Intermittent Pili-Mediated Forces Fluidize Neisseria meningitidis Aggregates Promoting Vascular Colonization.

Neisseria meningitidis, a bacterium responsible for meningitis and septicemia, proliferates and eventually fills the lumen of blood capillaries with multicellular aggregates. The impact of this aggregation process and its specific properties are unknown. We first show that aggregative properties are necessary for efficient infection and study their underlying physical mechanisms. Micropipette aspiration and single-cell tracking unravel unique features of an atypical fluidized phase, with single-cell diffusion exceeding that of isolated cells. A quantitative description of the bacterial pair interactions combined with active matter physics-based modeling show that this behavior relies on type IV pili active dynamics that mediate alternating phases of bacteria fast mutual approach, contact, and release. These peculiar fluid properties proved necessary to adjust to the geometry of capillaries upon bacterial proliferation. Intermittent attractive forces thus generate a fluidized phase that allows for efficient colonization of the blood capillary network during infection.

Activity waves and freestanding vortices in populations of subcritical Quincke rollers.

Virtually all of the many active matter systems studied so far are made of units (biofilaments, cells, colloidal particles, robots, animals, etc.) that move even when they are alone or isolated. Their collective properties continue to fascinate, and we now understand better how they are unique to the bulk transduction of energy into work. Here we demonstrate that systems in which isolated but potentially active particles do not move can exhibit specific and remarkable collective properties. Combining experiments, theory, and numerical simulations, we show that such subcritical active matter can be realized with Quincke rollers, that is, dielectric colloidal particles immersed in a conducting fluid subjected to a vertical DC electric field. Working below the threshold field value marking the onset of motion for a single colloid, we find fast activity waves, reminiscent of excitable systems, and stable, arbitrarily large self-standing vortices made of thousands of particles moving at the same speed. Our theoretical model accounts for these phenomena and shows how they can arise in the absence of confining boundaries and individual chirality. We argue that our findings imply that a faithful description of the collective properties of Quincke rollers need to consider the fluid surrounding particles.

Extreme Spontaneous Deformations of Active Crystals.

We demonstrate that two-dimensional crystals made of active particles can experience extremely large spontaneous deformations without melting. Using particles mostly interacting via pairwise repulsive forces, we show that such active crystals maintain long-range bond order and algebraically decaying positional order, but with an exponent η not limited by the 1/3 bound given by the (equilibrium) KTHNY theory. We rationalize our findings using linear elastic theory and show the existence of two well-defined effective temperatures quantifying respectively large-scale deformations and bond-order fluctuations. The root of these phenomena lies in the sole time-persistence of the intrinsic axes of particles, and they should thus be observed in many different situations.

Metastability of Discrete-Symmetry Flocks.

We study the stability of the ordered phase of flocking models with a scalar order parameter. Using both the active Ising model and a hydrodynamic description, we show that droplets of particles moving in the direction opposite to that of the ordered phase nucleate and grow. We characterize analytically this self-similar growth and demonstrate that droplets spread ballistically in all directions. Our results imply that, in the thermodynamic limit, discrete-symmetry flocks-and, by extension, continuous-symmetry flocks with rotational anisotropy-are metastable in all dimensions.

Weak synchronization and large-scale collective oscillation in dense bacterial suspensions.

Collective oscillatory behaviour is ubiquitous in nature, having a vital role in many biological processes from embryogenesis and organ development to pace-making in neuron networks. Elucidating the mechanisms that give rise to synchronization is essential to the understanding of biological self-organization. Collective oscillations in biological multicellular systems often arise from long-range coupling mediated by diffusive chemicals, by electrochemical mechanisms, or by biomechanical interaction between cells and their physical environment. In these examples, the phase of some oscillatory intracellular degree of freedom is synchronized. Here, in contrast, we report the discovery of a weak synchronization mechanism that does not require long-range coupling or inherent oscillation of individual cells. We find that millions of motile cells in dense bacterial suspensions can self-organize into highly robust collective oscillatory motion, while individual cells move in an erratic manner, without obvious periodic motion but with frequent, abrupt and random directional changes. So erratic are individual trajectories that uncovering the collective oscillations of our micrometre-sized cells requires individual velocities to be averaged over tens or hundreds of micrometres. On such large scales, the oscillations appear to be in phase and the mean position of cells typically describes a regular elliptic trajectory. We found that the phase of the oscillations is organized into a centimetre-scale travelling wave. We present a model of noisy self-propelled particles with strictly local interactions that accounts faithfully for our observations, suggesting that self-organized collective oscillatory motion results from spontaneous chiral and rotational symmetry breaking. These findings reveal a previously unseen type of long-range order in active matter systems (those in which energy is spent locally to produce non-random motion). This mechanism of collective oscillation may inspire new strategies to control the self-organization of active matter and swarming robots.

Susceptibility of Polar Flocks to Spatial Anisotropy.

We study the effect of spatial anisotropy on polar flocks by investigating active q-state clock models in two dimensions. In contrast to the equilibrium case, we find that any amount of anisotropy is asymptotically relevant, drastically altering the phenomenology from that of the rotationally invariant case. All of the well-known physics of the Vicsek model, from giant density fluctuations to microphase separation, is replaced by that of the active Ising model, with short-range correlations and complete phase separation. These changes appear beyond a length scale that diverges in the q→∞ limit, so that the Vicsek-model phenomenology is observed in finite systems for weak enough anisotropy, i.e., sufficiently high q. We provide a scaling argument which explains why anisotropy has such different effects in the passive and active cases.

Metastability of Constant-Density Flocks.

We study numerically the Toner-Tu field theory where the density field is maintained constant, a limit case of "Malthusian" flocks for which the asymptotic scaling of correlation functions in the ordered phase is known exactly. While we confirm these scaling laws, we also show that such constant-density flocks are metastable to the nucleation of a specific defect configuration, and are replaced by a globally disordered phase consisting of asters surrounded by shock lines that constantly evolves and remodels itself. We demonstrate that the main source of disorder lies along shock lines, rendering this active foam fundamentally different from the corresponding equilibrium system. We thus show that in the context of active matter also, a result obtained at all orders of perturbation theory can be superseded by nonperturbative effects, calling for a different approach.

Small Obstacle in a Large Polar Flock.

We show that arbitrarily large polar flocks are susceptible to the presence of a single small obstacle. In a wide region of parameter space, the obstacle triggers counterpropagating dense bands leading to reversals of the flow. In very large systems, these bands interact, yielding a never-ending chaotic dynamics that constitutes a new disordered phase of the system. While most of these results were obtained using simulations of aligning self-propelled particles, we find similar phenomena at the continuous level, not when considering the basic Toner-Tu hydrodynamic theory, but in simulations of truncations of the relevant Boltzmann equation.

Data-driven quantitative modeling of bacterial active nematics.

Active matter comprises individual units that convert energy into mechanical motion. In many examples, such as bacterial systems and biofilament assays, constituent units are elongated and can give rise to local nematic orientational order. Such "active nematics" systems have attracted much attention from both theorists and experimentalists. However, despite intense research efforts, data-driven quantitative modeling has not been achieved, a situation mainly due to the lack of systematic experimental data and to the large number of parameters of current models. Here, we introduce an active nematics system made of swarming filamentous bacteria. We simultaneously measure orientation and velocity fields and show that the complex spatiotemporal dynamics of our system can be quantitatively reproduced by a type of microscopic model for active suspensions whose important parameters are all estimated from comprehensive experimental data. This provides unprecedented access to key effective parameters and mechanisms governing active nematics. Our approach is applicable to different types of dense suspensions and shows a path toward more quantitative active matter research.

Long-Range Nematic Order in Two-Dimensional Active Matter.

Working in two space dimensions, we show that the orientational order emerging from self-propelled polar particles aligning nematically is quasi-long-ranged beyond ℓ_{r}, the scale associated to induced velocity reversals, which is typically extremely large and often cannot even be measured. Below ℓ_{r}, nematic order is long-range. We construct and study a hydrodynamic theory for this de facto phase and show that its structure and symmetries differ from conventional descriptions of active nematics. We check numerically our theoretical predictions, in particular the presence of π-symmetric propagative sound modes, and provide estimates of all scaling exponents governing long-range space-time correlations.

Susceptibility of Orientationally Ordered Active Matter to Chirality Disorder.

We investigate the susceptibility of long-range ordered phases of two-dimensional dry aligning active matter to population disorder, taken in the form of a distribution of intrinsic individual chiralities. Using a combination of particle-level models and hydrodynamic theories derived from them, we show that while in finite systems all ordered phases resist a finite amount of such chirality disorder, the homogeneous ones (polar flocks and active nematics) are unstable to any amount of disorder in the infinite-size limit. On the other hand, we find that the inhomogeneous solutions of the coexistence phase (bands) may resist a finite amount of chirality disorder even asymptotically.

Breakdown of Ergodicity and Self-Averaging in Polar Flocks with Quenched Disorder.

We show that spatial quenched disorder affects polar active matter in ways more complex and far reaching than heretofore believed. Using simulations of the 2D Vicsek model subjected to random couplings or a disordered scattering field, we find in particular that ergodicity is lost in the ordered phase, the nature of which we show to depend qualitatively on the type of quenched disorder: for random couplings, it remains long-range ordered, but qualitatively different from the pure (disorderless) case. For random scatterers, polar order varies with system size but we find strong non-self-averaging, with sample-to-sample fluctuations dominating asymptotically, which prevents us from elucidating the asymptotic status of order.

Fluctuation-Induced Phase Separation in Metric and Topological Models of Collective Motion.

We study the role of noise on the nature of the transition to collective motion in dry active matter. Starting from field theories that predict a continuous transition at the deterministic level, we show that fluctuations induce a density-dependent shift of the onset of order, which in turn changes the nature of the transition into a phase-separation scenario. Our results apply to a range of systems, including models in which particles interact with their "topological" neighbors that have been believed so far to exhibit a continuous onset of order. Our analytical predictions are confirmed by numerical simulations of fluctuating hydrodynamics and microscopic models.

Self-Organized Critical Coexistence Phase in Repulsive Active Particles.

We revisit motility-induced phase separation in two models of active particles interacting by pairwise repulsion and uncover new qualitative features: the resulting dense phase contains gas bubbles distributed algebraically up to a typically extremely large cutoff scale. At large enough system size and/or global density, all the gas may be contained inside the bubbles, at which point the system is microphase separated with a finite cutoff bubble scale. We further observe that the ordering is clearly anomalous, with different dynamics for the coarsening of the dense phase and of the gas bubbles. This self-organized critical phenomenology is reproduced by a "reduced bubble model" that implements the basic idea of reverse Ostwald ripening put forward in Tjhung et al. [Phys. Rev. X 8, 031080 (2018)PRXHAE2160-330810.1103/PhysRevX.8.031080].

Quantitative Assessment of the Toner and Tu Theory of Polar Flocks.

We present a quantitative assessment of the Toner and Tu theory describing the universal scaling of fluctuations in polar phases of dry active matter. Using large-scale simulations of the Vicsek model in two and three dimensions, we find the overall phenomenology and generic algebraic scaling predicted by Toner and Tu, but our data on density correlations reveal some qualitative discrepancies. The values of the associated scaling exponents we estimate differ significantly from those conjectured in 1995. In particular, we identify a large crossover scale beyond which flocks are only weakly anisotropic. We discuss the meaning and consequences of these results.

Convergence of Nonperturbative Approximations to the Renormalization Group.

We provide analytical arguments showing that the "nonperturbative" approximation scheme to Wilson's renormalization group known as the derivative expansion has a finite radius of convergence. We also provide guidelines for choosing the regulator function at the heart of the procedure and propose empirical rules for selecting an optimal one, without prior knowledge of the problem at stake. Using the Ising model in three dimensions as a testing ground and the derivative expansion at order six, we find fast convergence of critical exponents to their exact values, irrespective of the well-behaved regulator used, in full agreement with our general arguments. We hope these findings will put an end to disputes regarding this type of nonperturbative methods.

Understanding Dense Active Nematics from Microscopic Models.

We study dry, dense active nematics at both particle and continuous levels. Specifically, extending the Boltzmann-Ginzburg-Landau approach, we derive well-behaved hydrodynamic equations from a Vicsek-style model with nematic alignment and pairwise repulsion. An extensive study of the phase diagram shows qualitative agreement between the two levels of description. We find in particular that the dynamics of topological defects strongly depends on parameters and can lead to "arch" solutions forming a globally polar, smecticlike arrangement of Néel walls. We show how these configurations are at the origin of the defect ordered states reported previously. This work offers a detailed understanding of the theoretical description of dense active nematics directly rooted in their microscopic dynamics.

Disentangling and modeling interactions in fish with burst-and-coast swimming reveal distinct alignment and attraction behaviors.

The development of tracking methods for automatically quantifying individual behavior and social interactions in animal groups has open up new perspectives for building quantitative and predictive models of collective behavior. In this work, we combine extensive data analyses with a modeling approach to measure, disentangle, and reconstruct the actual functional form of interactions involved in the coordination of swimming in Rummy-nose tetra (Hemigrammus rhodostomus). This species of fish performs burst-and-coast swimming behavior that consists of sudden heading changes combined with brief accelerations followed by quasi-passive, straight decelerations. We quantify the spontaneous stochastic behavior of a fish and the interactions that govern wall avoidance and the reaction to a neighboring fish, the latter by exploiting general symmetry constraints for the interactions. In contrast with previous experimental works, we find that both attraction and alignment behaviors control the reaction of fish to a neighbor. We then exploit these results to build a model of spontaneous burst-and-coast swimming and interactions of fish, with all parameters being estimated or directly measured from experiments. This model quantitatively reproduces the key features of the motion and spatial distributions observed in experiments with a single fish and with two fish. This demonstrates the power of our method that exploits large amounts of data for disentangling and fully characterizing the interactions that govern collective behaviors in animals groups.

Large-scale vortex lattice emerging from collectively moving microtubules.

Spontaneous collective motion, as in some flocks of bird and schools of fish, is an example of an emergent phenomenon. Such phenomena are at present of great interest and physicists have put forward a number of theoretical results that so far lack experimental verification. In animal behaviour studies, large-scale data collection is now technologically possible, but data are still scarce and arise from observations rather than controlled experiments. Multicellular biological systems, such as bacterial colonies or tissues, allow more control, but may have many hidden variables and interactions, hindering proper tests of theoretical ideas. However, in systems on the subcellular scale such tests may be possible, particularly in in vitro experiments with only few purified components. Motility assays, in which protein filaments are driven by molecular motors grafted to a substrate in the presence of ATP, can show collective motion for high densities of motors and attached filaments. This was demonstrated recently for the actomyosin system, but a complete understanding of the mechanisms at work is still lacking. Here we report experiments in which microtubules are propelled by surface-bound dyneins. In this system it is possible to study the local interaction: we find that colliding microtubules align with each other with high probability. At high densities, this alignment results in self-organization of the microtubules, which are on average 15 µm long, into vortices with diameters of around 400 µm. Inside the vortices, the microtubules circulate both clockwise and anticlockwise. On longer timescales, the vortices form a lattice structure. The emergence of these structures, as verified by a mathematical model, is the result of the smooth, reptation-like motion of single microtubules in combination with local interactions (the nematic alignment due to collisions)--there is no need for long-range interactions. Apart from its potential relevance to cortical arrays in plant cells and other biological situations, our study provides evidence for the existence of previously unsuspected universality classes of collective motion phenomena.