When an active bath behaves as an equilibrium one.

Active scalar baths consisting of active Brownian particles are characterized by a non-Gaussian velocity distribution, a kinetic temperature, and a diffusion coefficient that scale with the square of the active velocity v_{0}. While these results hold in overdamped active systems, inertial effects lead to normal velocity distributions, with kinetic temperature and diffusion coefficient increasing as ∼v_{0}^{α} with 1<α<2. Remarkably, the late-time diffusivity and mobility decrease with mass. Moreover, we show that the equilibrium Einstein relation is asymptotically recovered with inertia. In summary, the inertial mass restores an equilibriumlike behavior.

Reversible adhesion by type IV pili leads to formation of permanent localized clusters.

The formation of long-lived, multicellular clusters is a fundamental step in the physiopathology of many disease-causing bacteria. Experiments on abiotic surfaces suggest that bacterial colonization, including initial cluster formation, requires (1) irreversible adhesion, (2) cell proliferation, and (3) a phenotypic transition. However, here we show that on infection of a polarized MDCK epithelium, Pseudomonas aeruginosa (PA) forms long-lived - i.e., permanent - bacterial clusters without requiring irreversible adhesion, cell proliferation, or a phenotypic transition. By combining experiments and a mathematical model, we reveal that the cluster formation process is mediated by type IV pili (T4P). Furthermore, we unveil how T4P quantitatively operate during adhesion, finding that it is a stochastic process that involves an activation time, requires the retraction of pili, and results in reversible attachment. We explain how such reversible attachment process leads to the formation of permanent bacterial clusters and quantify the cluster growth dynamics.

Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores.

Phytophthora species cause diseases in a large variety of plants and represent a serious agricultural threat, leading, every year, to multibillion dollar losses. Infection occurs when their biflagellated zoospores move across the soil at their characteristic high speed and reach the roots of a host plant. Despite the relevance of zoospore spreading in the epidemics of plant diseases, individual swimming of zoospores have not been fully investigated. It remains unknown about the characteristics of two opposite beating flagella during translation and turning, and the roles of each flagellum on zoospore swimming. Here, combining experiments and modeling, we show how these two flagella contribute to generate thrust when beating together, and identify the mastigonemes-attached anterior flagellum as the main source of thrust. Furthermore, we find that turning involves a complex active process, in which the posterior flagellum temporarily stops, while the anterior flagellum keeps on beating and changes its gait from sinusoidal waves to power and recovery strokes, similar to Chlamydomonas's breaststroke, to reorient its body to a new direction. Our study is a fundamental step toward a better understanding of the spreading of plant pathogens' motile forms, and shows that the motility pattern of these biflagellated zoospores represents a distinct eukaryotic version of the celebrated 'run-and-tumble' motility class exhibited by peritrichous bacteria.

Microorganisms of the Phytophthora genus are serious agricultural pests. They cause diseases in many crops, including potato, onion, tomato, tobacco, cotton, peppers, and citrus. These diseases cause billions of dollars in losses each year. Learning more about how the tiny creatures disseminate and reach host plants could help scientists develop new ways to prevent such crop damage. The spore cells of Phytophthora, also known as zoospores, have two appendages called flagella on their bodies. A tinsel-shaped flagellum is near the front of the creature and a long smooth filament-like flagellum is near the posterior. Zoospores use their flagella to swim at high speeds through liquid toward potential plant hosts. Their complex swimming patterns change in response to different physical, chemical, and electrical signals in the environment. But exactly how they use their flagella to generate these movements is not clear. Tran et al. reveal new details about zoospore locomotion. In the experiments, Tran et al. recorded the movements of zoospores in a tiny 'swimming pool' of fluid on top of a glass slide and analyzed the movements using statistical and mathematical models. The results uncovered coordinated actions of the flagella when zoospores swim in a straight line and when they turn. The tinsel-like front flagellum provides most of the force that propels the zoospore forward. To do this, it beats with an undulating wave pattern. It shifts the beating to a breast-stroke pattern to change direction. The posterior flagellum provides a smaller forward thrust and temporarily pauses during turns. The study provides new details about zoospore's movements that may help scientists develop new strategies to control these pests. It also offers more information about how flagella coordinate their actions to switch speeds or change directions that may be of interest to other scientists studying organisms that use flagella to move.

Statistics of pathogenic bacteria in the search of host cells.

A crucial phase in the infection process, which remains poorly understood, is the localization of suitable host cells by bacteria. It is often assumed that chemotaxis plays a key role during this phase. Here, we report a quantitative study on how Salmonella Typhimurium search for T84 human colonic epithelial cells. Combining time-lapse microscopy and mathematical modeling, we show that bacteria can be described as chiral active particles with strong active speed fluctuations, which are of biological, as opposed to thermal, origin. We observe that there exists a giant range of inter-individual variability of the bacterial exploring capacity. Furthermore, we find Salmonella Typhimurium does not exhibit biased motion towards the cells and show that the search time statistics is consistent with a random search strategy. Our results indicate that in vitro localization of host cells, and also cell infection, are random processes, not involving chemotaxis, that strongly depend on bacterial motility parameters.

Revisiting the emergence of order in active matter.

The emergence of orientational order plays a central role in active matter theory and is deeply based in the study of active systems with a velocity alignment mechanism, whose most prominent example is the so-called Vicsek model. Such active systems have been used to describe bird flocks, bacterial swarms, and active colloidal systems, among many other examples. Under the assumption that the large-scale properties of these models remain unchanged as long as the polar symmetry of the interactions is not affected, implementations have been performed using, out of convenience, either additive or non-additive interactions; the latter are found for instance in the original formulation of the Vicsek model. Here, we perform a careful analysis of active systems with velocity alignment, comparing additive and non-additive interactions, and show that the macroscopic properties of these active systems are fundamentally different. Our results call into question our current understanding of the onset of order in active systems.

A particle-field approach bridges phase separation and collective motion in active matter.

Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

Learning to flock through reinforcement.

Flocks of birds, schools of fish, and insect swarms are examples of the coordinated motion of a group that arises spontaneously from the action of many individuals. Here, we study flocking behavior from the viewpoint of multiagent reinforcement learning. In this setting, a learning agent tries to keep contact with the group using as sensory input the velocity of its neighbors. This goal is pursued by each learning individual by exerting a limited control on its own direction of motion. By means of standard reinforcement learning algorithms we show that (i) a learning agent exposed to a group of teachers, i.e., hard-wired flocking agents, learns to follow them, and (ii) in the absence of teachers, a group of independently learning agents evolves towards a state where each agent knows how to flock. In both scenarios, the emergent policy (or navigation strategy) corresponds to the polar velocity alignment mechanism of the well-known Vicsek model. These results (a) show that such a velocity alignment may have naturally evolved as an adaptive behavior that aims at minimizing the rate of neighbor loss, and (b) prove that this alignment does not only favor (local) polar order, but it corresponds to the best policy or strategy to keep group cohesion when the sensory input is limited to the velocity of neighboring agents. In short, to stay together, steer together.

Modelling collective cell motion: are on- and off-lattice models equivalent?

Biological processes, such as embryonic development, wound repair and cancer invasion, or bacterial swarming and fruiting body formation, involve collective motion of cells as a coordinated group. Collective cell motion of eukaryotic cells often includes interactions that result in polar alignment of cell velocities, while bacterial patterns typically show features of apolar velocity alignment. For analysing the population-scale effects of these different alignment mechanisms, various on- and off-lattice agent-based models have been introduced. However, discriminating model-specific artefacts from general features of collective cell motion is challenging. In this work, we focus on equivalence criteria at the population level to compare on- and off-lattice models. In particular, we define prototypic off- and on-lattice models of polar and apolar alignment, and show how to obtain an on-lattice from an off-lattice model of velocity alignment. By characterizing the behaviour and dynamical description of collective migration models at the macroscopic level, we suggest the type of phase transitions and possible patterns in the approximative macroscopic partial differential equation descriptions as informative equivalence criteria between on- and off-lattice models. This article is part of the theme issue 'Multi-scale analysis and modelling of collective migration in biological systems'.

Flocking in complex environments-Attention trade-offs in collective information processing.

The ability of biological and artificial collectives to outperform solitary individuals in a wide variety of tasks depends crucially on the efficient processing of social and environmental information at the level of the collective. Here, we model collective behavior in complex environments with many potentially distracting cues. Counter-intuitively, large-scale coordination in such environments can be maximized by strongly limiting the cognitive capacity of individuals, where due to self-organized dynamics the collective self-isolates from disrupting information. We observe a fundamental trade-off between coordination and collective responsiveness to environmental cues. Our results offer important insights into possible evolutionary trade-offs in collective behavior in biology and suggests novel principles for design of artificial swarms exploiting attentional bottlenecks.

The 2020 motile active matter roadmap.

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

Phase separation and emergence of collective motion in a one-dimensional system of active particles.

We study numerically a one-dimensional system of self-propelled particles, where the state of the particles is given by their moving direction (left or right), which is encoded by a spin-like variable, and their position. Particles interact by short-ranged, spring-like attractive forces and do not possess spin-spin interactions (i.e., velocity alignment). Newton's third law is broken in this model by assuming an asymmetric interaction range that is larger in the direction of the moving direction of the particle. We show that in this nonequilibrium system, due to the absence of the action-reaction symmetry, there exists an intimate link between phase separation and the formation of highly coherent, spatially localized, moving flocks (i.e., collective motion). More specifically, we prove the existence of two fundamentally different types of active phase separation, which we refer to as neutral phase separation (NPS) and polar phase separation. Furthermore, we indicate that NPS is subdivided in two classes with distinct critical exponents. These results are of key importance to understand that in active matter, there exist several phase-separation classes and that the emergence of polar, self-organized patterns (i.e., flocks) does not require the presence of a velocity alignment.

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.

An ant navigation model based on Weber's law.

We analyze an ant navigation model based on Weber's law, where the ants move across a pheromone landscape sensing the area using two antennae. The key parameter of the model is the angle [Formula: see text] representing the span of the ant's sensing area. We show that when [Formula: see text] ants are able to follow (straight) pheromone trails proving that for initial conditions close to the trail, there exists a Lyapunov function that ensures ant trajectories converge on and follow the pheromone trail, with these solutions being locally asymptotically stable. Furthermore, we indicate that the features of the ant trajectories such as convergence speed or oscillation wave length are controlled by the angle [Formula: see text]. For [Formula: see text], we present numerical evidence that indicates that ants are unable to follow pheromone trails. We also assess our model by comparing it to previous experimental results, showing that the solutions' behavior falls into biologically meaningful ranges. Our work provides solid mathematical support for experimental studies where it was found that ant perception follows a Weber's law, by proving that such models lead to the desired robust and stable trail following.

Cold Active Motion: How Time-Independent Disorder Affects the Motion of Self-Propelled Agents.

Assemblages of self-propelled particles, often termed active matter, exhibit collective behavior due to competition between neighbor alignment and noise-induced decoherence. However, very little is known of how the quenched (i.e., time-independent) disorder impacts active motion. Here we report on the effects of quenched disorder on the dynamics of self-propelled point particles. We identified three major types of quenched disorder relevant in the context of active matter: random torque, force, and stress. We demonstrate that even in the absence of external fluctuations ("cold active matter"), quenched disorder results in nontrivial dynamic phases not present in their "hot" counterpart. In particular, by analyzing when the equations of motion exhibit a Hamiltonian structure and when attractors may be present, we identify in which scenarios particle trapping, i.e., the asymptotic convergence of particle trajectories to bounded areas in space ("traps"), can and cannot occur. Our study provides new fundamental insights into active systems realized by self-propelled particles on natural and synthetic disordered substrates.

Markovian robots: Minimal navigation strategies for active particles.

We explore minimal navigation strategies for active particles in complex, dynamical, external fields, introducing a class of autonomous, self-propelled particles which we call Markovian robots (MR). These machines are equipped with a navigation control system (NCS) that triggers random changes in the direction of self-propulsion of the robots. The internal state of the NCS is described by a Boolean variable that adopts two values. The temporal dynamics of this Boolean variable is dictated by a closed Markov chain-ensuring the absence of fixed points in the dynamics-with transition rates that may depend exclusively on the instantaneous, local value of the external field. Importantly, the NCS does not store past measurements of this value in continuous, internal variables. We show that despite the strong constraints, it is possible to conceive closed Markov chain motifs that lead to nontrivial motility behaviors of the MR in one, two, and three dimensions. By analytically reducing the complexity of the NCS dynamics, we obtain an effective description of the long-time motility behavior of the MR that allows us to identify the minimum requirements in the design of NCS motifs and transition rates to perform complex navigation tasks such as adaptive gradient following, detection of minima or maxima, or selection of a desired value in a dynamical, external field. We put these ideas in practice by assembling a robot that operates by the proposed minimalistic NCS to evaluate the robustness of MR, providing a proof of concept that is possible to navigate through complex information landscapes with such a simple NCS whose internal state can be stored in one bit. These ideas may prove useful for the engineering of miniaturized robots.

A polar bundle of flagella can drive bacterial swimming by pushing, pulling, or coiling around the cell body.

Bacteria swim in sequences of straight runs that are interrupted by turning events. They drive their swimming locomotion with the help of rotating helical flagella. Depending on the number of flagella and their arrangement across the cell body, different run-and-turn patterns can be observed. Here, we present fluorescence microscopy recordings showing that cells of the soil bacterium Pseudomonas putida that are decorated with a polar tuft of helical flagella, can alternate between two distinct swimming patterns. On the one hand, they can undergo a classical push-pull-push cycle that is well known from monopolarly flagellated bacteria but has not been reported for species with a polar bundle of multiple flagella. Alternatively, upon leaving the pulling mode, they can enter a third slow swimming phase, where they propel themselves with their helical bundle wrapped around the cell body. A theoretical estimate based on a random-walk model shows that the spreading of a population of swimmers is strongly enhanced when cycling through a sequence of pushing, pulling, and wrapped flagellar configurations as compared to the simple push-pull-push pattern.

Large-Scale Patterns in a Minimal Cognitive Flocking Model: Incidental Leaders, Nematic Patterns, and Aggregates.

We study a minimal cognitive flocking model, which assumes that the moving entities navigate using the available instantaneous visual information exclusively. The model consists of active particles, with no memory, that interact by a short-ranged, position-based, attractive force, which acts inside a vision cone (VC), and lack velocity-velocity alignment. We show that this active system can exhibit-due to the VC that breaks Newton's third law-various complex, large-scale, self-organized patterns. Depending on parameter values, we observe the emergence of aggregates or millinglike patterns, the formation of moving-locally polar-files with particles at the front of these structures acting as effective leaders, and the self-organization of particles into macroscopic nematic structures leading to long-ranged nematic order. Combining simulations and nonlinear field equations, we show that position-based active models, as the one analyzed here, represent a new class of active systems fundamentally different from other active systems, including velocity-alignment-based flocking systems. The reported results are of prime importance in the study, interpretation, and modeling of collective motion patterns in living and nonliving active systems.

Mesoscale pattern formation of self-propelled rods with velocity reversal.

We study self-propelled particles with velocity reversal interacting by uniaxial (nematic) alignment within a coarse-grained hydrodynamic theory. Combining analytical and numerical continuation techniques, we show that the physics of this active system is essentially controlled by the reversal frequency. In particular, we find that elongated, high-density, ordered patterns, called bands, emerge via subcritical bifurcations from spatially homogeneous states. Our analysis reveals further that the interaction of bands is weakly attractive and, consequently, bands fuse upon collision in analogy with nonequilibrium nucleation processes. Moreover, we demonstrate that a renormalized positive line tension can be assigned to stable bands below a critical reversal rate, beyond which they are transversally unstable. In addition, we discuss the kinetic roughening of bands as well as their nonlinear dynamics close to the threshold of transversal instability. Altogether, the reduction of the multiparticle system onto the dynamics of bands provides a unified framework to understand the emergence and stability of nonequilibrium patterns in this self-propelled particle system. In this regard, our results constitute a proof of principle in favor of the hypothesis in microbiology that velocity reversal of gliding rod-shaped bacteria regulates the transitions between various self-organized patterns observed during the bacterial life cycle.

Superdiffusion, large-scale synchronization, and topological defects.

We study an ensemble of random walkers carrying internal noisy phase oscillators which are synchronized among the walkers by local interactions. Due to individual mobility, the interaction partners of every walker change randomly, hereby introducing an additional, independent source of fluctuations, thus constituting the intrinsic nonequilibrium nature of the temporal dynamics. We employ this paradigmatic model system to discuss how the emergence of order is affected by the motion of individual entities. In particular, we consider both normal diffusive motion and superdiffusion. A non-Hamiltonian field theory including multiplicative noise terms is derived which describes the nonequilibrium dynamics at the macroscale. This theory reveals a defect-mediated transition from incoherence to quasi-long-range order for normal diffusion of oscillators in two dimensions, implying a power-law dependence of all synchronization properties on system size. In contrast, superdiffusive transport suppresses the emergence of topological defects, thereby inducing a continuous synchronization transition to long-range order in two dimensions. These results are consistent with particle-based simulations.