemblies of active particles undergo a nonequilibrium glass transition that is profoundly affected by self-propulsion mechanisms.

Clustering and heterogeneous dynamics in a kinetic Monte Carlo model of self-propelled hard disks

We introduce a kinetic Monte Carlo model for self-propelled hard disks to capture with minimal ingredients the interplay between thermal fluctuations, excluded volume, and self-propulsion in large assemblies of active particles. We analyze in detail the resulting (density, self-propulsion) nonequilibrium phase diagram over a broad range of parameters. We find that purely repulsive hard disks spontaneously aggregate into fractal clusters as self-propulsion is increased and rationalize the evolution of the average cluster size by developing a kinetic model of reversible aggregation. As density is increased, the nonequilibrium clusters percolate to form a ramified structure reminiscent of a physical gel. We show that the addition of a finite amount of noise is needed to trigger a nonequilibrium phase separation, showing that demixing in active Brownian particles results from a delicate balance between noise, interparticle interactions, and self-propulsion. We show that self-propulsion has a profound influence on the dynamics of the active fluid. We find that the diffusion constant has a nonmonotonic behavior as self-propulsion is increased at finite density and that activity produces strong deviations from Fickian diffusion that persist over large time scales and length scales, suggesting that systems of active particles generically behave as dynamically heterogeneous systems.

Hydrodynamics determines collective motion and phase behavior of active colloids in quasi-two-dimensional confinement

We study the collective motion of confined spherical microswimmers such as active colloids which we model by so-called squirmers. To simulate hydrodynamic flow fields including thermal noise, we use the method of multiparticle collision dynamics. We demonstrate that hydrodynamic near fields acting between squirmers as well as between squirmers and bounding walls crucially determine their collective motion. In particular, with increasing density we observe a clear phase separation into a gaslike and cluster phase for neutral squirmers whereas strong pushers and pullers more gradually approach the hexagonal cluster state.

Active Brownian agents with concentration-dependent chemotactic sensitivity

We study a biologically motivated model of overdamped, autochemotactic Brownian agents with concentration-dependent chemotactic sensitivity. The agents in our model move stochastically and produce a chemical ligand at their current position. The ligand concentration obeys a reaction-diffusion equation and acts as a chemoattractant for the agents, which bias their motion towards higher concentrations of the dynamically altered chemical field. We explore the impact of concentration-dependent response to chemoattractant gradients on large-scale pattern formation, by deriving a coarse-grained macroscopic description of the individual-based model, and compare the conditions for emergence of inhomogeneous solutions for different variants of the chemotactic sensitivity. We focus primarily on the so-called receptor-law sensitivity, which models a nonlinear decrease of chemotactic sensitivity with increasing ligand concentration. Our results reveal qualitative differences between the receptor law, the constant chemotactic response, and the so-called log law, with respect to stability of the homogeneous solution, as well as the emergence of different patterns (labyrinthine structures, clusters, and bubbles) via spinodal decomposition or nucleation. We discuss two limiting cases, where the model can be reduced to the dynamics of single species: (I) the agent density governed by a density-dependent effective diffusion coefficient and (II) the ligand field with an effective bistable, time-dependent reaction rate. In the end, we turn to single clusters of agents, studying domain growth and determining mean characteristics of the stationary inhomogeneous state. Analytical results are confirmed and extended by large-scale GPU simulations of the individual based model.

Collective dynamics in systems of active Brownian particles with dissipative interactions

We use computer simulations to study the onset of collective motion in systems of interacting active particles. Our model is a swarm of active Brownian particles with an internal energy depot and interactions inspired by the dissipative particle dynamics method, imposing pairwise friction force on the nearest neighbors. We study orientational ordering in a 2D system as a function of energy influx rate and particle density. The model demonstrates a transition into the ordered state on increasing the particle density and increasing the input power. Although both the alignment mechanism and the character of individual motion in our model differ from those in the well-studied Vicsek model, it demonstrates identical statistical properties and phase behavior.

Periodic and quasiperiodic motion of an elongated microswimmer in Poiseuille flow

We study the dynamics of a prolate spheroidal microswimmer in Poiseuille flow for different flow geometries. When moving between two parallel plates or in a cylindrical microchannel, the swimmer performs either periodic swinging or periodic tumbling motion. Although the trajectories of spherical and elongated swimmers are qualitatively similar, the swinging and tumbling frequency strongly depends on the aspect ratio of the swimmer. In channels with reduced symmetry the swimmers perform quasiperiodic motion which we demonstrate explicitly for swimming in a channel with elliptical cross-section.

Collective chemotactic dynamics in the presence of self-generated fluid flows

In microswimmer suspensions locomotion necessarily generates fluid motion, and it is known that such flows can lead to collective behavior from unbiased swimming. We examine the complementary problem of how chemotaxis is affected by self-generated flows. A kinetic theory coupling run-and-tumble chemotaxis to the flows of collective swimming shows separate branches of chemotactic and hydrodynamic instabilities for isotropic suspensions, the first driving aggregation, the second producing increased orientational order in suspensions of "pushers" and maximal disorder in suspensions of "pullers." Nonlinear simulations show that hydrodynamic interactions can limit and modify chemotactically driven aggregation dynamics. In puller suspensions the dynamics form aggregates that are mutually repelling due to the nontrivial flows. In pusher suspensions chemotactic aggregation can lead to destabilizing flows that fragment the regions of aggregation.