Directional reversals enable Myxococcus xanthus cells to produce collective one-dimensional streams during fruiting-body formation

Individual particle persistence antagonizes global ordering in populations of nematically aligning self-propelled particles

The transition from individual to collective motion plays a significant role in many biological processes. While the implications of different types of particle-particle interactions for the emergence of particular modes of collective motion have been well studied, it is unclear how particular types of individual migration patterns influence collective motion. Here, motivated by swarming bacteria Myxococcus xanthus, we investigate the combined effects of the individual pattern of migration and particle-particle interactions on the emergence of collective migration. We analyze the effects of a feature of individual pattern migration, the persistence of motion, on the collective properties of the system that emerge from interactions among individuals, particularly when nematic velocity alignment interaction mediates collective dynamics. We find, through computer simulations and mathematical analysis, that an initially disordered migratory state can become globally ordered by increasing either the particle-particle alignment interaction strength or the persistence of individual migration. In contrast, we find that persistence prevents the emergence of global nematic order when both persistence and nematic alignment are comparatively high. We conclude that behavior at the population level not only depends on interactions between individuals but also on their own intrinsic behavior.

Local polar order controls mechanical stress and triggers layer formation in Myxococcus xanthus colonies

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are substantially larger than the mean due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.

Unravelling a diversity of cellular structures and aggregation dynamics during the early development of Myxococcus xanthus

Aggregation underlies the collective dynamics of a diversity of organisms, enabling the formation of complex structures and emergent behaviours on interaction with the environment. Cellular aggregation constitutes one of the routes to collective motility and multicellular development. Myxococcus xanthus, a social bacterium, is a valuable model for studying the aggregative path to multicellularity, a major transition in the evolutionary history of life. While the collective developmental behaviour of M. xanthus has been largely studied in high cellular densities, there is a lack of understanding at low-density conditions that can be ecologically relevant. In this work, we study the early stages of emergent collective behaviour of M. xanthus under nutrient-poor and low-density conditions, uncovering the formation of diverse cellular structures with different shapes and sizes, ranging from individual cells to networks comprising thousands of cells. We study their motility patterns and their prevalence along development and discuss their cross-scale role on the population's exploratory dynamics. This work contributes to understanding key, yet largely understudied, aspects in the early stages of multicellular development in myxobacteria, shedding light on the dynamics underlying aggregative processes in this and other taxa and study systems.

Breakdown of Boltzmann-type models for the alignment of self-propelled rods

Studies in the collective motility of organisms use a range of analytical approaches to formulate continuous kinetic models of collective dynamics from rules or equations describing agent interactions. However, the derivation of these kinetic models often relies on Boltzmann's "molecular chaos" hypothesis, which assumes that correlations between individuals are short-lived. While this assumption is often the simplest way to derive tractable models, it is often not valid in practice due to the high levels of cooperation and self-organization present in biological systems. In this work, we illustrated this point by considering a general Boltzmann-type kinetic model for the alignment of self-propelled rods where rod reorientation occurs upon binary collisions. We examine the accuracy of the kinetic model by comparing numerical solutions of the continuous equations to an agent-based model that implements the underlying rules governing microscopic alignment. Even for the simplest case considered, our comparison demonstrates that the kinetic model fails to replicate the discrete dynamics due to the formation of rod clusters that violate statistical independence. Additionally, we show that introducing noise to limit cluster formation helps improve the agreement between the analytical model and agent simulations but does not restore the agreement completely. These results highlight the need to both develop and disseminate improved moment-closure methods for modeling biological and active matter systems.

Capillary interactions drive the self-organization of bacterial colonies

Many bacteria inhabit thin layers of water on solid surfaces both naturally in soils or on hosts or textiles and in the lab on agar hydrogels. In these environments, cells experience capillary forces, yet an understanding of how these forces shape bacterial collective behaviors remains elusive. Here, we show that the water menisci formed around bacteria lead to capillary attraction between cells while still allowing them to slide past one another. We develop an experimental apparatus that allows us to control bacterial collective behaviors by varying the strength and range of capillary forces. Combining 3D imaging and cell tracking with agent-based modeling, we demonstrate that capillary attraction organizes rod-shaped bacteria into densely packed, nematic groups, and profoundly influences their collective dynamics and morphologies. Our results suggest that capillary forces may be a ubiquitous physical ingredient in shaping microbial communities in partially hydrated environments.

A Cellular Potts Model of the interplay of synchronization and aggregation

We investigate the behavior of systems of cells with intracellular molecular oscillators ("clocks") where cell-cell adhesion is mediated by differences in clock phase between neighbors. This is motivated by phenomena in developmental biology and in aggregative multicellularity of unicellular organisms. In such systems, aggregation co-occurs with clock synchronization. To account for the effects of spatially extended cells, we use the Cellular Potts Model (CPM), a lattice agent-based model. We find four distinct possible phases: global synchronization, local synchronization, incoherence, and anti-synchronization (checkerboard patterns). We characterize these phases via order parameters. In the case of global synchrony, the speed of synchronization depends on the adhesive effects of the clocks. Synchronization happens fastest when cells in opposite phases adhere the strongest ("opposites attract"). When cells of the same clock phase adhere the strongest ("like attracts like"), synchronization is slower. Surprisingly, the slowest synchronization happens in the diffusive mixing case, where cell-cell adhesion is independent of clock phase. We briefly discuss potential applications of the model, such as pattern formation in the auditory sensory epithelium.

Mathematical modeling of mechanosensitive reversal control in Myxococcus xanthus

Adjusting motility patterns according to environmental cues is important for bacterial survival. Myxococcus xanthus, a bacterium moving on surfaces by gliding and twitching mechanisms, modulates the reversal frequency of its front-back polarity in response to mechanical cues like substrate stiffness and cell-cell contact. In this study, we propose that M. xanthus's gliding machinery senses environmental mechanical cues during force generation and modulates cell reversal accordingly. To examine our hypothesis, we expand an existing mathematical model for periodic polarity reversal in M. xanthus, incorporating the experimental data on the intracellular dynamics of the gliding machinery and the interaction between the gliding machinery and a key polarity regulator. The model successfully reproduces the dependence of cell reversal frequency on substrate stiffness observed in M. xanthus gliding. We further propose reversal control networks between the gliding and twitching motility machineries to explain the opposite reversal responses observed in wild type M. xanthus cells that possess both motility mechanisms. These results provide testable predictions for future experimental investigations. In conclusion, our model suggests that the gliding machinery in M. xanthus can function as a mechanosensor, which transduces mechanical cues into a cell reversal signal.

Cell behaviors underlying Myxococcus xanthus aggregate dispersal

IMPORTANCE

Understanding the processes behind bacterial biofilm formation, maintenance, and dispersal is essential for addressing their effects on health and ecology. Within these multicellular communities, various cues can trigger differentiation into distinct cell types, allowing cells to adapt to their specific local environment. The soil bacterium Myxococcus xanthus forms biofilms in response to starvation, marked by cells aggregating into mounds. Some aggregates persist as spore-filled fruiting bodies, while others disperse after initial formation for unknown reasons. Here, we use a combination of cell tracking analysis and computational simulations to identify behaviors at the cellular level that contribute to aggregate dispersal. Our results suggest that cells in aggregates actively determine whether to disperse or persist and undergo a transition to sporulation based on a self-produced cue related to the aggregate size. Identifying these cues is an important step in understanding and potentially manipulating bacterial cell-fate decisions.

Local polar order controls mechanical stress and triggers layer formation in developing Myxococcus xanthus colonies

Colonies of the social bacterium Myxococcus xanthus go through a morphological transition from a thin colony of cells to three-dimensional droplet-like fruiting bodies as a strategy to survive starvation. The biological pathways that control the decision to form a fruiting body have been studied extensively. However, the mechanical events that trigger the creation of multiple cell layers and give rise to droplet formation remain poorly understood. By measuring cell orientation, velocity, polarity, and force with cell-scale resolution, we reveal a stochastic local polar order in addition to the more obvious nematic order. Average cell velocity and active force at topological defects agree with predictions from active nematic theory, but their fluctuations are anomalously large due to polar active forces generated by the self-propelled rod-shaped cells. We find that M. xanthus cells adjust their reversal frequency to tune the magnitude of this local polar order, which in turn controls the mechanical stresses and triggers layer formation in the colonies.

Molecular-scale substrate anisotropy, crowding and division drive collective behaviours in cell monolayers

The ability of cells to reorganize in response to external stimuli is important in areas ranging from morphogenesis to tissue engineering. While nematic order is common in biological tissues, it typically only extends to small regions of cells interacting via steric repulsion. On isotropic substrates, elongated cells can co-align due to steric effects, forming ordered but randomly oriented finite-size domains. However, we have discovered that flat substrates with nematic order can induce global nematic alignment of dense, spindle-like cells, thereby influencing cell organization and collective motion and driving alignment on the scale of the entire tissue. Remarkably, single cells are not sensitive to the substrate's anisotropy. Rather, the emergence of global nematic order is a collective phenomenon that requires both steric effects and molecular-scale anisotropy of the substrate. To quantify the rich set of behaviours afforded by this system, we analyse velocity, positional and orientational correlations for several thousand cells over days. The establishment of global order is facilitated by enhanced cell division along the substrate's nematic axis, and associated extensile stresses that restructure the cells' actomyosin networks. Our work provides a new understanding of the dynamics of cellular remodelling and organization among weakly interacting cells.

Ensemble Deep Learning Object Detection Fusion for Cell Tracking, Mitosis, and Lineage

Cell tracking and motility analysis are essential for understanding multicellular processes, automated quantification in biomedical experiments, and medical diagnosis and treatment. However, manual tracking is labor-intensive, tedious, and prone to selection bias and errors. Building upon our previous work, we propose a new deep learning-based method, EDNet, for cell detection, tracking, and motility analysis that is more robust to shape across different cell lines, and models cell lineage and proliferation. EDNet uses an ensemble approach for 2D cell detection that is deep-architecture-agnostic and achieves state-of-the-art performance surpassing single-model YOLO and FasterRCNN convolutional neural networks. EDNet detections are used in our M2Track multiobject tracking algorithm for tracking cells, detecting cell mitosis (cell division) events, and cell lineage graphs. Our methods produce state-of-the-art performance on the Cell Tracking and Mitosis (CTMCv1) dataset with a Multiple Object Tracking Accuracy (MOTA) score of 50.6% and tracking lineage graph edit (TRA) score of 52.5%. Additionally, we compare our detection and tracking methods to human performance on external data in studying the motility of muscle stem cells with different physiological and molecular stimuli. We believe that our method has the potential to improve the accuracy and efficiency of cell tracking and motility analysis. This could lead to significant advances in biomedical research and medical diagnosis. Our code is made publicly available on GitHub.

Active nematic defects in compressible and incompressible flows

We study the dynamics of active nematic films on a substrate driven by active flows with or without the incompressible constraint. Through simulations and theoretical analysis, we show that arch patterns are stable in the compressible case, while they become unstable under the incompressibility constraint. For compressible flows at high enough activity, stable arches organize themselves into a smecticlike pattern, which induce an associated global polar ordering of +1/2 nematic defects. By contrast, divergence-free flows give rise to a local nematic order of the +1/2 defects, consisting of antialigned pairs of neighboring defects, as established in previous studies.

Polar Fluctuations Lead to Extensile Nematic Behavior in Confluent Tissues

How can a collection of motile cells, each generating contractile nematic stresses in isolation, become an extensile nematic at the tissue level? Understanding this seemingly contradictory experimental observation, which occurs irrespective of whether the tissue is in the liquid or solid states, is not only crucial to our understanding of diverse biological processes, but is also of fundamental interest to soft matter and many-body physics. Here, we resolve this cellular to tissue level disconnect in the small fluctuation regime by using analytical theories based on hydrodynamic descriptions of confluent tissues, in both liquid and solid states. Specifically, we show that a collection of microscopic constituents with no inherently nematic extensile forces can exhibit active extensile nematic behavior when subject to polar fluctuating forces. We further support our findings by performing cell level simulations of minimal models of confluent tissues.

Direction reversing active Brownian particle in a harmonic potential

We study the two-dimensional motion of an active Brownian particle of speed v₀, with intermittent directional reversals in the presence of a harmonic trap of strength μ. The presence of the trap ensures that the position of the particle eventually reaches a steady state where it is bounded within a circular region of radius v₀/μ, centered at the minimum of the trap. Due to the interplay between the rotational diffusion constant D_R, reversal rate γ, and the trap strength μ, the steady state distribution shows four different types of shapes, which we refer to as active-I & II, and passive-I & II phases. In the active-I phase, the weight of the distribution is concentrated along an annular region close to the circular boundary, whereas in active-II, an additional central diverging peak appears giving rise to a Mexican hat-like shape of the distribution. The passive-I is marked by a single Boltzmann-like centrally peaked distribution in the large D_R limit. On the other hand, while the passive-II phase also shows a single central peak, it is distinguished from passive-I by a non-Boltzmann like divergence near the origin. We characterize these phases by calculating the exact analytical forms of the distributions in various limiting cases. In particular, we show that for D_R ≪ γ, the shape transition of the two-dimensional position distribution from active-II to passive-II occurs at μ = γ. We compliment these analytical results with numerical simulations beyond the limiting cases and obtain a qualitative phase diagram in the (D_R, γ, μ^-1) space.

Cell density, alignment, and orientation correlate with C-signal-dependent gene expression during Myxococcus xanthus development

Starving Myxococcus xanthus bacteria use short-range C-signaling to coordinate their movements and construct multicellular mounds, which mature into fruiting bodies as rods differentiate into spherical spores. Differentiation requires efficient C-signaling to drive the expression of developmental genes, but how the arrangement of cells within nascent fruiting bodies (NFBs) affects C-signaling is not fully understood. Here, we used confocal microscopy and cell segmentation to visualize and quantify the arrangement, morphology, and gene expression of cells near the bottom of NFBs at much higher resolution than previously achieved. We discovered that "transitioning cells" (TCs), intermediate in morphology between rods and spores, comprised 10 to 15% of the total population. Spores appeared midway between the center and the edge of NFBs early in their development and near the center as maturation progressed. The developmental pattern, as well as C-signal-dependent gene expression in TCs and spores, were correlated with cell density, the alignment of neighboring rods, and the tangential orientation of rods early in the development of NFBs. These dynamic radial patterns support a model in which the arrangement of cells within the NFBs affects C-signaling efficiency to regulate precisely the expression of developmental genes and cellular differentiation in space and time. Developmental patterns in other bacterial biofilms may likewise rely on short-range signaling to communicate multiple aspects of cellular arrangement, analogous to juxtacrine and paracrine signaling during animal development.

Scattered migrating colony formation in the filamentous cyanobacterium, Pseudanabaena sp. NIES-4403

Background

Bacteria have been reported to exhibit complicated morphological colony patterns on solid media, depending on intracellular, and extracellular factors such as motility, cell propagation, and cell-cell interaction. We isolated the filamentous cyanobacterium, Pseudanabaena sp. NIES-4403 (Pseudanabaena, hereafter), that forms scattered (discrete) migrating colonies on solid media. While the scattered colony pattern has been observed in some bacterial species, the mechanism underlying such a pattern still remains obscure.

Results

We studied the morphology of Pseudanabaena migrating collectively and found that this species forms randomly scattered clusters varying in size and further consists of a mixture of comet-like wandering clusters and disk-like rotating clusters. Quantitative analysis of the formation of these wandering and rotating clusters showed that bacterial filaments tend to follow trajectories of previously migrating filaments at velocities that are dependent on filament length. Collisions between filaments occurred without crossing paths, which enhanced their nematic alignments, giving rise to bundle-like colonies. As cells increased and bundles aggregated, comet-like wandering clusters developed. The direction and velocity of the movement of cells in comet-like wandering clusters were highly coordinated. When the wandering clusters entered into a circular orbit, they turned into rotating clusters, maintaining a more stable location. Disk-like rotating clusters may rotate for days, and the speed of cells within a rotating cluster increases from the center to the outmost part of the cluster. Using a mathematical modeling with simplified assumption we reproduced some features of the scattered pattern including migrating clusters.

Conclusion

Based on these observations, we propose that Pseudanabaena forms scattered migrating colonies that undergo a series of transitions involving several morphological patterns. A simplified model is able to reproduce some features of the observed migrating clusters.

Supplementary Information

The online version contains supplementary material available at 10.1186/s12866-021-02183-5.

The environment topography alters the way to multicellularity in Myxococcus xanthus

The social soil-dwelling bacterium Myxococcus xanthus can form multicellular structures, known as fruiting bodies. Experiments in homogeneous environments have shown that this process is affected by the physicochemical properties of the substrate, but they have largely neglected the role of complex topographies. We experimentally demonstrate that the topography alters single-cell motility and multicellular organization in M. xanthus In topographies realized by randomly placing silica particles over agar plates, we observe that the cells' interaction with particles drastically modifies the dynamics of cellular aggregation, leading to changes in the number, size, and shape of the fruiting bodies and even to arresting their formation in certain conditions. We further explore this type of cell-particle interaction in a computational model. These results provide fundamental insights into how the environment topography influences the emergence of complex multicellular structures from single cells, which is a fundamental problem of biological, ecological, and medical relevance.

Mechanotaxis directs Pseudomonas aeruginosa twitching motility

Single cells across kingdoms of life explore, prey, escape, or congregate using surface-specific motility. Motile eukaryotic cells use chemotaxis to direct migration on surfaces. However, how bacteria control surface motility remains underexplored. Pseudomonas aeruginosa twitches on surfaces by successive extension and retraction of extracellular filaments called type IV pili. Here, we show that P. aeruginosa directs twitching by sensing mechanical input generated by type IV pili. The Chp sensory system performs spatially resolved mechanosensing by harnessing two response regulators with antagonistic functions. Our results demonstrate that sensory systems, whose input often remains elusive, can sense mechanical signals to actively steer motility. Furthermore, Chp establishes a signaling principle shared with higher-order organisms, identifying a conserved strategy to transduce spatially resolved signals.

The opportunistic pathogen Pseudomonas aeruginosa explores surfaces using twitching motility powered by retractile extracellular filaments called type IV pili (T4P). Single cells twitch by sequential T4P extension, attachment, and retraction. How single cells coordinate T4P to efficiently navigate surfaces remains unclear. We demonstrate that P. aeruginosa actively directs twitching in the direction of mechanical input from T4P in a process called mechanotaxis. The Chp chemotaxis-like system controls the balance of forward and reverse twitching migration of single cells in response to the mechanical signal. Collisions between twitching cells stimulate reversals, but Chp mutants either always or never reverse. As a result, while wild-type cells colonize surfaces uniformly, collision-blind Chp mutants jam, demonstrating a function for mechanosensing in regulating group behavior. On surfaces, Chp senses T4P attachment at one pole, thereby sensing a spatially resolved signal. As a result, the Chp response regulators PilG and PilH control the polarization of the extension motor PilB. PilG stimulates polarization favoring forward migration, while PilH inhibits polarization, inducing reversal. Subcellular segregation of PilG and PilH efficiently orchestrates their antagonistic functions, ultimately enabling rapid reversals upon perturbations. The distinct localization of response regulators establishes a signaling landscape known as local excitation–global inhibition in higher-order organisms, identifying a conserved strategy to transduce spatially resolved signals.

Active Brownian motion with directional reversals

Active Brownian motion with intermittent direction reversals is common in bacteria like Myxococcus xanthus and Pseudomonas putida. We show that, for such a motion in two dimensions, the presence of the two timescales set by the rotational diffusion constant D_{R} and the reversal rate γ gives rise to four distinct dynamical regimes: (I) t≪min(γ^{-1},D_{R}^{-1}), (II) γ^{-1}≪t≪D_{R}^{-1}, (III) D_{R}^{-1}≪t≪γ^{-1}, and (IV) t≫max(γ^{-1}, D_{R}^{-1}), showing distinct behaviors. We characterize these behaviors by analytically computing the position distribution and persistence exponents. The position distribution shows a crossover from a strongly nondiffusive and anisotropic behavior at short times to a diffusive isotropic behavior via an intermediate regime, II or III. In regime II, we show that, the position distribution along the direction orthogonal to the initial orientation is a function of the scaled variable z∝x_{⊥}/t with a nontrivial scaling function, f(z)=(2π^{3})^{-1/2}Γ(1/4+iz)Γ(1/4-iz). Furthermore, by computing the exact first-passage time distribution, we show that a persistence exponent α=1 emerges due to the direction reversal in this regime.

Pattern formation and polarity sorting of driven actin filaments on lipid membranes

Pattern formation processes in active systems give rise to a plethora of collective structures. Predicting how the emergent structures depend on the microscopic interactions between the moving agents remains a challenge. By introducing a high-density actin gliding assay on a fluid membrane, we demonstrate the emergence of polar structures in a regime of nematic binary interactions dominated by steric repulsion. The transition from a microscopic nematic symmetry to a macroscopic polar structure is linked to microscopic polarity sorting mechanisms, including accumulation in wedge-like topological defects. Our results should be instrumental for a better understanding of pattern formation and polarity sorting processes in active matter.

Collective motion of active matter is ubiquitously observed, ranging from propelled colloids to flocks of bird, and often features the formation of complex structures composed of agents moving coherently. However, it remains extremely challenging to predict emergent patterns from the binary interaction between agents, especially as only a limited number of interaction regimes have been experimentally observed so far. Here, we introduce an actin gliding assay coupled to a supported lipid bilayer, whose fluidity forces the interaction between self-propelled filaments to be dominated by steric repulsion. This results in filaments stopping upon binary collisions and eventually aligning nematically. Such a binary interaction rule results at high densities in the emergence of dynamic collectively moving structures including clusters, vortices, and streams of filaments. Despite the microscopic interaction having a nematic symmetry, the emergent structures are found to be polar, with filaments collectively moving in the same direction. This is due to polar biases introduced by the stopping upon collision, both on the individual filaments scale as well as on the scale of collective structures. In this context, positive half-charged topological defects turn out to be a most efficient trapping and polarity sorting conformation.

Interplay of mesoscale physics and agent-like behaviors in the parallel evolution of aggregative multicellularity

Myxobacteria and dictyostelids are prokaryotic and eukaryotic multicellular lineages, respectively, that after nutrient depletion aggregate and develop into structures called fruiting bodies. The developmental processes and resulting morphological outcomes resemble one another to a remarkable extent despite their independent origins, the evolutionary distance between them and the lack of traceable homology in molecular mechanisms. We hypothesize that the morphological parallelism between the two lineages arises as the consequence of the interplay within multicellular aggregates between generic processes, physical and physicochemical processes operating similarly in living and non-living matter at the mesoscale (~10^-3-10^-1 m) and agent-like behaviors, unique to living systems and characteristic of the constituent cells, considered as autonomous entities acting according to internal rules in a shared environment. Here, we analyze the contributions of generic and agent-like determinants in myxobacteria and dictyostelid development and their roles in the generation of their common traits. Consequent to aggregation, collective cell-cell contacts mediate the emergence of liquid-like properties, making nascent multicellular masses subject to novel patterning and morphogenetic processes. In both lineages, this leads to behaviors such as streaming, rippling, and rounding-up, as seen in non-living fluids. Later the aggregates solidify, leading them to exhibit additional generic properties and motifs. Computational models suggest that the morphological phenotypes of the multicellular masses deviate from the predictions of generic physics due to the contribution of agent-like behaviors of cells such as directed migration, quiescence, and oscillatory signal transduction mediated by responses to external cues. These employ signaling mechanisms that reflect the evolutionary histories of the respective organisms. We propose that the similar developmental trajectories of myxobacteria and dictyostelids are more due to shared generic physical processes in coordination with analogous agent-type behaviors than to convergent evolution under parallel selection regimes. Insights from the biology of these aggregative forms may enable a unified understanding of developmental evolution, including that of animals and plants.

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.

Dynamic polarity control by a tunable protein oscillator in bacteria

In bacteria, cell polarization involves the controlled targeting of specific proteins to the poles, defining polar identity and function. How a specific protein is targeted to one pole and what are the processes that facilitate its dynamic relocalization to the opposite pole is still unclear. The Myxococcus xanthus polarization example illustrates how the dynamic and asymmetric localization of polar proteins enable a controlled and fast switch of polarity. In M. xanthus, the opposing polar distribution of the small GTPase MglA and its cognate activating protein MglB defines the direction of movement of the cell. During a reversal event, the switch of direction is triggered by the Frz chemosensory system, which controls polarity reversals through a so-called gated relaxation oscillator. In this review, we discuss how this genetic architecture can provoke sharp behavioral transitions depending on Frz activation levels, which is central to multicellular behaviors in this bacterium.

Nonequilibrium dynamics of isostatic spring networks

Marginally stable systems exhibit rich critical mechanical behavior. Such isostatic assemblies can be actively driven, but it is unclear how their critical nature affects their nonequilibrium dynamics. Here, we study the influence of isostaticity on the nonequilibrium dynamics of active spring networks. In our model, heterogeneously distributed white or colored, motorlike noise drives the system into a nonequilibrium steady state. We quantify the nonequilibrium dynamics of pairs of network nodes by the characteristic cycling frequency ω-an experimentally accessible measure of the circulation of the associated phase space currents. The distribution of these cycling frequencies exhibits critical scaling, which we approximately capture by a mean-field theory. Finally, we show that the scaling behavior of ω with distance is controlled by a diverging length scale. Overall, we provide a theoretical approach to elucidate the role of marginality in active disordered systems.

Self-Driven Phase Transitions Drive Myxococcus xanthus Fruiting Body Formation

Combining high-resolution single cell tracking experiments with numerical simulations, we show that starvation-induced fruiting body formation in Myxococcus xanthus is a phase separation driven by cells that tune their motility over time. The phase separation can be understood in terms of cell density and a dimensionless Péclet number that captures cell motility through speed and reversal frequency. Our work suggests that M. xanthus takes advantage of a self-driven nonequilibrium phase transition that can be controlled at the single cell level.

Scaling behavior of nonequilibrium measures in internally driven elastic assemblies

Detecting and quantifying nonequilibrium activity is essential for studying internally driven assemblies, including synthetic active matter and complex living systems such as cells or tissue. We discuss a noninvasive approach of measuring nonequilibrium behavior based on the breaking of detailed balance. We focus on "cycling frequencies"-the average frequency with which the trajectories of pairs of degrees of freedom revolve in phase space-and explain their connection with other nonequilibrium measures, including the area enclosing rate and the entropy production rate. We test our approach on simple toy models composed of elastic networks immersed in a viscous fluid with site-dependent internal driving. We prove both numerically and analytically that the cycling frequencies obey a power law as a function of distance between the tracked degrees of freedom. Importantly, the behavior of the cycling frequencies contains information about the dimensionality of the system and the amplitude of active noise. The mapping we use in our analytical approach thus offers a convenient framework for predicting the behavior of two-point nonequilibrium measures for a given activity distribution in the network.

Trail-mediated self-interaction

A number of microorganisms leave persistent trails while moving along surfaces. For single-cell organisms, the trail-mediated self-interaction will influence the dynamics. It has been discussed recently [Kranz et al., Phys. Rev. Lett. 117, 038101 (2016)] that the self-interaction may localize the organism above a critical coupling χ_c to the trail. Here, we will derive a generalized active particle model capturing the key features of the self-interaction and analyze its behavior for smaller couplings χ < χ_c. We find that fluctuations in propulsion speed shift the localization transition to stronger couplings.

Modification of bacterial nanocellulose properties through mutation of motility related genes in Komagataeibacter hansenii ATCC 53582

Bacterial nanocellulose (BNC) produced by Komagataeibacter hansenii has received significant attention due to its unique supernetwork structure and properties. It is nevertheless necessary to modify bacterial nanocellulose to achieve materials with desired properties and thus with broader areas of application. The aim here was to influence the 3D structure of BNC by genetic modification of the cellulose producing K. hansenii strain ATCC 53582. Two genes encoding proteins with homology to the MotA and MotB proteins, which participate in motility and energy transfer, were selected for our studies. A disruption mutant of one or both genes and their respective complementation mutants were created. The phenotype analysis of the disruption mutants showed a reduction in motility, which resulted in higher compaction of nanocellulose fibers and improvement in their mechanical properties. The data strongly suggest that these genes play an important role in the formation of BNC membrane by Komagataeibacter species.

Advances in Biological Liquid Crystals

Biological liquid crystals, a rich set of soft materials with rod-like structures widely existing in nature, possess typical lyotropic liquid crystalline phase properties both in vitro (e.g., cellulose, peptides, and protein assemblies) and in vivo (e.g., cellular lipid membrane, packed DNA in bacteria, and aligned fibroblasts). Given the ability to undergo phase transition in response to various stimuli, numerous practices are exercised to spatially arrange biological liquid crystals. Here, a fundamental understanding of interactions between rod-shaped biological building blocks and their orientational ordering across multiple length scales is addressed. Discussions are made with regard to the dependence of physical properties of nonmotile objects on the first-order phase transition and the coexistence of multi-phases in passive liquid crystalline systems. This work also focuses on how the applied physical stimuli drives the reorganization of constituent passive particles for a new steady-state alignment. A number of recent progresses in the dynamics behaviors of active liquid crystals are presented, and particular attention is given to those self-propelled animate elements, like the formation of motile topological defects, active turbulence, correlation of orientational ordering, and cellular functions. Finally, future implications and potential applications of the biological liquid crystalline materials are discussed.

Shared behavioral mechanisms underlie C. elegans aggregation and swarming

In complex biological systems, simple individual-level behavioral rules can give rise to emergent group-level behavior. While collective behavior has been well studied in cells and larger organisms, the mesoscopic scale is less understood, as it is unclear which sensory inputs and physical processes matter a priori. Here, we investigate collective feeding in the roundworm C. elegans at this intermediate scale, using quantitative phenotyping and agent-based modeling to identify behavioral rules underlying both aggregation and swarming-a dynamic phenotype only observed at longer timescales. Using fluorescence multi-worm tracking, we quantify aggregation in terms of individual dynamics and population-level statistics. Then we use agent-based simulations and approximate Bayesian inference to identify three key behavioral rules for aggregation: cluster-edge reversals, a density-dependent switch between crawling speeds, and taxis towards neighboring worms. Our simulations suggest that swarming is simply driven by local food depletion but otherwise employs the same behavioral mechanisms as the initial aggregation.

Dynamical subclasses of dry active nematics

We show that the dominant mode of alignment plays an important role in dry active nematics, leading to two dynamical subclasses defined by the nature of the instability of the nematic bands that characterize, in these systems, the coexistence phase separating the isotropic and fluctuating nematic states. In addition to the well-known instability inducing long undulations along the band, another stronger instability leading to the breakup of the band in many transversal segments may arise. We elucidate the origin of this strong instability for a realistic model of self-propelled rods and determine the high-order nonlinear terms responsible for it at the hydrodynamic level.

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Capillary flow and mechanical buckling in a growing annular bacterial colony

A growing bacterial colony is a dense suspension of an increasing number of cells capable of individual as well as collective motion. After inoculating Pseudomonas aeruginosa over an annular area on an agar plate, we observe the growth and spread of the bacterial population, and model the process by considering the physical effects that account for the features observed. Over a course of 10-12 hours, the majority of bacteria migrate to and accumulate at the edges. We model the capillary flow induced by imbalanced evaporation flux as the cause for the accumulation, much like the well-known coffee stain phenomenon. Simultaneously, periodic buckles or protrusions occur at the inner edge. These buckles indicate that the crowding bacteria produce a jam, transforming the densely packed population at the inner edge to a solid state. The continued bacterial growth produces buckles. Subsequently, a ring of packed bacteria behind the inner edge detach from it and break into pieces, forming bacterial droplets. These droplets slowly coalesce while they continually grow and collectively surf on the agar surface in the region where the colony had previously spread over. Our study shows a clear example of how fluid dynamics and elasto-mechanics together govern the bacterial colony pattern evolution.

Low-noise phase of a two-dimensional active nematic system

We consider a collection of self-driven apolar particles on a substrate that organize into an active nematic phase at sufficiently high density or low noise. Using the dynamical renormalization group, we systematically study the two-dimensional fluctuating ordered phase in a coarse-grained hydrodynamic description involving both the nematic director and the conserved density field. In the presence of noise, we show that the system always displays only quasi-long-ranged orientational order beyond a crossover scale. A careful analysis of the nonlinearities permitted by symmetry reveals that activity is dangerously irrelevant over the linearized description, allowing giant number fluctuations to persist although now with strong finite-size effects and a nonuniversal scaling exponent. Nonlinear effects from the active currents lead to power-law correlations in the density field, thereby preventing macroscopic phase separation in the thermodynamic limit.

Development of semi-automatic procedure for detection and tracking of fiducial markers for orofacial kinematics during natural feeding

Feeding is a highly complex, essential behavior for survival in all species. Characterization of feeding behaviors has implications in basic science and translational medicine. We have been developing methods to study feeding behaviors using high speed videofluoroscopy (XROMM) in rats while self-feeding radiopaque flavored kibble. The rat is a popular model in translational medicine; however, it has not been studied using this methodology. Towards this goal, we surgically implanted radiopaque fiducial markers into the skull, mandible, and tongue of rats to enable motion tracking. We are developing computer vision tools to extract kinematics and behavioral features from XROMM videos to overcome barriers of current analysis methods. By understanding feeding dynamics, we will gain basic scientific knowledge and translational insights for feeding disorders caused by neurological conditions such as ALS, Parkinson's disease, and stroke.

Data-driven modeling reveals cell behaviors controlling self-organization during Myxococcus xanthus development

Collective cell movement is critical to the emergent properties of many multicellular systems, including microbial self-organization in biofilms, embryogenesis, wound healing, and cancer metastasis. However, even the best-studied systems lack a complete picture of how diverse physical and chemical cues act upon individual cells to ensure coordinated multicellular behavior. Known for its social developmental cycle, the bacterium Myxococcus xanthus uses coordinated movement to generate three-dimensional aggregates called fruiting bodies. Despite extensive progress in identifying genes controlling fruiting body development, cell behaviors and cell-cell communication mechanisms that mediate aggregation are largely unknown. We developed an approach to examine emergent behaviors that couples fluorescent cell tracking with data-driven models. A unique feature of this approach is the ability to identify cell behaviors affecting the observed aggregation dynamics without full knowledge of the underlying biological mechanisms. The fluorescent cell tracking revealed large deviations in the behavior of individual cells. Our modeling method indicated that decreased cell motility inside the aggregates, a biased walk toward aggregate centroids, and alignment among neighboring cells in a radial direction to the nearest aggregate are behaviors that enhance aggregation dynamics. Our modeling method also revealed that aggregation is generally robust to perturbations in these behaviors and identified possible compensatory mechanisms. The resulting approach of directly combining behavior quantification with data-driven simulations can be applied to more complex systems of collective cell movement without prior knowledge of the cellular machinery and behavioral cues.

Exopolysaccharides promote Myxococcus xanthus social motility by inhibiting cellular reversals

The biofilm-forming bacterium Myxococcus xanthus moves on surfaces as structured swarms utilizing type IV pili-dependent social (S) motility. In contrast to isolated cells that reverse their moving direction frequently, individual cells within swarms rarely reverse. The regulatory mechanisms that inhibit cellular reversal and promote the formation of swarms are not well understood. Here we show that exopolysaccharides (EPS), the major extracellular components of M. xanthus swarms, inhibit cellular reversal in a concentration-dependent manner. Thus, individual wild-type cells reverse less frequently in swarms due to high local EPS concentrations. In contrast, cells defective in EPS production hyper-reverse their moving direction and show severe defects in S-motility. Surprisingly, S-motility and wild-type reversal frequency are restored in double mutants that are defective in both EPS production and the Frz chemosensory system, indicating that EPS regulates cellular reversal in parallel to the Frz pathway. Here we clarify that besides functioning as the structural scaffold in biofilms, EPS is a self-produced signal that coordinates the group motion of the social bacterium M. xanthus.

Mesoscale pattern formation of self-propelled rods with velocity reversal

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

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

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

Regulations governing the multicellular lifestyle of Myxococcus xanthus

In living organisms, cooperative cell movements underlie the formation of differentiated tissues. In bacteria, Myxococcus xanthus uses cooperative group movements, to predate on prey and to form multicellular fruiting bodies, where the cells differentiate into dormant spores. Motility is controlled by a central signaling Che-like pathway, Frz. Single cell studies indicate Frz regulates the frequency at which cells reverse their direction of movement by transmitting signals to a molecular system that controls the spatial activity of the motility engines. This regulation is central to all Myxococcus multicellular behaviors but how Frz signaling generates ordered patterns is poorly understood. In this review, we first discuss the genetic structure of the Frz pathway and possible regulations that could explain its action during Myxococcus development.

Peroxiredoxin 6 (Prdx6) supports NADPH oxidase1 (Nox1)-based superoxide generation and cell migration

Nox1 is an abundant source of reactive oxygen species (ROS) in colon epithelium recently shown to function in wound healing and epithelial homeostasis. We identified Peroxiredoxin 6 (Prdx6) as a novel binding partner of Nox activator 1 (Noxa1) in yeast two-hybrid screening experiments using the Noxa1 SH3 domain as bait. Prdx6 is a unique member of the Prdx antioxidant enzyme family exhibiting both glutathione peroxidase and phospholipase A2 activities. We confirmed this interaction in cells overexpressing both proteins, showing Prdx6 binds to and stabilizes wild type Noxa1, but not the SH3 domain mutant form, Noxa1 W436R. We demonstrated in several cell models that Prdx6 knockdown suppresses Nox1 activity, whereas enhanced Prdx6 expression supports higher Nox1-derived superoxide production. Both peroxidase- and lipase-deficient mutant forms of Prdx6 (Prdx6 C47S and S32A, respectively) failed to bind to or stabilize Nox1 components or support Nox1-mediated superoxide generation. Furthermore, the transition-state substrate analogue inhibitor of Prdx6 phospholipase A2 activity (MJ-33) was shown to suppress Nox1 activity, suggesting Nox1 activity is regulated by the phospholipase activity of Prdx6. Finally, wild type Prdx6, but not lipase or peroxidase mutant forms, supports Nox1-mediated cell migration in the HCT-116 colon epithelial cell model of wound closure. These findings highlight a novel pathway in which this antioxidant enzyme positively regulates an oxidant-generating system to support cell migration and wound healing.

Hysteresis, reentrance, and glassy dynamics in systems of self-propelled rods

Nonequilibrium active matter made up of self-driven particles with short-range repulsive interactions is a useful minimal system to study active matter as the system exhibits collective motion and nonequilibrium order-disorder transitions. We studied high-aspect-ratio self-propelled rods over a wide range of packing fractions and driving to determine the nonequilibrium state diagram and dynamic properties. Flocking and nematic-laning states occupy much of the parameter space. In the flocking state, the average internal pressure is high and structural and mechanical relaxation times are long, suggesting that rods in flocks are in a translating glassy state despite overall flock motion. In contrast, the nematic-laning state shows fluidlike behavior. The flocking state occupies regions of the state diagram at both low and high packing fraction separated by nematic-laning at low driving and a history-dependent region at higher driving; the nematic-laning state transitions to the flocking state for both compression and expansion. We propose that the laning-flocking transitions are a type of glass transition that, in contrast to other glass-forming systems, can show fluidization as density increases. The fluid internal dynamics and ballistic transport of the nematic-laning state may promote collective dynamics of rod-shaped micro-organisms.

Mechanism for Collective Cell Alignment in Myxococcus xanthus Bacteria

Myxococcus xanthus cells self-organize into aligned groups, clusters, at various stages of their lifecycle. Formation of these clusters is crucial for the complex dynamic multi-cellular behavior of these bacteria. However, the mechanism underlying the cell alignment and clustering is not fully understood. Motivated by studies of clustering in self-propelled rods, we hypothesized that M. xanthus cells can align and form clusters through pure mechanical interactions among cells and between cells and substrate. We test this hypothesis using an agent-based simulation framework in which each agent is based on the biophysical model of an individual M. xanthus cell. We show that model agents, under realistic cell flexibility values, can align and form cell clusters but only when periodic reversals of cell directions are suppressed. However, by extending our model to introduce the observed ability of cells to deposit and follow slime trails, we show that effective trail-following leads to clusters in reversing cells. Furthermore, we conclude that mechanical cell alignment combined with slime-trail-following is sufficient to explain the distinct clustering behaviors observed for wild-type and non-reversing M. xanthus mutants in recent experiments. Our results are robust to variation in model parameters, match the experimentally observed trends and can be applied to understand surface motility patterns of other bacterial species.