Mechanism for Collective Cell Alignment in Myxococcus xanthus Bacteria

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.

Derivation and simulation of a computational model of active cell populations: How overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces affect alignment

Collective alignment of cell populations is a commonly observed phenomena in biology. An important example are aligning fibroblasts in healthy or scar tissue. In this work we derive and simulate a mechanistic agent-based model of the collective behaviour of actively moving and interacting cells, with a focus on understanding collective alignment. The derivation strategy is based on energy minimisation. The model ingredients are motivated by data on the behaviour of different populations of aligning fibroblasts and include: Self-propulsion, overlap avoidance, deformability, cell-cell junctions and cytoskeletal forces. We find that there is an optimal ratio of self-propulsion speed and overlap avoidance that maximises collective alignment. Further we find that deformability aids alignment, and that cell-cell junctions by themselves hinder alignment. However, if cytoskeletal forces are transmitted via cell-cell junctions we observe strong collective alignment over large spatial scales.

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.

Active many-particle systems and the emergent behavior of dense ant collectives

This article discusses recent work with fire ants,Solenopisis invicta, to illustrate the use of the framework of active matter as a base to rationalize their complex collective behavior. We review much of the work that physicists have done on the group dynamics of these ants, and compare their behavior to two minimal models of active matter, and to the behavior of the synthetic systems that have served to test and drive these models.

Self-Organized States from Solutions of Active Ring Polymers in Bulk and under Confinement

In the present work, we study, by means of numerical simulations, the structural and dynamical behavior of a suspension of active ring polymers in bulk and under lateral confinement. At high activity, when changing the distance between the confining planes and the polymers' density, we identify the emergence of a self-organized dynamical state, characterized by the coexistence of slowly diffusing clusters of rotating disks and faster rings moving in between them. We further assess that self-organization is robust in a range of polymer sizes, and we identify a critical value of the activity, necessary to trigger cluster formation. This system has distinctive features resembling at the same time polymers, liquid crystals, and active systems, where the interplay between activity, topology, and confinement leads to a spontaneous segregation in an initially one-component solution.

Conformation and dynamics of partially active linear polymers

We perform numerical simulations of isolated, partially active polymers, driven out-of-equilibrium by a fraction of their monomers. We show that, if the active beads are all gathered in a contiguous block, the position of the section along the chain determines the conformational and dynamical properties of the system. Notably, one can modulate the diffusion coefficient of the polymer from active-like to passive-like just by changing the position of the active block. Further, we show that a slight modification of the self-propulsion rule may give rise to an enhancement of diffusion under certain conditions, despite a decrease of the overall polymer activity. Our findings may help in the modelisation of active biophysical systems, such as filamentous bacteria or worms.

Mean-field model for nematic alignment of self-propelled rods

Self-propelled rods are a facet of the field of active matter relevant to many physical systems ranging in scale from shaken granular media and bacterial alignment to the flocking dynamics of animals. In this paper we develop a model for nematic alignment of self-propelled rods interacting through binary collisions. We avoid phenomenological descriptions of rod interaction in favor of rigorously using a set of microscopic-level rules. Under the assumption that each collision results in a small change to a rod's orientation, we derive the Fokker-Planck equation for the evolution of the kinetic density function. Using analytical and numerical methods, we study the emergence of the nematic order from a homogeneous, uniform steady state of the mean-field equation. We compare the level of orientational noise needed to destabilize this nematic order and compare our results to an existing phenomenological model that does not explicitly account for the physical collisions of rods. We show the presence of an additional geometric factor in our equations reflecting a reduced collision rate between nearly aligned rods that reduces the level of noise at which nematic order is destroyed, suggesting that alignment that depends on purely physical collisions is less robust.

Emergent Myxobacterial Behaviors Arise from Reversal Suppression Induced by Kin Contacts

A wide range of biological systems, from microbial swarms to bird flocks, display emergent behaviors driven by coordinated movement of individuals. To this end, individual organisms interact by recognizing their kin and adjusting their motility based on others around them. However, even in the best-studied systems, the mechanistic basis of the interplay between kin recognition and motility coordination is not understood. Here, using a combination of experiments and mathematical modeling, we uncover the mechanism of an emergent social behavior in Myxococcus xanthus. By overexpressing the cell surface adhesins TraA and TraB, which are involved in kin recognition, large numbers of cells adhere to one another and form organized macroscopic circular aggregates that spin clockwise or counterclockwise. Mechanistically, TraAB adhesion results in sustained cell-cell contacts that trigger cells to suppress cell reversals, and circular aggregates form as the result of cells’ ability to follow their own cellular slime trails. Furthermore, our in silico simulations demonstrate a remarkable ability to predict self-organization patterns when phenotypically distinct strains are mixed. For example, defying naive expectations, both models and experiments found that strains engineered to overexpress different and incompatible TraAB adhesins nevertheless form mixed circular aggregates. Therefore, this work provides key mechanistic insights into M. xanthus social interactions and demonstrates how local cell contacts induce emergent collective behaviors by millions of cells.

IMPORTANCE In many species, large populations exhibit emergent behaviors whereby all related individuals move in unison. For example, fish in schools can all dart in one direction simultaneously to avoid a predator. Currently, it is impossible to explain how such animals recognize kin through brain cognition and elicit such behaviors at a molecular level. However, microbes also recognize kin and exhibit emergent collective behaviors that are experimentally tractable. Here, using a model social bacterium, we engineer dispersed individuals to organize into synchronized collectives that create emergent patterns. With experimental and mathematical approaches, we explain how this occurs at both molecular and population levels. The results demonstrate how the combination of local physical interactions triggers intracellular signaling, which in turn leads to emergent behaviors on a population scale.

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.

Linking single-cell decisions to collective behaviours in social bacteria

Social bacteria display complex behaviours whereby thousands of cells collectively and dramatically change their form and function in response to nutrient availability and changing environmental conditions. In this review, we focus on Myxococcus xanthus motility, which supports spectacular transitions based on prey availability across its life cycle. A large body of work suggests that these behaviours require sensory capacity implemented at the single-cell level. Focusing on recent genetic work on a core cellular pathway required for single-cell directional decisions, we argue that signal integration, multi-modal sensing and memory are at the root of decision making leading to multicellular behaviours. Hence, Myxococcus may be a powerful biological system to elucidate how cellular building blocks cooperate to form sensory multicellular assemblages, a possible origin of cognitive mechanisms in biological systems. This article is part of the theme issue 'Basal cognition: conceptual tools and the view from the single cell'.

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.

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.

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.

Contrarian compulsions produce exotic time-dependent flocking of active particles

Animals having a tendency to align their velocities to an average of those of their neighbors may flock as illustrated by the Vicsek model and its variants. If, in addition, they feel a systematic contrarian trend, the result may be a time periodic adjustment of the flock or period doubling in time. These exotic phases are predicted from kinetic theory and numerically found in a modified two-dimensional Vicsek model of self-propelled particles. Numerical simulations demonstrate striking effects of alignment noise on the polarization order parameter measuring particle flocking: maximum polarization length is achieved at an optimal nonzero noise level. When contrarian compulsions are more likely than conformist ones, nonuniform polarized phases appear as the noise surpasses threshold.

Agent-Based Modeling Reveals Possible Mechanisms for Observed Aggregation Cell Behaviors

Myxococcus xanthus is a soil bacterium that serves as a model system for biological self-organization. Cells form distinct, dynamic patterns depending on environmental conditions. An agent-based model was used to understand how M. xanthus cells aggregate into multicellular mounds in response to starvation. In this model, each cell is modeled as an agent represented by a point particle and characterized by its position and moving direction. At low agent density, the model recapitulates the dynamic patterns observed by experiments and a previous biophysical model. To study aggregation at high cell density, we extended the model based on the recent experimental observation that cells exhibit biased movement toward aggregates. We tested two possible mechanisms for this biased movement and demonstrate that a chemotaxis model with adaptation can reproduce the observed experimental results leading to the formation of stable aggregates. Furthermore, our model reproduces the experimentally observed patterns of cell alignment around aggregates.

Microbial multicellular development: mechanical forces in action

Multicellular development occurs in diverse microbial lineages and involves the complex interaction among biochemical, physical and ecological factors. We focus on the mechanical forces that appear to be relevant for the scale and material qualities of individual cells and small cellular conglomerates. We review the effects of such forces on the development of some paradigmatic microorganisms, as well as their overall consequences in multicellular structures. Microbes exhibiting multicellular development have been considered models for the evolutionary transition to multicellularity. Therefore, we discuss how comparative, integrative and dynamic approaches to the mechanical effects involved in microbial development can provide valuable insights into some of the principles behind the evolutionary transition to multicellularity.

Bacterial Surface Spreading Is More Efficient on Nematically Aligned Polysaccharide Substrates

Biofilm-forming bacteria typically deposit layers of polysaccharides on the surfaces they inhabit; hence, polysaccharides are their immediate environment on such surfaces. Previously, we showed that many biofilm-forming bacteria preferentially spread in the direction of aligned and densely packed polysaccharide fibers in compressed substrates, a behavior we referred to as polymertropism. This arrangement of polysaccharide fibers is likely to be similar to that found in the "slime" trails deposited by many biofilm-forming bacteria and would explain previous observations that bacteria tend to follow these trails of polysaccharides. Here, we show that groups of cells or flares spread more rapidly on substrates containing aligned and densely packed polysaccharide fibers. Flares also persist longer, tend to hold their trajectories parallel to the long axes of polysaccharide fibers longer, and ultimately show an increase in displacement away from their origin. On the basis of these findings and others, we propose a model for polymertropism. Namely, we suggest that the packing of the aligned polymers increases the efficiency of surface spreading in the direction of the polymer's long axes; therefore, bacteria tend to spread more rapidly in this direction. Additional work suggests that bacteria can leverage polymertropism, and presumably more efficient surface spreading, for a survival advantage. In particular, when two bacterial species were placed in close proximity and in competition with each other, the ability of one species to move rapidly and directly away from the other by utilizing the aligned polymers of compressed agar substrates led to a clear survival benefit.IMPORTANCE The directed movement of bacteria on compressed substrates was first described in the 1940s and referred to as elasticotaxis (R. Y. Stanier, J Bacteriol 44:405-412, 1942). More recently, this behavior was referred to as polymertropism, as it seems to be a response to the nematic alignment and tight packing of polymers in the substrate (D. J. Lemon, X. Yang, P. Srivastava, Y. Y. Luk, A. G. Garza, Sci Rep 7:7643, 2017, https://doi.org/10.1038/s41598-017-07486-0). The data presented here suggest that bacteria are more efficient at surface spreading when the polymers in the substrate are arranged in this manner. These data also suggest that bacteria can leverage polymertropism, and presumably more efficient surface spreading, for a survival advantage. Namely, one bacterial species was able to use its strong polymertropism response to escape from and survive competition with another species that normally outcompetes it.

Morphodynamics of a growing microbial colony driven by cell death

Bacterial cells can often self-organize into multicellular structures with complex spatiotemporal morphology. In this work, we study the spatiotemporal dynamics of a growing microbial colony in the presence of cell death. We present an individual-based model of nonmotile bacterial cells which grow and proliferate by consuming diffusing nutrients on a semisolid two-dimensional surface. The colony spreads by growth forces and sliding motility of cells and undergoes cell death followed by subsequent disintegration of the dead cells in the medium. We model cell death by considering two possible situations: In one of the cases, cell death occurs in response to the limitation of local nutrients, while the other case corresponds to an active death process, known as apoptotic or programmed cell death. We demonstrate how the colony morphology is influenced by the presence of cell death. Our results show that cell death facilitates transitions from roughly circular to highly branched structures at the periphery of an expanding colony. Interestingly, our results also reveal that for the colonies which are growing in higher initial nutrient concentrations, cell death occurs much earlier compared to the colonies which are growing in lower initial nutrient concentrations. This work provides new insights into the branched patterning of growing bacterial colonies as a consequence of complex interplay among the biochemical and mechanical effects.

An Evo-Devo Perspective on Multicellular Development of Myxobacteria

The transition to multicellularity, recognized as one the major transitions in evolution, has occurred independently several times. While multicellular development has been extensively studied in zygotic organisms including plant and animal groups, just a few aggregative multicellular organisms have been employed as model organisms for the study of multicellularity. Studying different evolutionary origins and modes of multicellularity enables comparative analyses that can help identifying lineage-specific aspects of multicellular evolution and generic factors and mechanisms involved in the transition to multicellularity. Among aggregative multicellular organisms, myxobacteria are a valuable system to explore the particularities that aggregation confers to the evolution of multicellularity and mechanisms shared with clonal organisms. Moreover, myxobacteria species develop fruiting bodies displaying a range of morphological diversity. In this review, we aim to synthesize diverse lines of evidence regarding myxobacteria development and discuss them in the context of Evo-Devo concepts and approaches. First, we briefly describe the developmental processes in myxobacteria, present an updated comparative analysis of the genes involved in their developmental processes and discuss these and other lines of evidence in terms of co-option and developmental system drift, two concepts key to Evo-Devo studies. Next, as has been suggested from Evo-Devo approaches, we discuss how broad comparative studies and integration of diverse genetic, physicochemical, and environmental factors into experimental and theoretical models can further our understanding of myxobacterial development, phenotypic variation, and evolution.

Polymertropism of rod-shaped bacteria: movement along aligned polysaccharide fibers

In nature, bacteria often live in surface-associated communities known as biofilms. Biofilm-forming bacteria typically deposit a layer of polysaccharide on the surfaces they inhabit; hence, polysaccharide is their immediate environment on many surfaces. In this study, we examined how the physical characteristics of polysaccharide substrates influence the behavior of the biofilm-forming bacterium Myxococcus xanthus. M. xanthus responds to the compression-induced deformation of polysaccharide substrates by preferentially spreading across the surface perpendicular to the axis of compression. Our results suggest that M. xanthus is not responding to the water that accumulates on the surface of the polysaccharide substrate after compression or to compression-induced changes in surface topography such as the formation of troughs. These directed surface movements do, however, consistently match the orientation of the long axes of aligned and tightly packed polysaccharide fibers in compressed substrates, as indicated by behavioral, birefringence and small angle X-ray scattering analyses. Therefore, we suggest that the directed movements are a response to the physical arrangement of the polymers in the substrate and refer to the directed movements as polymertropism. This behavior might be a common property of bacteria, as many biofilm-forming bacteria that are rod-shaped and motile on soft surfaces exhibit polymertropism.

On the mechanism of long-range orientational order of fibroblasts

Long-range alignment ordering of fibroblasts have been observed in the vicinity of cancerous tumors and can be recapitulated with in vitro experiments. However, the mechanisms driving their ordering are not understood. Here, we show that local collision-driven nematic alignment interactions among fibroblasts are insufficient to explain observed long-range alignment. One possibility is that there exists another orientation field coevolving with the cells and reinforcing their alignment. We propose that this field reflects the mechanical cross-talk between the fibroblasts and the underlying fibrous material on which they move. We show that this long-range interaction can give rise to high nematic order and to the observed patterning of the cancer microenvironment.

Modeling mechanical interactions in growing populations of rod-shaped bacteria

Advances in synthetic biology allow us to engineer bacterial collectives with pre-specified characteristics. However, the behavior of these collectives is difficult to understand, as cellular growth and division as well as extra-cellular fluid flow lead to complex, changing arrangements of cells within the population. To rationally engineer and control the behavior of cell collectives we need theoretical and computational tools to understand their emergent spatiotemporal dynamics. Here, we present an agent-based model that allows growing cells to detect and respond to mechanical interactions. Crucially, our model couples the dynamics of cell growth to the cell's environment: Mechanical constraints can affect cellular growth rate and a cell may alter its behavior in response to these constraints. This coupling links the mechanical forces that influence cell growth and emergent behaviors in cell assemblies. We illustrate our approach by showing how mechanical interactions can impact the dynamics of bacterial collectives growing in microfluidic traps.

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.

Reversals and collisions optimize protein exchange in bacterial swarms

Swarming groups of bacteria coordinate their behavior by self-organizing as a population to move over surfaces in search of nutrients and optimal niches for colonization. Many open questions remain about the cues used by swarming bacteria to achieve this self-organization. While chemical cue signaling known as quorum sensing is well-described, swarming bacteria often act and coordinate on time scales that could not be achieved via these extracellular quorum sensing cues. Here, cell-cell contact-dependent protein exchange is explored as a mechanism of intercellular signaling for the bacterium Myxococcus xanthus. A detailed biologically calibrated computational model is used to study how M. xanthus optimizes the connection rate between cells and maximizes the spread of an extracellular protein within the population. The maximum rate of protein spreading is observed for cells that reverse direction optimally for swarming. Cells that reverse too slowly or too fast fail to spread extracellular protein efficiently. In particular, a specific range of cell reversal frequencies was observed to maximize the cell-cell connection rate and minimize the time of protein spreading. Furthermore, our findings suggest that predesigned motion reversal can be employed to enhance the collective behavior of biological synthetic active systems.

Emergent pattern formation in an interstitial biofilm

Collective behavior of bacterial colonies plays critical roles in adaptability, survivability, biofilm expansion and infection. We employ an individual-based model of an interstitial biofilm to study emergent pattern formation based on the assumptions that rod-shaped bacteria furrow through a viscous environment and excrete extracellular polymeric substances which bias their rate of motion. Because the bacteria furrow through their environment, the substratum stiffness is a key control parameter behind the formation of distinct morphological patterns. By systematically varying this property (which we quantify with a stiffness coefficient γ), we show that subtle changes in the substratum stiffness can give rise to a stable state characterized by a high degree of local order and long-range pattern formation. The ordered state exhibits characteristics typically associated with bacterial fitness advantages, even though it is induced by changes in environmental conditions rather than changes in biological parameters. Our findings are applicable to a broad range of biofilms and provide insights into the relationship between bacterial movement and their environment, and basic mechanisms behind self-organization of biophysical systems.

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.

Colony Expansion of Socially Motile Myxococcus xanthus Cells Is Driven by Growth, Motility, and Exopolysaccharide Production

Myxococcus xanthus, a model organism for studies of multicellular behavior in bacteria, moves exclusively on solid surfaces using two distinct but coordinated motility mechanisms. One of these, social (S) motility is powered by the extension and retraction of type IV pili and requires the presence of exopolysaccharides (EPS) produced by neighboring cells. As a result, S motility requires close cell-to-cell proximity and isolated cells do not translocate. Previous studies measuring S motility by observing the colony expansion of cells deposited on agar have shown that the expansion rate increases with initial cell density, but the biophysical mechanisms involved remain largely unknown. To understand the dynamics of S motility-driven colony expansion, we developed a reaction-diffusion model describing the effects of cell density, EPS deposition and nutrient exposure on the expansion rate. Our results show that at steady state the population expands as a traveling wave with a speed determined by the interplay of cell motility and growth, a well-known characteristic of Fisher’s equation. The model explains the density-dependence of the colony expansion by demonstrating the presence of a lag phase–a transient period of very slow expansion with a duration dependent on the initial cell density. We propose that at a low initial density, more time is required for the cells to accumulate enough EPS to activate S-motility resulting in a longer lag period. Furthermore, our model makes the novel prediction that following the lag phase the population expands at a constant rate independent of the cell density. These predictions were confirmed by S motility experiments capturing long-term expansion dynamics.

Collective motility is a key mechanism bacteria use to self-organize into multicellular structures and to adapt to various environments. An important example of such behavior is social (S) motility in the gram-negative bacterium Myxococcus xanthus. S-motile cells are restricted to movement in groups and do not move as individual cells. S-motility is powered by type IV pili (TFP)–multi-subunit filaments, which extrude from the cell poles, adhere to the substrate and retract, pulling the cell forward. TFP retraction or adhesion is suggested to be triggered by extracellular exopolysaccharides (EPS) deposited by cells on the substrate. As individual cells synthesize both pili and EPS, it is unclear why S-motile cells only exhibit group movement. Moreover, the experimentally observed initial cell-density dependence of S-motility remains unexplained. To understand these phenomena, we developed a mathematical model for the colony expansion of S-motile cells. Our model hypothesizes that the EPS level regulates the TFP activity that initiates collective cell movements. With this assumption, the model quantitatively matches the density-dependent expansion rate. Moreover, the model predicts two phases during colony expansion: an initial density-dependent lag phase with a slow expansion rate, followed by a faster expansion phase with a density-independent rate. These model predictions were confirmed by long-term colony expansion experiments.

Myxobacteria: Moving, Killing, Feeding, and Surviving Together

Myxococcus xanthus, like other myxobacteria, is a social bacterium that moves and feeds cooperatively in predatory groups. On surfaces, rod-shaped vegetative cells move in search of the prey in a coordinated manner, forming dynamic multicellular groups referred to as swarms. Within the swarms, cells interact with one another and use two separate locomotion systems. Adventurous motility, which drives the movement of individual cells, is associated with the secretion of slime that forms trails at the leading edge of the swarms. It has been proposed that cellular traffic along these trails contributes to M. xanthus social behavior via stigmergic regulation. However, most of the cells travel in groups by using social motility, which is cell contact-dependent and requires a large number of individuals. Exopolysaccharides and the retraction of type IV pili at alternate poles of the cells are the engines associated with social motility. When the swarms encounter prey, the population of M. xanthus lyses and takes up nutrients from nearby cells. This cooperative and highly density-dependent feeding behavior has the advantage that the pool of hydrolytic enzymes and other secondary metabolites secreted by the entire group is shared by the community to optimize the use of the degradation products. This multicellular behavior is especially observed in the absence of nutrients. In this condition, M. xanthus swarms have the ability to organize the gliding movements of 1000s of rods, synchronizing rippling waves of oscillating cells, to form macroscopic fruiting bodies, with three subpopulations of cells showing division of labor. A small fraction of cells either develop into resistant myxospores or remain as peripheral rods, while the majority of cells die, probably to provide nutrients to allow aggregation and spore differentiation. Sporulation within multicellular fruiting bodies has the benefit of enabling survival in hostile environments, and increases germination and growth rates when cells encounter favorable conditions. Herein, we review how these social bacteria cooperate and review the main cell–cell signaling systems used for communication to maintain multicellularity.

Velocity Condensation for Magnetotactic Bacteria

Magnetotactic swimmers tend to align along magnetic field lines against stochastic reorientations. We show that the swimming strategy, e.g., active Brownian motion versus run-and-tumble dynamics, strongly affects the orientation statistics. The latter can exhibit a velocity condensation whereby the alignment probability density diverges. As a consequence, we find that the swimming strategy affects the nature of the phase transition to collective motion, indicating that Lévy run-and-tumble walks can outperform active Brownian processes as strategies to trigger collective behavior.

Wavelength selection of rippling patterns in myxobacteria

Rippling patterns of myxobacteria appear in starving colonies before they aggregate to form fruiting bodies. These periodic traveling cell density waves arise from the coordination of individual cell reversals, resulting from an internal clock regulating them and from contact signaling during bacterial collisions. Here we revisit a mathematical model of rippling in myxobacteria due to Igoshin et al. [Proc. Natl. Acad. Sci. USA 98, 14913 (2001)PNASA60027-842410.1073/pnas.221579598 and Phys. Rev. E 70, 041911 (2004)PLEEE81539-375510.1103/PhysRevE.70.041911]. Bacteria in this model are phase oscillators with an extra internal phase through which they are coupled to a mean field of oppositely moving bacteria. Previously, patterns for this model were obtained only by numerical methods, and it was not possible to find their wave number analytically. We derive an evolution equation for the reversal point density that selects the pattern wave number in the weak signaling limit, shows the validity of the selection rule by solving numerically the model equations, and describes other stable patterns in the strong signaling limit. The nonlocal mean-field coupling tends to decohere and confine patterns. Under appropriate circumstances, it can annihilate the patterns leaving a constant density state via a nonequilibrium phase transition reminiscent of destruction of synchronization in the Kuramoto model.