Physical mechanisms for chemotactic pattern formation by bacteria

Spatiotemporal control of structure and dynamics in a polar active fluid

We apply optimal control theory to a model of a polar active fluid (the Toner-Tu model), with the objective of driving the system into particular emergent dynamical behaviors or programming switching between states on demand. We use the effective self-propulsion speed as the control parameter (i.e. the means of external actuation). We identify control protocols that achieve outcomes such as relocating asters to targeted positions, forcing propagating solitary waves to reorient to a particular direction, and switching between stationary asters and propagating fronts. We analyze the solutions to identify generic principles for controlling polar active fluids. Our findings have implications for achieving spatiotemporal control of active polar systems in experiments, particularly in vitro cytoskeletal systems. Additionally, this research paves the way for leveraging optimal control methods to engineer the structure and dynamics of active fluids more broadly.

Mobility and growth in confined spaces are important mechanisms for the establishment of Bacillus subtilis in the rhizosphere

The rhizosphere hosts complex and abundant microbiomes whose structure and composition are now well described by metagenomic studies. However, the dynamic mechanisms that enable micro-organisms to establish along a growing plant root are poorly characterized. Here, we studied how a motile bacterium utilizes the microhabitats created by soil pore space to establish in the proximity of plant roots. We have established a model system consisting of Bacillus subtilis and lettuce seedlings co-inoculated in transparent soil microcosms. We carried out live imaging experiments and developed image analysis pipelines to quantify the abundance of the bacterium as a function of time and position in the pore space. Results showed that the establishment of the bacterium in the rhizosphere follows a precise sequence of events where small islands of mobile bacteria were first seen forming near the root tip within the first 12-24 h of inoculation. Biofilm was then seen forming on the root epidermis at distances of about 700-1000 µm from the tip. Bacteria accumulated predominantly in confined pore spaces within 200 µm from the root or the surface of a particle. Using probabilistic models, we could map the complete sequence of events and propose a conceptual model of bacterial establishment in the pore space. This study therefore advances our understanding of the respective role of growth and mobility in the efficient colonization of bacteria in the rhizosphere.

Self-organization of active colloids mediated by chemical interactions

Self-propelled colloidal particles exhibit rich non-equilibrium phenomena and have promising applications in fields such as drug delivery and self-assembled active materials. Previous experimental and theoretical studies have shown that chemically active colloids that consume or produce a chemical can self-organize into clusters with diverse characteristics depending on the effective phoretic interactions. In this paper, we investigate self-organization in systems with multiple chemical species that undergo a network of reactions and multiple colloidal species that participate in different reactions. Active colloids propelled by complex chemical reactions with potentially nonlinear kinetics can be realized using enzymatic reactions that occur on the surface of enzyme-coated particles. To demonstrate how the self-organizing behavior depends on the chemical reactions active colloids catalyze and their chemical environment, we consider first a single type of colloid undergoing a simple catalytic reaction, and compare this often-studied case with self-organization in binary mixtures of colloids with sequential reactions, and binary mixtures with nonlinear autocatalytic reactions. Our results show that in general active colloids at low particle densities can form localized clusters in the presence of bulk chemical reactions and phoretic attractions. The characteristics of the clusters, however, depend on the reaction kinetics in the bulk and on the particles and phoretic coefficients. With one or two chemical species that only undergo surface reactions, the space for possible self-organizations are limited. By considering the additional system parameters that enter the chemical reaction network involving reactions on the colloids and in the fluid, the design space of colloidal self-organization can be enlarged, leading to a variety of non-equilibrium structures.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

Non-reciprocity across scales in active mixtures

In active matter, particles typically experience mediated interactions, which are not constrained by Newton's third law and are therefore generically non-reciprocal. Non-reciprocity leads to a rich set of emerging behaviors that are hard to account for starting from the microscopic scale, due to the absence of a generic theoretical framework out of equilibrium. Here we consider bacterial mixtures that interact via mediated, non-reciprocal interactions (NRI) like quorum-sensing and chemotaxis. By explicitly relating microscopic and macroscopic dynamics, we show that, under conditions that we derive explicitly, non-reciprocity may fade upon coarse-graining, leading to large-scale equilibrium descriptions. In turn, this allows us to account quantitatively, and without fitting parameters, for the rich behaviors observed in microscopic simulations including phase separation, demixing, and multi-phase coexistence. We also derive the condition under which non-reciprocity survives coarse-graining, leading to a wealth of dynamical patterns. Again, our analytical approach allows us to predict the phase diagram of the system starting from its microscopic description. All in all, our work demonstrates that the fate of non-reciprocity across scales is a subtle and important question.

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

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

Bacterial bioconvection confers context-dependent growth benefits and is robust under varying metabolic and genetic conditions

Microbes often respond to environmental cues by adopting collective behaviors-like biofilms or swarming-that benefit the population. During "bioconvection," microbes gather in dense groups and plume downward through fluid environments, driving flow and mixing on the scale of millions of cells. Though bioconvection was observed a century ago, the effects of differing physical and chemical inputs and its potential selective advantages for different species of microbes remain largely unexplored. In Bacillus subtilis, vertical oxygen gradients that originate from air-liquid interfaces create cell-density inversions that drive bioconvection. Here, we develop Escherichia coli as a complementary model for the study of bioconvection. In the context of a still fluid, we found that motile and chemotactic genotypes of both E. coli and B. subtilis bioconvect and show increased growth compared to immotile or non-chemotactic genotypes, whereas in a well-mixed fluid, there is no growth advantage to motility or chemotaxis. We found that fluid depth, cell concentration, and carbon availability affect the emergence and timing of bioconvective patterns. Also, whereas B. subtilis requires oxygen gradients to bioconvect, E. coli deficient in aerotaxis (Δaer) or energy-taxis (Δtsr) still bioconvects, as do cultures that lack an air-liquid interface. Thus, in two distantly related microbes, bioconvection may confer context-dependent growth benefits, and E. coli bioconvection is robustly elicited by multiple types of chemotaxis. These results greatly expand the set of physical and metabolic conditions in which this striking collective behavior can be expected and demonstrate its potential to be a generic force for behavioral selection across ecological contexts. IMPORTANCE Individual microorganisms frequently move in response to gradients in their fluid environment, with corresponding metabolic benefits. At a population level, such movements can create density variations in a fluid that couple to gravity and drive large-scale convection and mixing called bioconvection. In this work, we provide evidence that this collective behavior confers a selective benefit on two distantly related species of bacteria. We develop new methods for quantifying this behavior and show that bioconvection in Escherichia coli is surprisingly robust to changes in cell concentration, fluid depth, interface conditions, metabolic sensing, and carbon availability. These results greatly expand the set of conditions known to elicit this collective behavior and indicate its potential to be a selective pressure across ecological contexts.

Pattern formation by bacteria-phage interactions

The interactions between bacteria and phages-viruses that infect bacteria-play critical roles in agriculture, ecology, and medicine; however, how these interactions influence the spatial organization of both bacteria and phages remain largely unexplored. Here, we address this gap in knowledge by developing a theoretical model of motile, proliferating bacteria that aggregate via motility-induced phase separation (MIPS) and encounter phage that infect and lyse the cells. We find that the non-reciprocal predator-prey interactions between phage and bacteria strongly alter spatial organization, in some cases giving rise to a rich array of finite-scale stationary and dynamic patterns in which bacteria and phage coexist. We establish principles describing the onset and characteristics of these diverse behaviors, thereby helping to provide a biophysical basis for understanding pattern formation in bacteria-phage systems, as well as in a broader range of active and living systems with similar predator-prey or other non-reciprocal interactions.

Chemotactic Motility-Induced Phase Separation

Collectives of actively moving particles can spontaneously separate into dilute and dense phases-a fascinating phenomenon known as motility-induced phase separation (MIPS). MIPS is well-studied for randomly moving particles with no directional bias. However, many forms of active matter exhibit collective chemotaxis, directed motion along a chemical gradient that the constituent particles can generate themselves. Here, using theory and simulations, we demonstrate that collective chemotaxis strongly competes with MIPS-in some cases, arresting or completely suppressing phase separation, or in other cases, generating fundamentally new dynamic instabilities. We establish principles describing this competition, thereby helping to reveal and clarify the rich physics underlying active matter systems that perform chemotaxis, ranging from cells to robots.

Direct measurement of dynamic attractant gradients reveals breakdown of the Patlak-Keller-Segel chemotaxis model

Chemotactic bacteria not only navigate chemical gradients, but also shape their environments by consuming and secreting attractants. Investigating how these processes influence the dynamics of bacterial populations has been challenging because of a lack of experimental methods for measuring spatial profiles of chemoattractants in real time. Here, we use a fluorescent sensor for aspartate to directly measure bacterially generated chemoattractant gradients during collective migration. Our measurements show that the standard Patlak-Keller-Segel model for collective chemotactic bacterial migration breaks down at high cell densities. To address this, we propose modifications to the model that consider the impact of cell density on bacterial chemotaxis and attractant consumption. With these changes, the model explains our experimental data across all cell densities, offering new insight into chemotactic dynamics. Our findings highlight the significance of considering cell density effects on bacterial behavior, and the potential for fluorescent metabolite sensors to shed light on the complex emergent dynamics of bacterial communities.

Individual-Based Modeling of Spatial Dynamics of Chemotactic Microbial Populations

One important direction of synthetic biology is to establish desired spatial structures from microbial populations. Underlying this structural development process are different driving factors, among which bacterial motility and chemotaxis serve as a major force. Here, we present an individual-based, biophysical computational framework for mechanistic and multiscale simulation of the spatiotemporal dynamics of motile and chemotactic microbial populations. The framework integrates cellular movement with spatial population growth, mechanical and chemical cellular interactions, and intracellular molecular kinetics. It is validated by a statistical comparison of single-cell chemotaxis simulations with reported experiments. The framework successfully captures colony range expansion of growing isogenic populations and also reveals chemotaxis-modulated, spatial patterns of a two-species amensal community. Partial differential equation-based models subsequently validate these simulation findings. This study provides a versatile computational tool to uncover the fundamentals of microbial spatial ecology as well as to facilitate the design of synthetic consortia for desired spatial patterns.

Multi-scale organization in communicating active matter

The emergence of collective motion among interacting, self-propelled agents is a central paradigm in non-equilibrium physics. Examples of such active matter range from swimming bacteria and cytoskeletal motility assays to synthetic self-propelled colloids and swarming microrobots. Remarkably, the aggregation capabilities of many of these systems rely on a theme as fundamental as it is ubiquitous in nature: communication. Despite its eminent importance, the role of communication in the collective organization of active systems is not yet fully understood. Here we report on the multi-scale self-organization of interacting self-propelled agents that locally process information transmitted by chemical signals. We show that this communication capacity dramatically expands their ability to form complex structures, allowing them to self-organize through a series of collective dynamical states at multiple hierarchical levels. Our findings provide insights into the role of self-sustained signal processing for self-organization in biological systems and open routes to applications using chemically driven colloids or microrobots.

IGDQ motogenic peptide gradient induces directional cell migration through integrin (αv)β3 activation in MDA-MB-231 metastatic breast cancer cells

In the context of breast cancer metastasis study, we have shown in an in vitro model of cell migration that IGDQ-exposing (IsoLeu-Gly-Asp-Glutamine type I Fibronectin motif) monolayers (SAMs) on gold sustain the adhesion of breast cancer MDA-MB-231 cells by triggering Focal Adhesion Kinase and integrin activation. Such tunable scaffolds are used to mimic the tumor extracellular environment, inducing and controlling cell migration. The observed migratory behavior induced by the IGDQ-bearing peptide gradient along the surface allows to separate cell subpopulations with a "stationary" or "migratory" phenotype. In this work, we knocked down the integrins α5(β1) and (αv)β since they are already known to be implicated in cell migration. To this aim, a whole proteomic analysis was performed in beta 3 integrin (ITGB3) or alpha 5 integrin (ITGA5) knock-down MDA-MB-231 cells, in order to highlight the pathways implied in the integrin-dependent cell migration. Our results showed that i) ITGB3 depletion influenced ITGA5 mRNA expression, ii) ITGB3 and ITGA5 were both necessary for IGDQ-mediated directional single cell migration and iii) integrin (αv)β3 was activated by IGDQ fibronectin type I motif. Finally, the proteomic analysis suggested that co-regulation of recycling transport of ITGB3 by ITGA5 is potentially necessary for directional IGDQ-mediated cell migration.

Chemotactic self-caging in active emulsions

The out-of-equilibrium dynamics of chemotactic active matter—be it animate or inanimate—is closely coupled to the environment, a chemical landscape shaped by secretions from the motile agents, fuel uptake, or autochemotactic signaling. This gives rise to complex collective effects, which can be exploited by the agents for colony migration strategies or pattern formation. We study such effects using an idealized experimental system: self-propelled microdroplets that communicate via chemorepulsive trails. We present a comprehensive experimental analysis that involves direct probing of the diffusing chemical trails and the trail–droplet interactions and use it to construct a generic theoretical model. We connect these repulsive autochemotactic interactions to the collective dynamics in emulsions, demonstrating a state of dynamical arrest: chemotactic self-caging.

A common feature of biological self-organization is how active agents communicate with each other or their environment via chemical signaling. Such communications, mediated by self-generated chemical gradients, have consequences for both individual motility strategies and collective migration patterns. Here, in a purely physicochemical system, we use self-propelling droplets as a model for chemically active particles that modify their environment by leaving chemical footprints, which act as chemorepulsive signals to other droplets. We analyze this communication mechanism quantitatively both on the scale of individual agent–trail collisions as well as on the collective scale where droplets actively remodel their environment while adapting their dynamics to that evolving chemical landscape. We show in experiment and simulation how these interactions cause a transient dynamical arrest in active emulsions where swimmers are caged between each other’s trails of secreted chemicals. Our findings provide insight into the collective dynamics of chemically active particles and yield principles for predicting how negative autochemotaxis shapes their navigation strategy.

Spatial patterns in ecological systems: from microbial colonies to landscapes

Self-organized spatial patterns are ubiquitous in ecological systems and allow populations to adopt non-trivial spatial distributions starting from disordered configurations. These patterns form due to diverse nonlinear interactions among organisms and between organisms and their environment, and lead to the emergence of new (eco)system-level properties unique to self-organized systems. Such pattern consequences include higher resilience and resistance to environmental changes, abrupt ecosystem collapse, hysteresis loops, and reversal of competitive exclusion. Here, we review ecological systems exhibiting self-organized patterns. We establish two broad pattern categories depending on whether the self-organizing process is primarily driven by nonlinear density-dependent demographic rates or by nonlinear density-dependent movement. Using this organization, we examine a wide range of observational scales, from microbial colonies to whole ecosystems, and discuss the mechanisms hypothesized to underlie observed patterns and their system-level consequences. For each example, we review both the empirical evidence and the existing theoretical frameworks developed to identify the causes and consequences of patterning. Finally, we trace qualitative similarities across systems and propose possible ways of developing a more quantitative understanding of how self-organization operates across systems and observational scales in ecology.

Cellular Sensing Governs the Stability of Chemotactic Fronts

In contexts ranging from embryonic development to bacterial ecology, cell populations migrate chemotactically along self-generated chemical gradients, often forming a propagating front. Here, we theoretically show that the stability of such chemotactic fronts to morphological perturbations is determined by limitations in the ability of individual cells to sense and thereby respond to the chemical gradient. Specifically, cells at bulging parts of a front are exposed to a smaller gradient, which slows them down and promotes stability, but they also respond more strongly to the gradient, which speeds them up and promotes instability. We predict that this competition leads to chemotactic fingering when sensing is limited at too low chemical concentrations. Guided by this finding and by experimental data on E. coli chemotaxis, we suggest that the cells' sensory machinery might have evolved to avoid these limitations and ensure stable front propagation. Finally, as sensing of any stimuli is necessarily limited in living and active matter in general, the principle of sensing-induced stability may operate in other types of directed migration such as durotaxis, electrotaxis, and phototaxis.

Chemotactic smoothing of collective migration

Collective migration-the directed, coordinated motion of many self-propelled agents-is a fascinating emergent behavior exhibited by active matter with functional implications for biological systems. However, how migration can persist when a population is confronted with perturbations is poorly understood. Here, we address this gap in knowledge through studies of bacteria that migrate via directed motion, or chemotaxis, in response to a self-generated nutrient gradient. We find that bacterial populations autonomously smooth out large-scale perturbations in their overall morphology, enabling the cells to continue to migrate together. This smoothing process arises from spatial variations in the ability of cells to sense and respond to the local nutrient gradient-revealing a population-scale consequence of the manner in which individual cells transduce external signals. Altogether, our work provides insights to predict, and potentially control, the collective migration and morphology of cellular populations and diverse other forms of active matter.

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows

The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their different mechanistic origins. We employ a recently-developed macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species (both referred to as "colloids") in a circular tube under a steady pressure-driven flow (referred to as hydrodynamic flow) and transient solute gradient. First, we derive an exact solution to the log-sensing chemotactic/diffusiophoretic macrotransport equation. We demonstrate that a strong hydrodynamic flow can reduce spreading of solute-repelled colloids, by eliminating super-diffusion which occurs in an otherwise quiescent system. In contrast, hydrodynamic flows always enhance spreading of solute-attracted colloids. Second, we generalize the exact solution to show that the above tunable spreading phenomena by hydrodynamic flows persist quantitatively for decaying colloids, as may occur with cell death, for example. Third, we examine the spreading of chemotactic colloids by employing a more general model that captures a hallmark of chemotaxis, that log-sensing occurs only over a finite range of solute concentration. Apart from demonstrating for the first time the generality of the macrotransport theory to incorporate an arbitrary chemotactic flow model, we reveal via numerical solutions new regimes of anomalous spreading, which match qualitatively with experiments and are tunable by hydrodynamic flows. The results presented here could be employed to tailor chemotactic/diffusiophoretic colloid transport using hydrodynamic flows, which are central to applications such as oil recovery and bioremediation of aquifers.

Formation, collective motion, and merging of macroscopic bacterial aggregates

Chemotactic bacteria form emergent spatial patterns of variable cell density within cultures that are initially spatially uniform. These patterns are the result of chemical gradients that are created from the directed movement and metabolic activity of billions of cells. A recent study on pattern formation in wild bacterial isolates has revealed unique collective behaviors of the bacteria Enterobacter cloacae. As in other bacterial species, Enterobacter cloacae form macroscopic aggregates. Once formed, these bacterial clusters can migrate several millimeters, sometimes resulting in the merging of two or more clusters. To better understand these phenomena, we examine the formation and dynamics of thousands of bacterial clusters that form within a 22 cm square culture dish filled with soft agar over two days. At the macroscale, the aggregates display spatial order at short length scales, and the migration of cell clusters is superdiffusive, with a merging acceleration that is correlated with aggregate size. At the microscale, aggregates are composed of immotile cells surrounded by low density regions of motile cells. The collective movement of the aggregates is the result of an asymmetric flux of bacteria at the boundary. An agent-based model is developed to examine how these phenomena are the result of both chemotactic movement and a change in motility at high cell density. These results identify and characterize a new mechanism for collective bacterial motility driven by a transient, density-dependent change in motility.

Bacteria growing and swimming in soft agar often aggregate to form elaborate spatial patterns. Here we examine the patterns formed by the bacteria Enterobacter cloacae. An unusual behavior of these bacteria is the collective movement of cells after the initial aggregation into a tiny spot. Despite the majority of the cells within an aggregate being immotile at any point in the time, the flux of cells entering and leaving the aggregate, as motility is lost and regained in individual cells, led to a net, collective movement of the aggregate. These spots sometimes run into each other and combine. By looking at the cells within these spots under a microscope, we find that cells within each spot stop swimming. The process of switching back and forth between swimming and not swimming causes the movement and fusion of the spots. A numerical simulation shows that the migration and merging of these spots can be expected if the cells swim towards regions of space with high concentrations of attractant molecules and stop swimming in locations crowded with many cells. This work identifies a novel process through which populations of bacteria cooperate and control the movement of large groups of cells.

A traveling-wave solution for bacterial chemotaxis with growth

Bacterial cells navigate their environment by directing their movement along chemical gradients. This process, known as chemotaxis, can promote the rapid expansion of bacterial populations into previously unoccupied territories. However, despite numerous experimental and theoretical studies on this classical topic, chemotaxis-driven population expansion is not understood in quantitative terms. Building on recent experimental progress, we here present a detailed analytical study that provides a quantitative understanding of how chemotaxis and cell growth lead to rapid and stable expansion of bacterial populations. We provide analytical relations that accurately describe the dependence of the expansion speed and density profile of the expanding population on important molecular, cellular, and environmental parameters. In particular, expansion speeds can be boosted by orders of magnitude when the environmental availability of chemicals relative to the cellular limits of chemical sensing is high. Analytical understanding of such complex spatiotemporal dynamic processes is rare. Our analytical results and the methods employed to attain them provide a mathematical framework for investigations of the roles of taxis in diverse ecological contexts across broad parameter regimes.

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

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

Theoretical Constraints Imposed by Gradient Detection and Dispersal on Microbial Size in Astrobiological Environments

The capacity to sense gradients efficiently and acquire information about the ambient environment confers many advantages such as facilitating movement toward nutrient sources or away from toxic chemicals. The amplified dispersal evinced by organisms endowed with motility is possibly beneficial in related contexts. Hence, the connections between information acquisition, motility, and microbial size are explored from an explicitly astrobiological standpoint. By using prior theoretical models, the constraints on organism size imposed by gradient detection and motility are elucidated in the form of simple heuristic scaling relations. It is argued that environments such as alkaline hydrothermal vents, which are distinguished by the presence of steep gradients, might be conducive to the existence of "small" microbes (with radii of ≳0.1 μm) in principle, when only the above two factors are considered; other biological functions (e.g., metabolism and genetic exchange) could, however, regulate the lower bound on microbial size and elevate it. The derived expressions are potentially applicable to a diverse array of settings, including those entailing solvents other than water; for example, the lakes and seas of Titan. The article concludes with a brief exposition of how this formalism may be of practical and theoretical value to astrobiology.

Flow-mediated olfactory communication in honeybee swarms

Honeybee swarms are a landmark example of collective behavior. To become a coherent swarm, bees locate their queen by tracking her pheromones. But how can distant individuals exploit these chemical signals, which decay rapidly in space and time? Here, we combine a behavioral assay with the machine vision detection of organism location and scenting (pheromone propagation via wing fanning) behavior to track the search and aggregation dynamics of the honeybee Apis mellifera L. We find that bees collectively create a scenting-mediated communication network by arranging in a specific spatial distribution where there is a characteristic distance between individuals and directional signaling away from the queen. To better understand such a flow-mediated directional communication strategy, we developed an agent-based model where bee agents obeying simple, local behavioral rules exist in a flow environment in which the chemical signals diffuse and decay. Our model serves as a guide to exploring how physical parameters affect the collective scenting behavior and shows that increased directional bias in scenting leads to a more efficient aggregation process that avoids local equilibrium configurations of isotropic (nondirectional and axisymmetric) communication, such as small bee clusters that persist throughout the simulation. Our results highlight an example of extended classical stigmergy: Rather than depositing static information in the environment, individual bees locally sense and globally manipulate the physical fields of chemical concentration and airflow.

Emergent Field-Driven Robot Swarm States

We present an ecology-inspired form of active matter consisting of a robot swarm. Each robot moves over a planar dynamic resource environment represented by a large light-emitting diode array in search of maximum light intensity; the robots deplete (dim) locally by their presence the local light intensity and seek maximum light intensity. Their movement is directed along the steepest local light intensity gradient; we call this emergent symmetry breaking motion "field drive." We show there emerge dynamic and spatial transitions similar to gas, crystalline, liquid, glass, and jammed states as a function of robot density, resource consumption rates, and resource recovery rates. Paradoxically the nongas states emerge from smooth, flat resource landscapes, not rough ones, and each state can directly move to a glassy state if the resource recovery rate is slow enough, at any robot density.

Lamellar to Micellar Phases and Beyond: When Tactic Active Systems Admit Free Energy Functionals

We consider microscopic models of active particles whose velocities, rotational diffusivities, and tumbling rates depend on the gradient of a local field that is either externally imposed or depends on all particle positions. Despite the fundamental differences between active and passive dynamics at the microscopic scale, we show that a large class of such tactic active systems admit fluctuating hydrodynamics equivalent to those of interacting Brownian colloids in equilibrium. We exploit this mapping to show how taxis may lead to the lamellar and micellar phases observed for soft repulsive colloids. In the context of chemotaxis, we show how the competition between chemoattractant and chemorepellent may lead to a bona fide equilibrium liquid-gas phase separation in which a loss of thermodynamic stability of the fluid signals the onset of a chemotactic collapse.

Pattern Formation in Precipitation Reactions: The Liesegang Phenomenon

Pattern formation is a frequent phenomenon in physics, chemistry, biology, and materials science. Bottom-up pattern formation usually occurs in the interaction of the transport phenomena of chemical species with their chemical reaction. The oldest pattern formation is the Liesegang phenomenon (or periodic precipitation), which was discovered and described in 1896 by Raphael Edward Liesegang, who was a German chemist and photographer who was born 150 years ago. The purpose of this feature article is to provide a comprehensive overview of this type of pattern formation. Liesegang banding occurs because of the coupling of the diffusion process of the reagents with their chemical reactions in solid hydrogels. We will discuss several phenomena observed and discovered in the past century, including reverse patterns, precipitation patterns with dissolution (due to complex formation), helicoidal patterns, and precipitation waves. Additionally, we will review all existing models of the Liesegang phenomenon including pre- and postnucleation scenarios. Finally, we will highlight several applications of periodic precipitation.

Ultrafast photomechanical transduction through thermophoretic implosion

Since the historical experiments of Crookes, the direct manipulation of matter by light has been both a challenge and a source of scientific debate. Here we show that laser illumination allows to displace a vial of nanoparticle solution over centimetre-scale distances. Cantilever-based force measurements show that the movement is due to millisecond-long force spikes, which are synchronised with a sound emission. We observe that the nanoparticles undergo negative thermophoresis, and ultrafast imaging reveals that the force spikes are followed by the explosive growth of a bubble in the solution. We propose a mechanism accounting for the propulsion based on a thermophoretic instability of the nanoparticle cloud, analogous to the Jeans’s instability that occurs in gravitational systems. Our experiments demonstrate a new type of laser propulsion and a remarkably violent actuation of soft matter, reminiscent of the strategy used by certain plants to propel their spores.

Here, the authors observe that laser illumination allows to displace a vial of nanoparticle solution over centimetre-scale distances. In order to explain this, they describe a novel mechanism for laser propulsion of a macroscopic object, based on light-induced thermophoresis.

Chemotaxis as a navigation strategy to boost range expansion

Bacterial chemotaxis, the directed movement of cells along gradients of chemoattractants, is among the best-characterized subjects in molecular biology^1-10, but much less is known about its physiological roles¹¹. It is commonly seen as a starvation response when nutrients run out, or as an escape response from harmful situations^12-16. Here we identify an alternative role of chemotaxis by systematically examining the spatiotemporal dynamics of Escherichia coli in soft agar^12,17,18. Chemotaxis in nutrient-replete conditions promotes the expansion of bacterial populations into unoccupied territories well before nutrients run out in the current environment. Low levels of chemoattractants act as aroma-like cues in this process, establishing the direction and enhancing the speed of population movement along the self-generated attractant gradients. This process of navigated range expansion spreads faster and yields larger population gains than unguided expansion following the canonical Fisher-Kolmogorov dynamics^19,20 and is therefore a general strategy to promote population growth in spatially extended, nutrient-replete environments.

Shape-programmed 3D printed swimming microtori for the transport of passive and active agents

Through billions of years of evolution, microorganisms mastered unique swimming behaviors to thrive in complex fluid environments. Limitations in nanofabrication have thus far hindered the ability to design and program synthetic swimmers with the same abilities. Here we encode multi-behavioral responses in microscopic self-propelled tori using nanoscale 3D printing. We show experimentally and theoretically that the tori continuously transition between two primary swimming modes in response to a magnetic field. The tori also manipulated and transported other artificial swimmers, bimetallic nanorods, as well as passive colloidal particles. In the first behavioral mode, the tori accumulated and transported nanorods; in the second mode, nanorods aligned along the toriʼs self-generated streamlines. Our results indicate that such shape-programmed microswimmers have a potential to manipulate biological active matter, e.g. bacteria or cells.

While there are many demonstrations of self-propelled synthetic particles, there are fewer realisations of multimode swimming for the same particle. Here the authors demonstrate two swimming behaviours in magnetically manipulated microtori and show that these can manipulate other active particles.

COMPUTATIONAL MODELING OF SELF-ORGANIZATION OF BACTERIAL POPULATION CONSISTING OF SUBPOPULATIONS OF ACTIVE AND PASSIVE CELLS

This paper deals with the computational modeling of the bioluminescence pattern formation in suspensions of Escherichia coli bacteria. The aim was to develop a computational model for simulating the bacterial populations consisting of two subpopulations of active and passive cells. A suitable model based on Keller–Segel and Fisher equations was proposed and the spatiotemporal patterns were simulated using the finite difference technique. The influence of cell activation, deactivation, chemotactic sensitivity, growth rate and saturating signal production parameter values on the pattern formation was investigated. The proposed model can be used to effectively simulate quasi-one-dimensional spatiotemporal patterns. We provide a simple qualitative explanation of the experimental results and estimated model parameters. In particular, it is argued that the effective model simulates patterns of evaporation-driven convection in open-to-air suspensions of cells that can be either active or passive.

Directed migration shapes cooperation in spatial ecological public goods games

From the microscopic to the macroscopic level, biological life exhibits directed migration in response to environmental conditions. Chemotaxis enables microbes to sense and move towards nutrient-rich regions or to avoid toxic ones. Socio-economic factors drive human populations from rural to urban areas. The effect of collective movement is especially significant when triggered in response to the generation of public goods. Microbial communities can, for instance, alter their environment through the secretion of extracellular substances. Some substances provide antibiotic-resistance, others provide access to nutrients or promote motility. However, in all cases the maintenance of public goods requires costly cooperation and is consequently susceptible to exploitation. The threat of exploitation becomes even more acute with motile individuals because defectors can avoid the consequences of their cheating. Here, we propose a model to investigate the effects of targeted migration and analyze the interplay between social conflicts and migration in ecological public goods. In particular, individuals can locate attractive regions by moving towards higher cooperator densities or avoid unattractive regions by moving away from defectors. Both migration patterns not only shape an individual's immediate environment but also affects the entire population. For example, defectors hunting cooperators have a homogenizing effect on population densities. This limits the production of the public good and hence inhibits the growth of the population. In contrast, aggregating cooperators promote the spontaneous formation of patterns through heterogeneous density distributions. The positive feedback between cooperator aggregation and public goods production, however, poses analytical and numerical challenges due to its tendency to develop discontinuous distributions. Thus, different modes of directed migration bear the potential to enhance or inhibit the emergence of complex and sometimes dynamic spatial arrangements. Interestingly, whenever patterns emerge, cooperation is promoted, on average, population densities rise, and the risk of extinction is reduced.

Rivalry in Bacillus subtilis colonies: enemy or family?

Two colonies of Bacillus subtilis of identical strains growing adjacent to each other on an agar plate exhibit two distinct types of interactions: they either merge as they grow or demarcation occurs leading to formation of a line of demarcation at the colony fronts. The nature of this interaction depends on the agar concentration in the growth medium and the initial separation between the colonies. When the agar concentration was 0.67% or lower, the two sibling colonies were found to always merge. At 1% or higher concentrations, the colonies formed a demarcation line only when their initial separation was 20 mm or higher. Interactions of a colony with solid structures and liquid drops have indicated that biochemical factors rather than the presence of physical obstacles are responsible for the demarcation line formation. A reaction diffusion model has been formulated to predict if two sibling colonies will form a demarcation line under given agar concentration and initial separation. The model prediction agrees well with experimental findings and generates a dimensionless phase diagram containing merging and demarcation regimes. The phase diagram is in terms of a dimensionless initial separation, d[combining macron], and a dimensionless diffusion coefficient, D[combining macron], of the colonies. The phase boundary between the two interaction regimes can be described by a power law relation between d[combining macron] and D[combining macron].

Osmosis, from molecular insights to large-scale applications

Osmosis is a universal phenomenon occurring in a broad variety of processes and fields. It is the archetype of entropic forces, both trivial in its fundamental expression - the van 't Hoff perfect gas law - and highly subtle in its physical roots. While osmosis is intimately linked with transport across membranes, it also manifests itself as an interfacial transport phenomenon: the so-called diffusio-osmosis and -phoresis, whose consequences are presently actively explored for example for the manipulation of colloidal suspensions or the development of active colloidal swimmers. Here we give a global and unifying view of the phenomenon of osmosis and its consequences with a multi-disciplinary perspective. Pushing the fundamental understanding of osmosis allows one to propose new perspectives for different fields and we highlight a number of examples along these lines, for example introducing the concepts of osmotic diodes, active separation and far from equilibrium osmosis, raising in turn fundamental questions in the thermodynamics of separation. The applications of osmosis are also obviously considerable and span very diverse fields. Here we discuss a selection of phenomena and applications where osmosis shows great promises: osmotic phenomena in membrane science (with recent developments in separation, desalination, reverse osmosis for water purification thanks in particular to the emergence of new nanomaterials); applications in biology and health (in particular discussing the kidney filtration process); osmosis and energy harvesting (in particular, osmotic power and blue energy as well as capacitive mixing); applications in detergency and cleaning, as well as for oil recovery in porous media.

Spatial self-organization resolves conflicts between individuality and collective migration

Collective behavior can spontaneously emerge when individuals follow common rules of interaction. However, the behavior of each individual differs due to existing genetic and non-genetic variation within the population. It remains unclear how this individuality is managed to achieve collective behavior. We quantify individuality in bands of clonal Escherichia coli cells that migrate collectively along a channel by following a self-generated gradient of attractant. We discover that despite substantial differences in individual chemotactic abilities, the cells are able to migrate as a coherent group by spontaneously sorting themselves within the moving band. This sorting mechanism ensures that differences between individual chemotactic abilities are compensated by differences in the local steepness of the traveling gradient each individual must navigate, and determines the minimum performance required to travel with the band. By resolving conflicts between individuality and collective migration, this mechanism enables populations to maintain advantageous diversity while on the move.

How bacteria migrate collectively despite individual phenotypic variation is not understood. Here, the authors show that cells spontaneously sort themselves within moving bands such that variations in individual tumble bias, a determinant of gradient climbing speed, are compensated by the local gradient steepness experienced by individuals.

Mechanism of Kin-Discriminatory Demarcation Line Formation between Colonies of Swarming Bacteria

Swarming bacteria use kin discrimination to preferentially associate with their clonemates for certain cooperative behaviors. Kin discrimination can manifest as an apparent demarcation line (a region lacking cells or with much lower cell density) between antagonist strains swarming toward each other. In contrast, two identical strains merge with no demarcation. Experimental studies suggest contact-dependent killing between different strains as a mechanism of kin discrimination, but it is not clear whether this killing is sufficient to explain the observed patterns. Here, we investigate the formation of demarcation line with a mathematical model. First, using data from competition experiments between kin discriminating strains of Myxococcus xanthus and Proteus mirabilis, we found the rates of killing between the strains to be highly asymmetric, i.e., one strain kills another at a much higher rate. Then, to investigate how such asymmetric interactions can lead to a stable demarcation line, we construct reaction-diffusion models for colony expansion of kin-discriminatory strains. Our results demonstrate that a stable demarcation line can form when both cell movement and cell growth cease at low nutrient levels. Further, our study suggests that, depending on the initial separation between the inoculated colonies, the demarcation line may move transiently before stabilizing. We validated these model predictions by observing dynamics of merger between two M. xanthus strains, where one strain expresses a toxin protein that kills a second strain lacking the corresponding antitoxin. Our study therefore provides a theoretical understanding of demarcation line formation between kin-discriminatory populations, and can be used for analyzing and designing future experiments.

Growth-mediated autochemotactic pattern formation in self-propelling bacteria

Bacteria, while developing a multicellular colony or biofilm, can undergo pattern formation by diverse intricate mechanisms. One such route is directional movement or chemotaxis toward or away from self-secreted or externally employed chemicals. In some bacteria, the self-produced signaling chemicals or autoinducers themselves act as chemoattractants or chemorepellents and thereby regulate the directional movements of the cells in the colony. In addition, bacteria follow a certain growth kinetics which is integrated in the process of colony development. Here, we study the interplay of bacterial growth dynamics, cell motility, and autochemotactic motion with respect to the self-secreted diffusive signaling chemicals in spatial pattern formation. Using a continuum model of motile bacteria, we show growth can act as a crucial tuning parameter in determining the spatiotemporal dynamics of a colony. In action of growth dynamics, while chemoattraction toward autoinducers creates arrested phase separation, pattern transitions and suppression can occur for a fixed chemorepulsive strength.

Active depinning of bacterial droplets: The collective surfing of Bacillus subtilis

How systems are endowed with migration capacity is a fascinating question with implications ranging from the design of novel active systems to the control of microbial populations. Bacteria, which can be found in a variety of environments, have developed among the richest set of locomotion mechanisms both at the microscopic and collective levels. Here, we uncover, experimentally, a mode of collective bacterial motility in humid environment through the depinning of bacterial droplets. Although capillary forces are notoriously enormous at the bacterial scale, even capable of pinning water droplets of millimetric size on inclined surfaces, we show that bacteria are able to harness a variety of mechanisms to unpin contact lines, hence inducing a collective slipping of the colony across the surface. Contrary to flagella-dependent migration modes like swarming, we show that this much faster "colony surfing" still occurs in mutant strains of Bacillus subtilis lacking flagella. The active unpinning seen in our experiments relies on a variety of microscopic mechanisms, which could each play an important role in the migration of microorganisms in humid environment.

Chemotaxis and autochemotaxis of self-propelling droplet swimmers

Chemotaxis and autochemotaxis play an important role in many essential biological processes. We present a self-propelling artificial swimmer system that exhibits chemotaxis as well as negative autochemotaxis. Oil droplets in an aqueous surfactant solution are driven by interfacial Marangoni flows induced by micellar solubilization of the oil phase. We demonstrate that chemotaxis along micellar surfactant gradients can guide these swimmers through a microfluidic maze. Similarly, a depletion of empty micelles in the wake of a droplet swimmer causes negative autochemotaxis and thereby trail avoidance. We studied autochemotaxis quantitatively in a microfluidic device of bifurcating channels: Branch choices of consecutive swimmers are anticorrelated, an effect decaying over time due to trail dispersion. We modeled this process by a simple one-dimensional diffusion process and stochastic Langevin dynamics. Our results are consistent with a linear surfactant gradient force and diffusion constants appropriate for micellar diffusion and provide a measure of autochemotactic feedback strength vs. stochastic forces. This assay is readily adaptable for quantitative studies of both artificial and biological autochemotactic systems.

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.

Effective Dynamics of Microorganisms That Interact with Their Own Trail

Like ants, some microorganisms are known to leave trails on surfaces to communicate. We explore how trail-mediated self-interaction could affect the behavior of individual microorganisms when diffusive spreading of the trail is negligible on the time scale of the microorganism using a simple phenomenological model for an actively moving particle and a finite-width trail. The effective dynamics of each microorganism takes on the form of a stochastic integral equation with the trail interaction appearing in the form of short-term memory. For a moderate coupling strength below an emergent critical value, the dynamics exhibits effective diffusion in both orientation and position after a phase of superdiffusive reorientation. We report experimental verification of a seemingly counterintuitive perpendicular alignment mechanism that emerges from the model.

Travelling wave analysis in chemotaxis: case of starvation

In this paper we investigate the existence of travelling wave solutions for a chemotaxis model under the scenarios of zero growth and constant growth rate. We use Lie symmetry analysis to generate generalized travelling wave solutions, a wider class of solutions than that obtained from the standard ansatz. Unlike previous approaches, we allow for diffusivity and signal degradation. We study the influence of cell growth, diffusivity and signal degradation on the behaviour of the system. We apply realistic boundary conditions to explicitly provide biologically relevant solutions. Our results generalize known results.

Collective chemotaxis and segregation of active bacterial colonies

Still recently, bacterial fluid suspensions have motivated a lot of works, both experimental and theoretical, with the objective to understand their collective dynamics from universal and simple rules. Since some species are active, most of these works concern the strong interactions that these bacteria exert on a forced flow leading to instabilities, chaos and turbulence. Here, we investigate the self-organization of expanding bacterial colonies under chemotaxis, proliferation and eventually active-reaction. We propose a simple model to understand and quantify the physical properties of these living organisms which either give cohesion or on the contrary dispersion to the colony. Taking into account the diffusion and capture of morphogens complicates the model since it induces a bacterial density gradient coupled to bacterial density fluctuations and dynamics. Nevertheless under some specific conditions, it is possible to investigate the pattern formation as a usual viscous fingering instability. This explains the similarity and differences of patterns according to the physical bacterial suspension properties and explain the factors which favor compactness or branching.

Collective Behavior of Quorum-Sensing Run-and-Tumble Particles under Confinement

We study a generic model for quorum-sensing bacteria in circular confinement. Every bacterium produces signaling molecules, the local concentration of which triggers a response when a certain threshold is reached. If this response lowers the motility, then an aggregation of bacteria occurs which differs fundamentally from standard motility-induced phase separation due to the long-ranged nature of the concentration of signal molecules. We analyze this phenomenon analytically and by numerical simulations employing two different protocols leading to stationary cluster and ring morphologies, respectively.

Self-organized anomalous aggregation of particles performing nonlinear and non-Markovian random walks

We present a nonlinear and non-Markovian random walks model for stochastic movement and the spatial aggregation of living organisms that have the ability to sense population density. We take into account social crowding effects for which the dispersal rate is a decreasing function of the population density and residence time. We perform stochastic simulations of random walks and discover the phenomenon of self-organized anomaly (SOA), which leads to a collapse of stationary aggregation pattern. This anomalous regime is self-organized and arises without the need for a heavy tailed waiting time distribution from the inception. Conditions have been found under which the nonlinear random walk evolves into anomalous state when all particles aggregate inside a tiny domain (anomalous aggregation). We obtain power-law stationary density-dependent survival function and define the critical condition for SOA as the divergence of mean residence time. The role of the initial conditions in different SOA scenarios is discussed. We observe phenomenon of transient anomalous bimodal aggregation.

Pili-Induced Clustering of N. gonorrhoeae Bacteria

Type IV pili (Tfp) are prokaryotic retractable appendages known to mediate surface attachment, motility, and subsequent clustering of cells. Tfp are the main means of motility for Neisseria gonorrhoeae, the causative agent of gonorrhea. Tfp are also involved in formation of the microcolonies, which play a crucial role in the progression of the disease. While motility of individual cells is relatively well understood, little is known about the dynamics of N. gonorrhoeae aggregation. We investigate how individual N. gonorrhoeae cells, initially uniformly dispersed on flat plastic or glass surfaces, agglomerate into spherical microcolonies within hours. We quantify the clustering process by measuring the area fraction covered by the cells, number of cell aggregates, and their average size as a function of time. We observe that the microcolonies are also able to move but their mobility rapidly vanishes as the size of the colony increases. After a certain critical size they become immobile. We propose a simple theoretical model which assumes a pili-pili interaction of cells as the main clustering mechanism. Numerical simulations of the model quantitatively reproduce the experimental data on clustering and thus suggest that the agglomeration process can be entirely explained by the Tfp-mediated interactions. In agreement with this hypothesis mutants lacking pili are not able to form colonies. Moreover, cells with deficient quorum sensing mechanism show similar aggregation as the wild-type bacteria. Therefore, our results demonstrate that pili provide an essential mechanism for colony formation, while additional chemical cues, for example quorum sensing, might be of secondary importance.

From Birds to Bacteria: Generalised Velocity Jump Processes with Resting States

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long-distance movement state and a resting or local movement state. Here, a mathematical description of this process is formulated, adapted from Friedrich et al. (Phys Rev E, 74:041103, 2006b). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of integro-partial differential equations is tumultuous, and therefore, it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived, which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally, a large time diffusive approximation is considered via a Cattaneo approximation (Hillen in Discrete Continuous Dyn Syst Ser B, 5:299–318, 2003). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.