Learning the space-time phase diagram of bacterial swarm expansion

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.

United under stress: High-speed transport network emerging at bacterial living edge

Individuals tend to move freely when there is enough room but would act collectively for their survival under external stress. In the case of living cells, for instance, when a drop of low-density flagellated bacterial solution is transferred onto the agar surface, the initially disordered movement of individual bacteria would be replaced with coordinated cell swarming after a lag phase of a few hours. Here, we study how such cooperation is established while overcoming the disorder at the onset of the lag phase with single nanoparticle tracking. Upon the spreading of the droplet, the bacteria in the solution cluster and align near the almost immobilized contact line confining the drop, forming a narrow ring of cells. As individual cells move in and out of the ring continuously, certain flow patterns emerge in the inter-bacterial fluid. We reveal high-speed long-distance unidirectional flows with definite chirality along the outside of the ring, along the inside of the ring and across the ring. We speculate that these flows enable the fast and efficient transport, facilitating the communication and unification of the bacterial community.

Computational modeling of angiogenesis: The importance of cell rearrangements during vascular growth

Angiogenesis is the process wherein endothelial cells (ECs) form sprouts that elongate from the pre-existing vasculature to create new vascular networks. In addition to its essential role in normal development, angiogenesis plays a vital role in pathologies such as cancer, diabetes and atherosclerosis. Mathematical and computational modeling has contributed to unraveling its complexity. Many existing theoretical models of angiogenic sprouting are based on the "snail-trail" hypothesis. This framework assumes that leading ECs positioned at sprout tips migrate toward low-oxygen regions while other ECs in the sprout passively follow the leaders' trails and proliferate to maintain sprout integrity. However, experimental results indicate that, contrary to the snail-trail assumption, ECs exchange positions within developing vessels, and the elongation of sprouts is primarily driven by directed migration of ECs. The functional role of cell rearrangements remains unclear. This review of the theoretical modeling of angiogenesis is the first to focus on the phenomenon of cell mixing during early sprouting. We start by describing the biological processes that occur during early angiogenesis, such as phenotype specification, cell rearrangements and cell interactions with the microenvironment. Next, we provide an overview of various theoretical approaches that have been employed to model angiogenesis, with particular emphasis on recent in silico models that account for the phenomenon of cell mixing. Finally, we discuss when cell mixing should be incorporated into theoretical models and what essential modeling components such models should include in order to investigate its functional role. This article is categorized under: Cardiovascular Diseases > Computational Models Cancer > Computational Models.

Simultaneous spatiotemporal transcriptomics and microscopy of Bacillus subtilis swarm development reveal cooperation across generations

Development of microbial communities is a complex multiscale phenomenon with wide-ranging biomedical and ecological implications. How biological and physical processes determine emergent spatial structures in microbial communities remains poorly understood due to a lack of simultaneous measurements of gene expression and cellular behaviour in space and time. Here we combined live-cell microscopy with a robotic arm for spatiotemporal sampling, which enabled us to simultaneously acquire phenotypic imaging data and spatiotemporal transcriptomes during Bacillus subtilis swarm development. Quantitative characterization of the spatiotemporal gene expression patterns revealed correlations with cellular and collective properties, and phenotypic subpopulations. By integrating these data with spatiotemporal metabolome measurements, we discovered a spatiotemporal cross-feeding mechanism fuelling swarm development: during their migration, earlier generations deposit metabolites which are consumed by later generations that swarm across the same location. These results highlight the importance of spatiotemporal effects during the emergence of phenotypic subpopulations and their interactions in bacterial communities.

Microbes from mature compost to promote bacterial chemotactic motility via tricarboxylic acid cycle-regulated biochemical metabolisms for enhanced composting performance

This study aims to reveal the underlying mechanisms of mature compost addition for improving organic waste composting. Composting experiments and metagenomic analysis were conducted to elucidate the role of mature compost addition to regulate microbial metabolisms and physiological behaviors for composting amelioration. Mature compost with or without inactivation pretreatment was added to the composting of kitchen and garden wastes at 0%, 5%, 10%, 15%, and 20% (by wet weight) for comparison. Results show that mature compost promoted pyruvate metabolism, tricarboxylic acid (TCA) cycle, and oxidative phosphorylation to produce heat and energy to accelerate temperature increase for composting initiation and biological contaminant removal (>78%) for pasteurization. Energy requirement drives bacterial chemotactic motility towards nutrient-rich regions to sustain organic biodegradation. Nevertheless, when NADH formation exceeded NAD+ regeneration in oxidative phosphorylation, TCA cycle was restrained to limit continuous temperature increase and recover high intracellular NAD+/NADH ratio to secure stable oxidation reactions.

Interplay of cell motility and self-secreted extracellular polymeric substance induced depletion effects on spatial patterning in a growing microbial colony

Reproducing bacteria self-organize to develop patterned biofilms in various conditions. Various factors contribute to the shaping of a multicellular bacterial organization. Here we investigate how motility force and self-secreted extracellular polymeric substances (EPS) influence bacterial cell aggregation, leading to phase-separated colonies using a particle-based/individual-based model. Our findings highlight the critical role of the interplay between motility force and depletion effects in regulating phase separation within a growing colony under far-from-equilibrium conditions. We observe that increased motility force hinders depletion-induced cell aggregation and phase segregation, necessitating a higher depletion effect for highly motile bacteria to undergo phase separation within a growing biofilm. We present a phase diagram illustrating the systematic variation of motility force and repulsive mechanical force, shedding light on the combined contributions of these two factors: self-propulsive motion and aggregation due to the depletion effect, resulting in the presence of small to large bacterial aggregates. Furthermore, our study reveals the dynamic nature of clustering, marked by changes in cluster size over time. Additionally, our findings suggest that differential dispersion among the components can lead to the localization of EPS at the periphery of a growing colony. Our study enhances the understanding of the collective dynamics of motile bacterial cells within a growing colony, particularly in the presence of a self-secreted polymer-driven depletion effect.

Tracking bacteria at high density with FAST, the Feature-Assisted Segmenter/Tracker

Most bacteria live attached to surfaces in densely-packed communities. While new experimental and imaging techniques are beginning to provide a window on the complex processes that play out in these communities, resolving the behaviour of individual cells through time and space remains a major challenge. Although a number of different software solutions have been developed to track microorganisms, these typically require users either to tune a large number of parameters or to groundtruth a large volume of imaging data to train a deep learning model-both manual processes which can be very time consuming for novel experiments. To overcome these limitations, we have developed FAST, the Feature-Assisted Segmenter/Tracker, which uses unsupervised machine learning to optimise tracking while maintaining ease of use. Our approach, rooted in information theory, largely eliminates the need for users to iteratively adjust parameters manually and make qualitative assessments of the resulting cell trajectories. Instead, FAST measures multiple distinguishing 'features' for each cell and then autonomously quantifies the amount of unique information each feature provides. We then use these measurements to determine how data from different features should be combined to minimize tracking errors. Comparing our algorithm with a naïve approach that uses cell position alone revealed that FAST produced 4 to 10 fold fewer tracking errors. The modular design of FAST combines our novel tracking method with tools for segmentation, extensive data visualisation, lineage assignment, and manual track correction. It is also highly extensible, allowing users to extract custom information from images and seamlessly integrate it into downstream analyses. FAST therefore enables high-throughput, data-rich analyses with minimal user input. It has been released for use either in Matlab or as a compiled stand-alone application, and is available at https://bit.ly/3vovDHn, along with extensive tutorials and detailed documentation.

Schooling of light reflecting fish

One of the hallmarks of the collective movement of large schools of pelagic fish are waves of shimmering flashes that propagate across the school, usually following an attack by a predator. Such flashes arise when sunlight is reflected off the specular (mirror-like) skin that characterizes many pelagic fishes, where it is otherwise thought to offer a means for camouflage in open waters. While it has been suggested that these 'shimmering waves' are a visual manifestation of the synchronized escape response of the fish, the phenomenon has been regarded only as an artifact of esthetic curiosity. In this study we apply agent-based simulations and deep learning techniques to show that, in fact, shimmering waves contain information on the behavioral dynamics of the school. Our analyses are based on a model that combines basic rules of collective motion and the propagation of light beams in the ocean, as they hit and reflect off the moving fish. We use the resulting reflection patterns to infer the essential dynamics and inter-individual interactions which are necessary to generate shimmering waves. Moreover, we show that light flashes observed by the school members themselves may extend the range at which information can be communicated across the school. Assuming that fish pay heed to this information, for example by entering an apprehensive state of reduced response-time, our analysis suggests that it can speed up the propagation of information across the school. Further still, we use an artificial neural network to show that light flashes are, on their own, indicative of the state and dynamics of the school, and are sufficient to infer the direction of attack and the shape of the school with high accuracy.

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.

Learning to cooperate for low-Reynolds-number swimming: a model problem for gait coordination

Biological microswimmers can coordinate their motions to exploit their fluid environment-and each other-to achieve global advantages in their locomotory performance. These cooperative locomotion require delicate adjustments of both individual swimming gaits and spatial arrangements of the swimmers. Here we probe the emergence of such cooperative behaviors among artificial microswimmers endowed with artificial intelligence. We present the first use of a deep reinforcement learning approach to empower the cooperative locomotion of a pair of reconfigurable microswimmers. The AI-advised cooperative policy comprises two stages: an approach stage where the swimmers get in close proximity to fully exploit hydrodynamic interactions, followed a synchronization stage where the swimmers synchronize their locomotory gaits to maximize their overall net propulsion. The synchronized motions allow the swimmer pair to move together coherently with an enhanced locomotion performance unattainable by a single swimmer alone. Our work constitutes a first step toward uncovering intriguing cooperative behaviors of smart artificial microswimmers, demonstrating the vast potential of reinforcement learning towards intelligent autonomous manipulations of multiple microswimmers for their future biomedical and environmental applications.

Proliferating active matter

The fascinating patterns of collective motion created by autonomously driven particles have fuelled active-matter research for over two decades. So far, theoretical active-matter research has often focused on systems with a fixed number of particles. This constraint imposes strict limitations on what behaviours can and cannot emerge. However, a hallmark of life is the breaking of local cell number conservation by replication and death. Birth and death processes must be taken into account, for example, to predict the growth and evolution of a microbial biofilm, the expansion of a tumour, or the development from a fertilized egg into an embryo and beyond. In this Perspective, we argue that unique features emerge in these systems because proliferation represents a distinct form of activity: not only do the proliferating entities consume and dissipate energy, they also inject biomass and degrees of freedom capable of further self-proliferation, leading to myriad dynamic scenarios. Despite this complexity, a growing number of studies document common collective phenomena in various proliferating soft-matter systems. This generality leads us to propose proliferation as another direction of active-matter physics, worthy of a dedicated search for new dynamical universality classes. Conceptual challenges abound, from identifying control parameters and understanding large fluctuations and nonlinear feedback mechanisms to exploring the dynamics and limits of information flow in self-replicating systems. We believe that, by extending the rich conceptual framework developed for conventional active matter to proliferating active matter, researchers can have a profound impact on quantitative biology and reveal fascinating emergent physics along the way.

Long-range alteration of the physical environment mediates cooperation between Pseudomonas aeruginosa swarming colonies

Pseudomonas aeruginosa makes and secretes massive amounts of rhamnolipid surfactants that enable swarming motility over biogel surfaces. But how these rhamnolipids interact with biogels to assist swarming remains unclear. Here, I use a combination of optical techniques across scales and genetically engineered strains to demonstrate that rhamnolipids can induce agar gel swelling over distances >10,000× the body size of an individual cell. The swelling front is on the micrometric scale and is easily visible using shadowgraphy. Rhamnolipid transport is not restricted to the surface of the gel but occurs through the whole thickness of the plate and, consequently, the spreading dynamics depend on the local thickness. Surprisingly, rhamnolipids can cross the whole gel and induce swelling on the opposite side of a two-face Petri dish. The swelling front delimits an area where the mechanical properties of the surface properties are modified: water wets the surface more easily, which increases the motility of individual bacteria and enables collective motility. A genetically engineered mutant unable to secrete rhamnolipids (ΔrhlA), and therefore unable to swarm, is rescued from afar with rhamnolipids produced by a remote colony. These results exemplify the remarkable capacity of bacteria to change the physical environment around them and its ecological consequences.

Learning hydrodynamic equations for active matter from particle simulations and experiments

Recent advances in high-resolution imaging techniques and particle-based simulation methods have enabled the precise microscopic characterization of collective dynamics in various biological and engineered active matter systems. In parallel, data-driven algorithms for learning interpretable continuum models have shown promising potential for the recovery of underlying partial differential equations (PDEs) from continuum simulation data. By contrast, learning macroscopic hydrodynamic equations for active matter directly from experiments or particle simulations remains a major challenge, especially when continuum models are not known a priori or analytic coarse graining fails, as often is the case for nondilute and heterogeneous systems. Here, we present a framework that leverages spectral basis representations and sparse regression algorithms to discover PDE models from microscopic simulation and experimental data, while incorporating the relevant physical symmetries. We illustrate the practical potential through a range of applications, from a chiral active particle model mimicking nonidentical swimming cells to recent microroller experiments and schooling fish. In all these cases, our scheme learns hydrodynamic equations that reproduce the self-organized collective dynamics observed in the simulations and experiments. This inference framework makes it possible to measure a large number of hydrodynamic parameters in parallel and directly from video data.

A mechanistic understanding of microcolony morphogenesis: coexistence of mobile and sessile aggregates

Most bacteria in the natural environment self-organize into collective phases such as cell clusters, swarms, patterned colonies, or biofilms. Several intrinsic and extrinsic factors, such as growth, motion, and physicochemical interactions, govern the occurrence of different phases and their coexistence. Hence, predicting the conditions under which a collective phase emerges due to individual-level interactions is crucial. Here we develop a particle-based biophysical model of bacterial cells and self-secreted extracellular polymeric substances (EPS) to decipher the interplay of growth, motility-mediated dispersal, and mechanical interactions during microcolony morphogenesis. We show that the microcolony dynamics and architecture significantly vary depending upon the heterogeneous EPS production. In particular, microcolony shows the coexistence of both motile and sessile aggregates rendering a transition towards biofilm formation. We identified that the interplay of differential dispersion and the mechanical interactions among the components of the colony determines the fate of the colony morphology. Our results provide a significant understanding of the mechano-self-regulation during biofilm morphogenesis and open up possibilities of designing experiments to test the predictions.

Swarming Motility Assays in Salmonella

Salmonella enterica has six subspecies, of which the subspecies enterica is the most important for human health. The dispersal and infectivity of this species are dependent upon flagella-driven motility. Two kinds of flagella-mediated movements have been described-swimming individually in bulk liquid and swarming collectively over a surface substrate. During swarming, the bacteria acquire a distinct physiology, the most significant consequence of which is acquisition of adaptive resistance to antibiotics. Described here are protocols to cultivate, verify, and study swimming and swarming motility in S. enterica, and an additional "border-crossing" assay, where cells "primed" to swarm are presented with an environmental challenge such as antibiotics to assess their propensity to handle the challenge.

Active matter in space

In the last 20 years, active matter has been a highly dynamic field of research, bridging fundamental aspects of non-equilibrium thermodynamics with applications to biology, robotics, and nano-medicine. Active matter systems are composed of units that can harvest and harness energy and information from their environment to generate complex collective behaviours and forms of self-organisation. On Earth, gravity-driven phenomena (such as sedimentation and convection) often dominate or conceal the emergence of these dynamics, especially for soft active matter systems where typical interactions are of the order of the thermal energy. In this review, we explore the ongoing and future efforts to study active matter in space, where low-gravity and microgravity conditions can lift some of these limitations. We envision that these studies will help unify our understanding of active matter systems and, more generally, of far-from-equilibrium physics both on Earth and in space. Furthermore, they will also provide guidance on how to use, process and manufacture active materials for space exploration and colonisation.

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.

Emergent collective dynamics of pusher and puller squirmer rods: swarming, clustering, and turbulence

We study the interplay of steric and hydrodynamic interactions in suspensions of elongated microswimmers by simulating the full hydrodynamics of squirmer rods in the quasi two-dimensional geometry of a Hele-Shaw cell. To create pusher or puller-type squirmer rods, we concentrate the surface slip-velocity field more to the back or to the front of the rod and thereby are able to tune the rod's force-dipole strength. We study a wide range of aspect ratios and area fractions and provide corresponding state diagrams. The flow field of pusher-type squirmer rods destabilizes ordered structures and favors the disordered state at small area fractions and aspect ratios. Only when steric interactions become relevant, we observe a turbulent and dynamic cluster state, while for large aspect ratios a single swarm and jammed cluster occurs. The power spectrum of the turbulent state shows two distinct energy cascades at small and large wave numbers with power-law scaling and non-universal exponents. Pullers show a strong tendency to form swarms instead of the disordered state found for neutral and pusher rods. At large area fractions a dynamic cluster is observed and at larger aspect ratio a single swarm or jammed cluster occurs.

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.

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.

Gyrotactic cluster formation of bottom-heavy squirmers

Squirmers that are bottom-heavy experience a torque that aligns them along the vertical so that they swim upwards. In a suspension of many squirmers, they also interact hydrodynamically via flow fields that are initiated by their swimming motion and by gravity. Swimming under the combined action of flow field vorticity and gravitational torque is called gyrotaxis. Using the method of multi-particle collision dynamics, we perform hydrodynamic simulations of a many-squirmer system floating above the bottom surface. Due to gyrotaxis they exhibit pronounced cluster formation with increasing gravitational torque. The clusters are more volatile at low values but compactify to smaller clusters at larger torques. The mean distance between clusters is mainly controlled by the gravitational torque and not the global density. Furthermore, we observe that neutral squirmers form clusters more easily, whereas pullers require larger gravitational torques due to their additional force-dipole flow fields. We do not observe clustering for pusher squirmers. Adding a rotlet dipole to the squirmer flow field induces swirling clusters. At high gravitational strengths, the hydrodynamic interactions with the no-slip boundary create an additional vertical alignment for neutral squirmers, which also supports cluster formation.

Kin discrimination drives territorial exclusion during Bacillus subtilis swarming and restrains exploitation of surfactin

Swarming is the collective movement of bacteria across a surface. It requires the production of surfactants (public goods) to overcome surface tension and provides an excellent model to investigate bacterial cooperation. Previously, we correlated swarm interaction phenotypes with kin discrimination between B. subtilis soil isolates, by showing that less related strains form boundaries between swarms and highly related strains merge. However, how kin discrimination affects cooperation and territoriality in swarming bacteria remains little explored. Here we show that the pattern of surface colonization by swarming mixtures is influenced by kin types. Closely related strain mixtures colonize the surface in a mixed swarm, while mixtures of less related strains show competitive exclusion as only one strain colonizes the surface. The outcome of nonkin swarm expansion depends on the initial ratio of the competing strains, indicating positive frequency-dependent competition. We find that addition of surfactin (a public good excreted from cells) can complement the swarming defect of nonkin mutants, whereas close encounters in nonkin mixtures lead to territorial exclusion, which limits the exploitation of surfactin by nonkin nonproducers. The work suggests that kin discrimination driven competitive territorial exclusion may be an important determinant for the success of cooperative surface colonization.

Microbial Biofilms: Structural Plasticity and Emerging Properties

Microbial biofilms are found everywhere and can be either beneficial or detrimental, as they are involved in crucial ecological processes and in severe chronic infections. The functional properties of biofilms are closely related to their three-dimensional (3D) structure, and the ability of microorganisms to collectively and dynamically shape the community spatial organization in response to stresses in such biological edifices. A large number of works have shown a relationship between the modulation of the spatial organization and ecological interactions in biofilms in response to environmental fluctuations, as well as their emerging properties essential for nutrient cycling and bioremediation processes in natural environments. On the contrary, numerous studies have emphasized the role of structural rearrangements and matrix production in the increased tolerance of bacteria in biofilms toward antimicrobials. In these last few years, the development of innovative approaches, relying on recent technological advances in imaging, computing capacity, and other analytical tools, has led to the production of original data that have improved our understanding of this close relationship. However, it has also highlighted the need to delve deeper into the study of cell behavior in such complex communities during 3D structure development and maturation- from a single-cell to a multicellular scale- to better control or harness positive and negative impacts of biofilms. For this Special Issue, the interplay between biofilm emerging properties and their 3D spatial organization considering different models, from single bacteria to complex environmental communities, and various environments, from natural ecosystems to industrial and medical settings are addressed.

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

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

Multiple functions of flagellar motility and chemotaxis in bacterial physiology

Most swimming bacteria are capable of following gradients of nutrients, signaling molecules and other environmental factors that affect bacterial physiology. This tactic behavior became one of the most-studied model systems for signal transduction and quantitative biology, and underlying molecular mechanisms are well characterized in Escherichia coli and several other model bacteria. In this review, we focus primarily on less understood aspect of bacterial chemotaxis, namely its physiological relevance for individual bacterial cells and for bacterial populations. As evident from multiple recent studies, even for the same bacterial species flagellar motility and chemotaxis might serve multiple roles, depending on the physiological and environmental conditions. Among these, finding sources of nutrients and more generally locating niches that are optimal for growth appear to be one of the major functions of bacterial chemotaxis, which could explain many chemoeffector preferences as well as flagellar gene regulation. Chemotaxis might also generally enhance efficiency of environmental colonization by motile bacteria, which involves intricate interplay between individual and collective behaviors and trade-offs between growth and motility. Finally, motility and chemotaxis play multiple roles in collective behaviors of bacteria including swarming, biofilm formation and autoaggregation, as well as in their interactions with animal and plant hosts.

Snowdrift game induces pattern formation in systems of self-propelled particles

Evolutionary games between species are known to lead to intriguing spatiotemporal patterns in systems of diffusing agents. However, the role of interspecies interactions is hardly studied when agents are (self-)propelled, as is the case in many biological systems. Here, we combine aspects from active matter and evolutionary game theory and study a system of two species whose individuals are (self-)propelled and interact through a snowdrift game. We derive hydrodynamic equations for the density and velocity fields of both species from which we identify parameter regimes in which one or both species form macroscopic orientational order as well as regimes of propagating wave patterns. Interestingly, we find simultaneous wave patterns in both species that result from the interplay between alignment and snowdrift interactions-a feedback mechanism that we call game-induced pattern formation. We test these results in agent-based simulations and confirm the different regimes of order and spatiotemporal patterns as well as game-induced pattern formation.

Multi-particle collision dynamics with a non-ideal equation of state. II. Collective dynamics of elongated squirmer rods

Simulations of flow fields around microscopic objects typically require methods that both solve the Navier-Stokes equations and also include thermal fluctuations. One such method popular in the field of soft-matter physics is the particle-based simulation method of multi-particle collision dynamics (MPCD). However, in contrast to the typically incompressible real fluid, the fluid of the traditional MPCD methods obeys the ideal-gas equation of state. This can be problematic because most fluid properties strongly depend on the fluid density. In a recent article, we proposed an extended MPCD algorithm and derived its non-ideal equation of state and an expression for the viscosity. In the present work, we demonstrate its accuracy and efficiency for the simulations of the flow fields of single squirmers and of the collective dynamics of squirmer rods. We use two exemplary squirmer-rod systems for which we compare the outcome of the extended MPCD method to the well-established MPCD version with an Andersen thermostat. First, we explicitly demonstrate the reduced compressibility of the MPCD fluid in a cluster of squirmer rods. Second, for shorter rods, we show the interesting result that in simulations with the extended MPCD method, dynamic swarms are more pronounced and have a higher polar order. Finally, we present a thorough study of the state diagram of squirmer rods moving in the center plane of a Hele-Shaw geometry. From a small to large aspect ratio and density, we observe a disordered state, dynamic swarms, a single swarm, and a jammed cluster, which we characterize accordingly.

Bacterial motility: machinery and mechanisms

Bacteria have developed a large array of motility mechanisms to exploit available resources and environments. These mechanisms can be broadly classified into swimming in aqueous media and movement over solid surfaces. Swimming motility involves either the rotation of rigid helical filaments through the external medium or gyration of the cell body in response to the rotation of internal filaments. On surfaces, bacteria swarm collectively in a thin layer of fluid powered by the rotation of rigid helical filaments, they twitch by assembling and disassembling type IV pili, they glide by driving adhesins along tracks fixed to the cell surface and, finally, non-motile cells slide over surfaces in response to outward forces due to colony growth. Recent technological advances, especially in cryo-electron microscopy, have greatly improved our knowledge of the molecular machinery that powers the various forms of bacterial motility. In this Review, we describe the current understanding of the physical and molecular mechanisms that allow bacteria to move around.

Mechanistic underpinning of cell aspect ratio-dependent emergent collective motions in swarming bacteria

Self-propelled bacteria can exhibit a large variety of non-equilibrium self-organized phenomena. Swarming is one such fascinating dynamical scenario where a number of motile individuals group into dynamical clusters and move in synchronized flows and vortices. While precedent investigations into rod-like particles confirm that an increased aspect-ratio promotes alignment and order, recent experimental studies in bacteria Bacillus subtilis show a non-monotonic dependence of the cell-aspect ratio on their swarming motion. Here, by computer simulations of an agent-based model of self-propelled, mechanically interacting, rod-shaped bacteria under overdamped conditions, we explore the collective dynamics of a bacterial swarm subjected to a variety of cell-aspect ratios. When modeled with an identical self-propulsion speed across a diverse range of cell aspect ratios, simulations demonstrate that both shorter and longer bacteria exhibit slow dynamics whereas the fastest speed is obtained at an intermediate aspect ratio. Our investigation highlights that the origin of this observed non-monotonic trend of bacterial speed and vorticity with the cell-aspect ratio is rooted in the cell-size dependence of motility force. The swarming features remain robust for a wide range of surface density of the cells, whereas asymmetry in friction attributes a distinct effect. Our analysis identifies that at an intermediate aspect ratio, an optimum cell size and motility force promote alignment, which reinforces the mechanical interactions among neighboring cells leading to the overall fastest motion. Mechanistic underpinning of the collective motions reveals that it is a joint venture of the short-range repulsive and the size-dependent motility forces, which determines the characteristics of swarming.

Advances and opportunities in image analysis of bacterial cells and communities

The cellular morphology and sub-cellular spatial structure critically influence the function of microbial cells. Similarly, the spatial arrangement of genotypes and phenotypes in microbial communities has important consequences for cooperation, competition, and community functions. Fluorescence microscopy techniques are widely used to measure spatial structure inside living cells and communities, which often results in large numbers of images that are difficult or impossible to analyze manually. The rapidly evolving progress in computational image analysis has recently enabled the quantification of a large number of properties of single cells and communities, based on traditional analysis techniques and convolutional neural networks. Here, we provide a brief introduction to core concepts of automated image processing, recent software tools and how to validate image analysis results. We also discuss recent advances in image analysis of microbial cells and communities, and how these advances open up opportunities for quantitative studies of spatiotemporal processes in microbiology, based on image cytometry and adaptive microscope control.

'Chain and running' induced by mechanical interactions among cells of different phenotypes in the Bacillus subtilis biofilm

In either a living system or a non-living system, the interaction among its constituent cells or particles is a fundamental aspect at all scales. For example, during the Bacillus subtilis biofilm formation, cells differentiate into multiple phenotypes to adapt to the environments; few hours after the initial inoculation, we find the phenotype of matrix-producing cells form "chain" structure surrounding the phenotype of the "running" motile cells. We use "chain" to characterize the structure of matrix-producing cells, and "running" to characterize the proliferation and growth of motile cells. Due to a large number of cells in the biofilm, it is impossible to construct a traditional kinetic model to describe the causal link between the single-cell movement and the colony behavior. Here, we obtain cell state information and cell group shape information through experiments; after the image analysis, we get the key interaction rules between cells, and then, we simulate the comparable movement of two cell types and the resulting colony geometry using the multi-agent model. Our work makes a better understanding of the relationship between the macroscopic shape of colonies and microscopic mechanical interactions among cells in the early stage of biofilm growth.

Cryptic surface-associated multicellularity emerges through cell adhesion and its regulation

The repeated evolution of multicellularity led to a wide diversity of organisms, many of which are sessile, including land plants, many fungi, and colonial animals. Sessile organisms adhere to a surface for most of their lives, where they grow and compete for space. Despite the prevalence of surface-associated multicellularity, little is known about its evolutionary origin. Here, we introduce a novel theoretical approach, based on spatial lineage tracking of cells, to study this origin. We show that multicellularity can rapidly evolve from two widespread cellular properties: cell adhesion and the regulatory control of adhesion. By evolving adhesion, cells attach to a surface, where they spontaneously give rise to primitive cell collectives that differ in size, life span, and mode of propagation. Selection in favor of large collectives increases the fraction of adhesive cells until a surface becomes fully occupied. Through kin recognition, collectives then evolve a central-peripheral polarity in cell adhesion that supports a division of labor between cells and profoundly impacts growth. Despite this spatial organization, nascent collectives remain cryptic, lack well-defined boundaries, and would require experimental lineage tracking technologies for their identification. Our results suggest that cryptic multicellularity could readily evolve and originate well before multicellular individuals become morphologically evident.

Confinement discerns swarmers from planktonic bacteria

Powered by flagella, many bacterial species exhibit collective motion on a solid surface commonly known as swarming. As a natural example of active matter, swarming is also an essential biological phenotype associated with virulence, chemotaxis, and host pathogenesis. Physical changes like cell elongation and hyper-flagellation have been shown to accompany the swarming phenotype. Less studied, however, are the contrasts of collective motion between the swarming cells and their counterpart planktonic cells of comparable cell density. Here, we show that confining bacterial movement in circular microwells allows distinguishing bacterial swarming from collective swimming. On a soft agar plate, a novel bacterial strain Enterobacter sp. SM3 in swarming and planktonic states exhibited different motion patterns when confined to circular microwells of a specific range of sizes. When the confinement diameter was between 40 μm and 90 μm, swarming SM3 formed a single-swirl motion pattern in the microwells whereas planktonic SM3 formed multiple swirls. Similar differential behavior is observed across several other species of gram-negative bacteria. We also observed 'rafting behavior' of swarming bacteria upon dilution. We hypothesize that the rafting behavior might account for the motion pattern difference. We were able to predict these experimental features via numerical simulations where swarming cells are modeled with stronger cell-cell alignment interaction. Our experimental design using PDMS microchip disk arrays enabled us to observe bacterial swarming on murine intestinal surface, suggesting a new method for characterizing bacterial swarming under complex environments, such as in polymicrobial niches, and for in vivo swarming exploration.

Single-cell motile behaviour of [Formula: see text] in thin-layered fluid collectives

We describe a system for the analysis of an important unicellular eukaryotic flagellate in a confining and crowded environment. The parasite Trypanosoma brucei is arguably one of the most versatile microswimmers known. It has unique properties as a single microswimmer and shows remarkable adaptations (not only in motility, but prominently so), to its environment during a complex developmental cycle involving two different hosts. Specific life cycle stages show fascinating collective behaviour, as millions of cells can be forced to move together in extreme confinement. Our goal is to examine such motile behaviour directly in the context of the relevant environments. Therefore, for the first time, we analyse the motility behaviour of trypanosomes directly in a widely used assay, which aims to evaluate the parasites behaviour in collectives, in response to as yet unknown parameters. In a step towards understanding whether, or what type of, swarming behaviour of trypanosomes exists, we customised the assay for quantitative tracking analysis of motile behaviour on the single-cell level. We show that the migration speed of cell groups does not directly depend on single-cell velocity and that the system remains to be simplified further, before hypotheses about collective motility can be advanced.

Swarming bacteria undergo localized dynamic phase transition to form stress-induced biofilms

Self-organized multicellular behaviors enable cells to adapt and tolerate stressors to a greater degree than isolated cells. However, whether and how cellular communities alter their collective behaviors adaptively upon exposure to stress is largely unclear. Here, we investigate this question using Bacillus subtilis, a model system for bacterial multicellularity. We discover that, upon exposure to a spatial gradient of kanamycin, swarming bacteria activate matrix genes and transit to biofilms. The initial stage of this transition is underpinned by a stress-induced multilayer formation, emerging from a biophysical mechanism reminiscent of motility-induced phase separation (MIPS). The physical nature of the process suggests that stressors which suppress the expansion of swarms would induce biofilm formation. Indeed, a simple physical barrier also induces a swarm-to-biofilm transition. Based on the gained insight, we propose a strategy of antibiotic treatment to inhibit the transition from swarms to biofilms by targeting the localized phase transition.

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.

How Physical Interactions Shape Bacterial Biofilms

Biofilms are structured communities formed by a single or multiple microbial species. Within biofilms, bacteria are embedded into extracellular matrix, allowing them to build macroscopic objects. Biofilm structure can respond to environmental changes such as the presence of antibiotics or predators. By adjusting expression levels of surface and extracellular matrix components, bacteria tune cell-to-cell interactions. One major challenge in the field is the fact that these components are very diverse among different species. Deciphering how physical interactions within biofilms are affected by changes in gene expression is a promising approach to obtaining a more unified picture of how bacteria modulate biofilms. This review focuses on recent advances in characterizing attractive and repulsive forces between bacteria in correlation with biofilm structure, dynamics, and spreading. How bacteria control physical interactions to maximize their fitness is an emerging theme.

Topological Metric Detects Hidden Order in Disordered Media

Recent advances in microscopy techniques make it possible to study the growth, dynamics, and response of complex biophysical systems at single-cell resolution, from bacterial communities to tissues and organoids. In contrast to ordered crystals, it is less obvious how one can reliably distinguish two amorphous yet structurally different cellular materials. Here, we introduce a topological earth mover's (TEM) distance between disordered structures that compares local graph neighborhoods of the microscopic cell-centroid networks. Leveraging structural information contained in the neighborhood motif distributions, the TEM metric allows an interpretable reconstruction of equilibrium and nonequilibrium phase spaces and embedded pathways from static system snapshots alone. Applied to cell-resolution imaging data, the framework recovers time ordering without prior knowledge about the underlying dynamics, revealing that fly wing development solves a topological optimal transport problem. Extending our topological analysis to bacterial swarms, we find a universal neighborhood size distribution consistent with a Tracy-Widom law.

Valuing what happens: a biogenic approach to valence and (potentially) affect

Valence is half of the pair of properties that constitute core affect, the foundation of emotion. But what is valence, and where is it found in the natural world? Currently, this question cannot be answered. The idea that emotion is the body's way of driving the organism to secure its survival, thriving and reproduction runs like a leitmotif from the pathfinding work of Antonio Damasio through four book-length neuroscientific accounts of emotion recently published by the field's leading practitioners. Yet while Damasio concluded 20 years ago that the homeostasis-affect linkage is rooted in unicellular life, no agreement exists about whether even non-human animals with brains experience emotions. Simple neural animals-those less brainy than bees, fruit flies and other charismatic invertebrates-are not even on the radar of contemporary affective research, to say nothing of aneural organisms. This near-sightedness has effectively denied the most productive method available for getting a grip on highly complex biological processes to a scientific domain whose importance for understanding biological decision-making cannot be underestimated. Valence arguably is the fulcrum around which the dance of life revolves. Without the ability to discriminate advantage from harm, life very quickly comes to an end. In this paper, we review the concept of valence, where it came from, the work it does in current leading theories of emotion, and some of the odd features revealed via experiment. We present a biologically grounded framework for investigating valence in any organism and sketch a preliminary pathway to a computational model. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

Machine learning forecasting of active nematics

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic models, which accurately describe idealized flows and many of the steady-state properties, but do not capture certain detailed dynamics of experimental active nematics. We have developed a deep learning approach that uses a Convolutional Long-Short-Term-Memory (ConvLSTM) algorithm to automatically learn and forecast the dynamics of active nematics. We demonstrate our purely data-driven approach on experiments of 2D unconfined active nematics of extensile microtubule bundles, as well as on data from numerical simulations of active nematics.

Biofilm and swarming emergent behaviours controlled through the aid of biophysical understanding and tools

Bacteria can organise themselves into communities in the forms of biofilms and swarms. Through chemical and physical interactions between cells, these communities exhibit emergent properties that individual cells alone do not have. While bacterial communities have been mainly studied in the context of biochemistry and molecular biology, recent years have seen rapid advancements in the biophysical understanding of emergent phenomena through physical interactions in biofilms and swarms. Moreover, new technologies to control bacterial emergent behaviours by physical means are emerging in synthetic biology. Such technologies are particularly promising for developing engineered living materials (ELM) and devices and controlling contamination and biofouling. In this minireview, we overview recent studies unveiling physical and mechanical cues that trigger and affect swarming and biofilm development. In particular, we focus on cell shape, motion and density as the key parameters for mechanical cell-cell interactions within a community. We then showcase recent studies that use physical stimuli for patterning bacterial communities, altering collective behaviours and preventing biofilm formation. Finally, we discuss the future potential extension of biophysical and bioengineering research on microbial communities through computational modelling and deeper investigation of mechano-electrophysiological coupling.

Constrained optimal foraging by marine bacterioplankton on particulate organic matter

Patch use theory predicts that organisms foraging in a heterogeneous resource landscape balance their residence time on a patch yielding diminishing returns with the sum of the metabolic, predation, and opportunity costs of foraging. By combining single-cell tracking with mathematical modeling, we show that bacteria foraging on seascapes of organic particles switch between attached and planktonic lifestyles and tune the time spent on particles to increase individual fitness. As predicted by patch use theory, bacteria remain longer on particles of higher quality and in poor environments, or when search times for fresh particles are longer. These results show that patch use theory can be a valuable framework to understand not only animals, but also microorganisms, and ultimately their ecosystem-level consequences.

Optimal foraging theory provides a framework to understand how organisms balance the benefits of harvesting resources within a patch with the sum of the metabolic, predation, and missed opportunity costs of foraging. Here, we show that, after accounting for the limited environmental information available to microorganisms, optimal foraging theory and, in particular, patch use theory also applies to the behavior of marine bacteria in particle seascapes. Combining modeling and experiments, we find that the marine bacterium Vibrio ordalii optimizes nutrient uptake by rapidly switching between attached and planktonic lifestyles, departing particles when their nutrient concentration is more than hundredfold higher than background. In accordance with predictions from patch use theory, single-cell tracking reveals that bacteria spend less time on nutrient-poor particles and on particles within environments that are rich or in which the travel time between particles is smaller, indicating that bacteria tune the nutrient concentration at detachment to increase their fitness. A mathematical model shows that the observed behavioral switching between exploitation and dispersal is consistent with foraging optimality under limited information, namely, the ability to assess the harvest rate of nutrients leaking from particles by molecular diffusion. This work demonstrates how fundamental principles in behavioral ecology traditionally applied to animals can hold right down to the scale of microorganisms and highlights the exquisite adaptations of marine bacterial foraging. The present study thus provides a blueprint for a mechanistic understanding of bacterial uptake of dissolved organic matter and bacterial production in the ocean—processes that are fundamental to the global carbon cycle.

Squirmer rods as elongated microswimmers: flow fields and confinement

Microswimmers or active elements, such as bacteria and active filaments, have an elongated shape, which determines their individual and collective dynamics. There is still a need to identify what role long-range hydrodynamic interactions play in their fascinating dynamic structure formation. We construct rods of different aspect ratios using several spherical squirmer model swimmers. With the help of the mesoscale simulation method of multi-particle collision dynamics we analyze the flow fields of these squirmer rods both in a bulk fluid and in Hele-Shaw geometries of different slab widths. Based on the hydrodynamic multipole expansion either for bulk or confinement between two parallel plates, we categorize the different multipole contributions of neutral as well as pusher-type squirmer rods. We demonstrate how confinement alters the radial decay of the flow fields for a given force or source multipole moment compared to the bulk fluid.

Bacterial surface motility is modulated by colony-scale flow and granular jamming

Microbes routinely face the challenge of acquiring territory and resources on wet surfaces. Cells move in large groups inside thin, surface-bound water layers, often achieving speeds of 30 µm s^-1 within this environment, where viscous forces dominate over inertial forces (low Reynolds number). The canonical Gram-positive bacterium Bacillus subtilis is a model organism for the study of collective migration over surfaces with groups exhibiting motility on length-scales three orders of magnitude larger than themselves within a few doubling times. Genetic and chemical studies clearly show that the secretion of endogenous surfactants and availability of free surface water are required for this fast group motility. Here, we show that: (i) water availability is a sensitive control parameter modulating an abiotic jamming-like transition that determines whether the group remains fluidized and therefore collectively motile, (ii) groups self-organize into discrete layers as they travel, (iii) group motility does not require proliferation, rather groups are pulled from the front, and (iv) flow within expanding groups is capable of moving material from the parent colony into the expanding tip of a cellular dendrite with implications for expansion into regions of varying nutrient content. Together, these findings illuminate the physical structure of surface-motile groups and demonstrate that physical properties, like cellular packing fraction and flow, regulate motion from the scale of individual cells up to length scales of centimetres.

Emergent collective dynamics of bottom-heavy squirmers under gravity

We present the results of hydrodynamic simulations using the method of multi-particle collision dynamics for a system of squirmer microswimmers moving under the influence of gravity at low Reynolds numbers. In addition, the squirmers are bottom-heavy so that they experience a torque which aligns them along the vertical. The squirmers interact hydrodynamically by the flow fields of a stokeslet and rotlet, which are initiated by the acting gravitational force and torque, respectively, and by their own flow fields. By varying the ratio of swimming to bulk sedimentation velocity and the torque, we determine state diagrams for the emergent collective dynamics of neutral squirmers as well as strong pushers and pullers. For low swimming velocity and torque we observe conventional sedimentation, while the sedimentation profile becomes inverted when their values are increased. For neutral squirmers we discover convective rolls of circulating squirmers between both sedimentation states, which sit at the bottom of the system and are fed by plumes made of collectively sinking squirmers. At larger torques porous clusters occur that spawn single squirmers. The two latter states can also occur transiently starting from a uniform squirmer distribution and then disappear in the long-time limit. For strong pushers and pullers only weak plume formation is observed.

One-dimensional model for chemotaxis with hard-core interactions

In this paper we consider a biased velocity jump process with excluded-volume interactions for chemotaxis, where we account for the size of each particle. Starting with a system of N individual hard rod particles in one dimension, we derive a nonlinear kinetic model using two different approaches. The first approach is a systematic derivation for small occupied fraction of particles based on the method of matched asymptotic expansions. The second approach, based on a compression method that exploits the single-file motion of hard core particles, does not have the limitation of a small occupied fraction but requires constant tumbling rates. We validate our nonlinear model with numerical simulations, comparing its solutions with the corresponding noninteracting linear model as well as stochastic simulations of the underlying particle system.

Two-dimensional active motion

The diffusion in two dimensions of noninteracting active particles that follow an arbitrary motility pattern is considered for analysis. A Fokker-Planck-like equation is generalized to take into account an arbitrary distribution of scattered angles of the swimming direction, which encompasses the pattern of active motion of particles that move at constant speed. An exact analytical expression for the marginal probability density of finding a particle on a given position at a given instant, independently of its direction of motion, is provided, and a connection with a generalized diffusion equation is unveiled. Exact analytical expressions for the time dependence of the mean-square displacement and of the kurtosis of the distribution of the particle positions are presented. The analysis is focused in the intermediate-time regime, where the effects of the specific pattern of active motion are conspicuous. For this, it is shown that only the expectation value of the first two harmonics of the scattering angle of the direction of motion are needed. The effects of persistence and of circular motion are discussed for different families of distributions of the scattered direction of motion.