Topological defects in multi-layered swarming bacteria.

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid dynamics of swarming bacteria. The results are compared to the predictions of two-dimensional active nematics. We show that, even though some of the assumptions underlying the theory do not hold, the swarm dynamics is in agreement with two-dimensional nematic theory. In particular, we look into the multi-layered structure of the swarm, which is an important feature of real, natural colonies, and find a strong coupling between layers. Our results suggest that the defect-charge density is hyperuniform, i.e., that long range density-fluctuations are suppressed.

Detecting and characterizing phase transitions in active matter using entropy.

A major challenge in the study of active matter lies in quantitative characterization of phases and transitions between them. We show how the entropy of a collection of active objects can be used to classify regimes and spatial patterns in their collective behavior. Specifically, we estimate the contributions to the total entropy from correlations between the degrees of freedom of position and orientation. This analysis pin-points the flocking transition in the Vicsek model while clarifying the physical mechanism behind the transition. When applied to experiments on swarming Bacillus subtilis with different cell aspect ratios and overall bacterial area fractions, the entropy analysis reveals a rich phase diagram with transitions between qualitatively different swarm statistics. We discuss physical and biological implications of these findings.

Turbulence-induced clustering in compressible active fluids.

We study a novel phase of active polar fluids, which is characterized by the continuous creation and destruction of dense clusters due to self-sustained turbulence. This state arises due to the interplay between self-advection of the aligned swimmers and their defect topology. The typical cluster size is determined by the characteristic vortex size. Our results are obtained by investigating a continuum model of compressible polar active fluids, which incorporates typical experimental observations in bacterial suspensions, in particular a non-monotone dependence of speed on density.

Impact of Hydrodynamics on the First Stages of Biofilm Formation in Forward Osmosis with Spacers.

Initial deposition of bacteria is a critical stage during biofilm formation and biofouling development in membrane systems used in the water industry. However, the effects of hydrodynamic conditions on spatiotemporal deposition patterns of bacteria during the initial stages of biofilm formation remain unclear. Large field epifluorescence microscopy enabled in situ and real-time tracking of Bacillus subtilis in a forward osmosis system with spacers during the first 4 h of biofilm formation. This study quantitatively compares the spatiotemporal deposition patterns between different hydrodynamic conditions: high and low permeate water flux (6 or 30 L m-2 h-1) as well as high and low crossflow velocity (1 or 14 cm s-1). Low crossflow velocity and high permeate water flux maximized bacterial attachment to the membrane surface, which was 60 times greater (6 × 103 cells mm-2) than at high crossflow velocity and low permeate water flux (<100 cells mm-2). Imaging at 30 s intervals revealed three phases (i.e., lag, exponential, and linear) in the development of deposition over time. Quantification of spatial deposition patterns showed that an increase in the ratio of permeate water flux to crossflow velocity led to a homogeneous deposition, while a decrease had the opposite effect. The insights of this research indicate that an appropriate choice of hydrodynamic conditions can minimize bacteria accumulation prior to biofilm formation in new and cleaned FO membrane systems treating water of high fouling propensity.

Chaotic Model for Lévy Walks in Swarming Bacteria.

We describe a new mechanism for Lévy walks, explaining the recently observed superdiffusion of swarming bacteria. The model hinges on several key physical properties of bacteria, such as an elongated cell shape, self-propulsion, and a collectively generated regular vortexlike flow. In particular, chaos and Lévy walking are a consequence of group dynamics. The model explains how cells can fine-tune the geometric properties of their trajectories. Experiments confirm the spectrum of these patterns in fluorescently labeled swarming Bacillus subtilis.

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.

Anomalous Fluctuations in the Orientation and Velocity of Swarming Bacteria.

Simultaneous acquisition of phase-contrast light microscopy and fluorescently labeled bacteria, moving within a dense swarm, reveals the intricate interactions between cells and the collective flow around them. By comparing wild-type and immotile cells embedded in a dense wild-type swarm, the effect of the active thrust generated by the flagella can be singled out. It is shown that while the distribution of angles among cell velocity, cell orientation, and the local flow around it is Gaussian-like for immotile bacteria, wild-type cells exhibit anomalous non-Gaussian deviations and are able to move in trajectories perpendicular to the collective flow. Thus, cells can maneuver or switch between local streams and jets. A minimal model describing bacteria as hydrodynamic force dipoles shows that steric effects, hydrodynamics interactions, and local alignments all have to be taken into account to explain the observed dynamics. These findings shed light on the physical mechanisms underlying bacterial swarming and the balance between individual and collective dynamics.

Antibiotic-induced anomalous statistics of collective bacterial swarming.

Under sublethal antibiotics concentrations, the statistics of collectively swarming Bacillus subtilis transitions from normal to anomalous, with a heavy-tailed speed distribution and a two-step temporal correlation of velocities. The transition is due to changes in the properties of the bacterial motion and the formation of a motility-defective subpopulation that self-segregates into regions. As a result, both the colonial expansion and the growth rate are not affected by antibiotics. This phenomenon suggests a new strategy bacteria employ to fight antibiotic stress.

Periodic reversals in Paenibacillus dendritiformis swarming.

Bacterial swarming is a type of motility characterized by a rapid and collective migration of bacteria on surfaces. Most swarming species form densely packed dynamic clusters in the form of whirls and jets, in which hundreds of rod-shaped rigid cells move in circular and straight patterns, respectively. Recent studies have suggested that short-range steric interactions may dominate hydrodynamic interactions and that geometrical factors, such as a cell's aspect ratio, play an important role in bacterial swarming. Typically, the aspect ratio for most swarming species is only up to 5, and a detailed understanding of the role of much larger aspect ratios remains an open challenge. Here we study the dynamics of Paenibacillus dendritiformis C morphotype, a very long, hyperflagellated, straight (rigid), rod-shaped bacterium with an aspect ratio of ~20. We find that instead of swarming in whirls and jets as observed in most species, including the shorter T morphotype of P. dendritiformis, the C morphotype moves in densely packed straight but thin long lines. Within these lines, all bacteria show periodic reversals, with a typical reversal time of 20 s, which is independent of their neighbors, the initial nutrient level, agar rigidity, surfactant addition, humidity level, temperature, nutrient chemotaxis, oxygen level, illumination intensity or gradient, and cell length. The evolutionary advantage of this unique back-and-forth surface translocation remains unclear.

Collective motion and density fluctuations in bacterial colonies.

Flocking birds, fish schools, and insect swarms are familiar examples of collective motion that plays a role in a range of problems, such as spreading of diseases. Models have provided a qualitative understanding of the collective motion, but progress has been hindered by the lack of detailed experimental data. Here we report simultaneous measurements of the positions, velocities, and orientations as a function of time for up to a thousand wild-type Bacillus subtilis bacteria in a colony. The bacteria spontaneously form closely packed dynamic clusters within which they move cooperatively. The number of bacteria in a cluster exhibits a power-law distribution truncated by an exponential tail. The probability of finding clusters with large numbers of bacteria grows markedly as the bacterial density increases. The number of bacteria per unit area exhibits fluctuations far larger than those for populations in thermal equilibrium. Such "giant number fluctuations" have been found in models and in experiments on inert systems but not observed previously in a biological system. Our results demonstrate that bacteria are an excellent system to study the general phenomenon of collective motion.

Lethal protein produced in response to competition between sibling bacterial colonies.

Sibling Paenibacillus dendritiformis bacterial colonies grown on low-nutrient agar medium mutually inhibit growth through secretion of a lethal factor. Analysis of secretions reveals the presence of subtilisin (a protease) and a 12 kDa protein, termed sibling lethal factor (Slf). Purified subtilisin promotes the growth and expansion of P. dendritiformis colonies, whereas Slf is lethal and lyses P. dendritiformis cells in culture. Slf is encoded by a gene belonging to a large family of bacterial genes of unknown function, and the gene is predicted to encode a protein of approximately 20 kDa, termed dendritiformis sibling bacteriocin. The 20 kDa recombinant protein was produced and found to be inactive, but exposure to subtilisin resulted in cleavage to the active, 12 kDa form. The experimental results, combined with mathematical modeling, show that subtilisin serves to regulate growth of the colony. Below a threshold concentration, subtilisin promotes colony growth and expansion. However, once it exceeds a threshold, as occurs at the interface between competing colonies, Slf is then secreted into the medium to rapidly reduce cell density by lysis of the bacterial cells. The presence of genes encoding homologs of dendritiformis sibling bacteriocin in other bacterial species suggests that this mechanism for self-regulation of colony growth might not be limited to P. dendritiformis.

Scale-invariant correlations in dynamic bacterial clusters.

In Bacillus subtilis colonies, motile bacteria move collectively, spontaneously forming dynamic clusters. These bacterial clusters share similarities with other systems exhibiting polarized collective motion, such as bird flocks or fish schools. Here we study experimentally how velocity and orientation fluctuations within clusters are spatially correlated. For a range of cell density and cluster size, the correlation length is shown to be 30% of the spatial size of clusters, and the correlation functions collapse onto a master curve after rescaling the separation with correlation length. Our results demonstrate that correlations of velocity and orientation fluctuations are scale invariant in dynamic bacterial clusters.

Deadly competition between sibling bacterial colonies.

Bacteria can secrete a wide array of antibacterial compounds when competing with other bacteria for the same resources. Some of these compounds, such as bacteriocins, can affect bacteria of similar or closely related strains. In some cases, these secretions have been found to kill sibling cells that belong to the same colony. Here, we present experimental observations of competition between 2 sibling colonies of Paenibacillus dendritiformis grown on a low-nutrient agar gel. We find that neighboring colonies (growing from droplet inoculation) mutually inhibit growth through secretions that become lethal if the level exceeds a well-defined threshold. In contrast, within a single colony developing from a droplet inoculation, no growth inhibition is observed. However, growth inhibition and cell death are observed if material extracted from the agar between 2 growing colonies is introduced outside a growing single colony. To interpret the observations, we devised a simple mathematical model for the secretion of an antibacterial compound. Simulations of this model illustrate how secretions from neighboring colonies can be deadly, whereas secretions from a single colony growing from a droplet are not.

Physical characteristics of mixed-species swarming colonies.

In nature, bacterial collectives typically consist of multiple species, which are interacting both biochemically and physically. Nonetheless, past studies on the physical properties of swarming bacteria were focused on axenic (single-species) populations. In bacterial swarming, intricate interactions between the individuals lead to clusters, rapid jets, and vortices that depend on cell characteristics such as speed and length. In this work, we show the first results of rapidly swarming mixed-species populations of Bacillus subtilis and Serratia marcescens, two model swarm species that are known to swarm well in axenic situations. In mixed liquid cultures, both species have higher reproduction rates. We show that the mixed population swarms together well and that the fraction between the species determines all dynamical scales-from the microscopic (e.g., speed distribution), mesoscopic (vortex size), and macroscopic (colony structure and size). Understanding mixed-species swarms is essential for a comprehensive understanding of the bacterial swarming phenomenon and its biological and evolutionary implications.

Direct visualization of colloid transport over natural heterogeneous and artificial smooth rock surfaces.

Colloid transport in fractured rock formations is an important process impacting the fate of pollutants in the subsurface. Despite intensive and outstanding research on their transport phenomena, the impact of small-scale surface heterogeneity on colloid behavior at the fracture scale remains difficult to assess. In particular, there is relatively little direct experimental evidence on the impact of natural fracture surface heterogeneity on colloid transport. To investigate this, we developed an experimental setup allowing the direct visualization of fluorescent colloid transport in a flow cell containing a natural chalk rock sample while simultaneously monitoring effluent colloid concentrations. We used samples containing both a natural fracture surface and an artificially made smooth surface from the same chalk core. We characterized the roughness and chemical composition of both surface types and numerically calculated each surface's velocity field. From the experiments, we obtained direct images of colloid transport over the surfaces, from which we calculated their dispersion coefficients and quantified the residual deposition of colloids on the rock surface. We also measured the colloid breakthrough curves by collecting eluent samples from the flow cell outlet. The natural fracture surface exhibited larger physical and chemical heterogeneity than the smooth, artificially generated surface. The aperture variability across the natural surface led to preferential flow and colloid transport which was qualitatively apparent in the fluorescent images. The colloid transport patterns matched the calculated velocity fields well, directly linking the surface topography and aperture variation to colloid transport. Compared to the artificially made surface, the natural surface also showed higher dispersion coefficients, which corresponded to the colloids' earlier breakthrough from the flow cell. While we found differences between the elemental composition of the natural and artificially smooth surfaces, we could not observe their impact on the colloids' surface attachment and retention. The main novelty in this work is the coupling of direct colloid transport imaging, breakthrough curve measurements, and colloid surface deposition analyses, in a flow cell containing a natural carbonate rock sample. Our experimental setup can be used to further investigate the link between surface heterogeneity, both chemical and physical, and colloid transport and deposition in natural rock fractures.

Mixed-species bacterial swarms show an interplay of mixing and segregation across scales.

Bacterial swarms are a highly-researched example of natural active matter. In particular, the interplay between biological interactions and the physics underlying the swarming dynamics is of both biological and physical interest. In this paper, we study mixed swarms of Bacillus subtilis and Pseudomonas aeruginosa. We find intricate interactions between the species, showing both cooperation and segregation across different spatial and temporal scales. On one hand, even though axenic colonies grow on disparate time scale, an order of magnitude apart, the two-species swarm together, forming a single, combined colony. However, the rapidly moving populations are locally segregated, with different characteristic speeds and lengths (or cluster sizes) that depend on the ratio between the species. Comparison with controlled mutant strains suggest that both the physical and known biological differences in species characteristics may not be enough to explain the segregation between the species in the mixed swarm. We hypothesize that the heterogeneous spatial distribution is due to some mechanism that enables bacteria to recognize their own kind, whose precise origin we could not identify.

Biophysical aspects underlying the swarm to biofilm transition.

Bacteria organize in a variety of collective states, from swarming-rapid surface exploration, to biofilms-highly dense immobile communities attributed to stress resistance. It has been suggested that biofilm and swarming are oppositely controlled, making this transition particularly interesting for understanding the ability of bacterial colonies to adapt to challenging environments. Here, the swarm to biofilm transition is studied in Bacillus subtilis by analyzing the bacterial dynamics both on the individual and collective scales. We show that both biological and physical processes facilitate the transition. A few individual cells that initiate the biofilm program cause nucleation of large, approximately scale-free, stationary aggregates of trapped swarm cells. Around aggregates, cells continue swarming almost unobstructed, while inside, trapped cells are added to the biofilm. While our experimental findings rule out previously suggested purely physical effects as a trigger for biofilm formation, they show how physical processes, such as clustering and jamming, accelerate biofilm formation.

Collective motion of surfactant-producing bacteria imparts superdiffusivity to their upper surface.

Swarming bacteria move on agar surfaces in groups, using flagella as motive organelles. Motility depends critically on surface wetness, which is enabled by osmotic agents and surfactants secreted by the bacteria. In a recent study, the upper surface of an Escherichia coli swarm was found to be stationary, as determined from the motion of MgO particles deposited on the swarm. This led to the remarkable conclusion that the bacteria move between two stationary surfaces-the agar gel below and the liquid/air interface above. That study suggested that secreted surfactants may contribute to immobilizing the upper surface of a swarm. Here, we test this proposition using two robust surfactant-producing bacteria. We find antithetically that the upper surfaces of both these swarms are mobile, showing a superdiffusive behavior in swarms with stronger surfactant activity. Superdiffusive behavior was not observed on the surface of a drop of bacterial culture, on bacteria-free culture supernatant, or on nonswarming surfactant-producer colonies, which suggests that superdiffusion is an emergent property resulting from the interaction of the collective motion of the bacteria within the swarm with the surfactant layer above. Swarming not only allows bacteria to forage for food, but also confers protective advantages against antimicrobial agents. Our results are therefore relevant to superdiffusive strategies in biological foraging and survival.

Heterogeneous bacterial swarms with mixed lengths.

Heterogeneous systems of active matter exhibit a range of complex emergent dynamical patterns. In particular, it is difficult to predict the properties of the mixed system based on its constituents. These considerations are particularly significant for understanding realistic bacterial swarms, which typically develop heterogeneities even when grown from a single cell. Here, mixed swarms of cells with different aspect ratios are studied both experimentally and in simulations. In contrast with previous theory, there is no macroscopic phase segregation. However, locally, long cells act as nucleation cites, around which aggregates of short, rapidly moving cells can form, resulting in enhanced swarming speeds. On the other hand, high fractions of long cells form a bottleneck for efficient swarming. Our results suggest a physical advantage for the spontaneous heterogeneity of bacterial swarm populations.

Swarm Hunting and Cluster Ejections in Chemically Communicating Active Mixtures.

A large variety of microorganisms produce molecules to communicate via complex signaling mechanisms such as quorum sensing and chemotaxis. The biological diversity is enormous, but synthetic inanimate colloidal microswimmers mimic microbiological communication (synthetic chemotaxis) and may be used to explore collective behaviour beyond the one-species limit in simpler setups. In this work we combine particle based and continuum simulations as well as linear stability analyses, and study a physical minimal model of two chemotactic species. We observed a rich phase diagram comprising a "hunting swarm phase", where both species self-segregate and form swarms, pursuing, or hunting each other, and a "core-shell-cluster phase", where one species forms a dense cluster, which is surrounded by a (fluctuating) corona of particles from the other species. Once formed, these clusters can dynamically eject their core such that the clusters almost turn inside out. These results exemplify a physical route to collective behaviours in microorganisms and active colloids, which are so-far known to occur only for comparatively large and complex animals like insects or crustaceans.