Chemotactic migration of bacteria in porous media

Data-driven discovery of chemotactic migration of bacteria via coordinate-invariant machine learning

BACKGROUND

E. coli chemotactic motion in the presence of a chemonutrient field can be studied using wet laboratory experiments or macroscale-level partial differential equations (PDEs) (among others). Bridging experimental measurements and chemotactic Partial Differential Equations requires knowledge of the evolution of all underlying fields, initial and boundary conditions, and often necessitates strong assumptions. In this work, we propose machine learning approaches, along with ideas from the Whitney and Takens embedding theorems, to circumvent these challenges.

RESULTS

Machine learning approaches for identifying underlying PDEs were (a) validated through the use of simulation data from established continuum models and (b) used to infer chemotactic PDEs from experimental data. Such data-driven models were surrogates either for the entire chemotactic PDE right-hand-side (black box models), or, in a more targeted fashion, just for the chemotactic term (gray box models). Furthermore, it was demonstrated that a short history of bacterial density may compensate for the missing measurements of the field of chemonutrient concentration. In fact, given reasonable conditions, such a short history of bacterial density measurements could even be used to infer chemonutrient concentration.

CONCLUSION

Data-driven PDEs are an important modeling tool when studying Chemotaxis at the macroscale, as they can learn bacterial motility from various data sources, fidelities (here, computational models, experiments) or coordinate systems. The resulting data-driven PDEs can then be simulated to reproduce/predict computational or experimental bacterial density profile data independent of the coordinate system, approximate meaningful parameters or functional terms, and even possibly estimate the underlying (unmeasured) chemonutrient field evolution.

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.

Soft matter physics of the ground beneath our feet

The soft part of the Earth's surface - the ground beneath our feet - constitutes the basis for life and natural resources, yet a general physical understanding of the ground is still lacking. In this critical time of climate change, cross-pollination of scientific approaches is urgently needed to better understand the behavior of our planet's surface. The major topics in current research in this area cross different disciplines, spanning geosciences, and various aspects of engineering, material sciences, physics, chemistry, and biology. Among these, soft matter physics has emerged as a fundamental nexus connecting and underpinning many research questions. This perspective article is a multi-voice effort to bring together different views and approaches, questions and insights, from researchers that work in this emerging area, the soft matter physics of the ground beneath our feet. In particular, we identify four major challenges concerned with the dynamics in and of the ground: (I) modeling from the grain scale, (II) near-criticality, (III) bridging scales, and (IV) life. For each challenge, we present a selection of topics by individual authors, providing specific context, recent advances, and open questions. Through this, we seek to provide an overview of the opportunities for the broad Soft Matter community to contribute to the fundamental understanding of the physics of the ground, strive towards a common language, and encourage new collaborations across the broad spectrum of scientists interested in the matter of the Earth's surface.

Microbial-induced carbonate precipitation effectively prevents Pb2+ migration through the soil profile: Lab experiment and model simulation

Due to the inappropriate disposal of waste materials containing lead (Pb) and irrigation with sewage containing Pb, the migration of Pb2+ within the soil profile has been extensively investigated. The conventional Pb2+ block method is challenging to implement due to its complex operational procedures and high construction costs. To address this issue, this study introduces the microbial-induced carbonate precipitation (MICP) technique as a novel approach to impede the migration of Pb2+ in the soil profile. Soil acclimatization with urea resulted in an increased proportion of urease-producing microorganisms, including Bacillus, Paenibacillus, and Planococcaceae, along with heightened expression of urea-hydrolyzing genes (UreA, UreB, UreC, and UreG). This indicates that urea-acclimatized soil (Soil-MICP) possesses the potential to induce carbonate precipitation. Batch Pb2+ fixation experiments confirmed that the fixation efficiency of Soil-MICP on Pb2+ exceeded that of soil without MICP, attributed to the MICP process within the Soil-MICP group. Dynamic migration experiments revealed that the MICP reaction transformed exchangeable lead into carbonate-bound Pb, effectively impeding Pb2+ migration in the soil profile. Additionally, the migration rate of Pb2+ in Soil-MICP was influenced by varying urea amounts, pH levels, and pore flow rates, leading to a slowdown in migration. The Two-site sorption model aptly described the Pb2+ migration process in the Soil-MICP column. This study aims to elucidate the MICP biomineralization process, uncover the in-situ blocking mechanism of MICP on lead in soil, investigate the impact of Pb on key genes involved in urease metabolism, enhance the comprehension of the chemical morphology of lead mineralization products, and provide a theoretical foundation for MICP technology in preventing the migration of Pb2+ in soil profiles.

Design approaches for 3D cell culture and 3D bioprinting platforms

The natural habitat of most cells consists of complex and disordered 3D microenvironments with spatiotemporally dynamic material properties. However, prevalent methods of in vitro culture study cells under poorly biomimetic 2D confinement or homogeneous conditions that often neglect critical topographical cues and mechanical stimuli. It has also become increasingly apparent that cells in a 3D conformation exhibit dramatically altered morphological and phenotypical states. In response, efforts toward designing biomaterial platforms for 3D cell culture have taken centerstage over the past few decades. Herein, we present a broad overview of biomaterials for 3D cell culture and 3D bioprinting, spanning both monolithic and granular systems. We first critically evaluate conventional monolithic hydrogel networks, with an emphasis on specific experimental requirements. Building on this, we document the recent emergence of microgel-based 3D growth media as a promising biomaterial platform enabling interrogation of cells within porous and granular scaffolds. We also explore how jammed microgel systems have been leveraged to spatially design and manipulate cellular structures using 3D bioprinting. The advent of these techniques heralds an unprecedented ability to experimentally model complex physiological niches, with important implications for tissue bioengineering and biomedical applications.

Trade-offs in concentration sensing in dynamic environments

When cells measure concentrations of chemical signals, they may average multiple measurements over time in order to reduce noise in their measurements. However, when cells are in an environment that changes over time, past measurements may not reflect current conditions-creating a new source of error that trades off against noise in chemical sensing. What statistics in the cell's environment control this trade-off? What properties of the environment make it variable enough that this trade-off is relevant? We model a single eukaryotic cell sensing a chemical secreted from bacteria (e.g., folic acid). In this case, the environment changes because the bacteria swim-leading to changes in the true concentration at the cell. We develop analytical calculations and stochastic simulations of sensing in this environment. We find that cells can have a huge variety of optimal sensing strategies ranging from not time averaging at all to averaging over an arbitrarily long time or having a finite optimal averaging time. The factors that primarily control the ideal averaging are the ratio of sensing noise to environmental variation and the ratio of timescales of sensing to the timescale of environmental variation. Sensing noise depends on the receptor-ligand kinetics, while environmental variation depends on the density of bacteria and the degradation and diffusion properties of the secreted chemoattractant. Our results suggest that fluctuating environmental concentrations may be a relevant source of noise even in a relatively static environment.

Active Darcy's Law

While bacterial swarms can exhibit active turbulence in vacant spaces, they naturally inhabit crowded environments. We numerically show that driving disorderly active fluids through porous media enhances Darcy's law. While purely active flows average to zero flux, hybrid active/driven flows display greater drift than purely pressure-driven flows. This enhancement is nonmonotonic with activity, leading to an optimal activity to maximize flow rate. We incorporate the active contribution into an active Darcy's law, which may serve to help understand anomalous transport of swarming in porous media.

Interplay between environmental yielding and dynamic forcing modulates bacterial growth

Many bacterial habitats-ranging from gels and tissues in the body to cell-secreted exopolysaccharides in biofilms-are rheologically complex, undergo dynamic external forcing, and have unevenly distributed nutrients. How do these features jointly influence how the resident cells grow and proliferate? Here, we address this question by studying the growth of Escherichia coli dispersed in granular hydrogel matrices with defined and highly tunable structural and rheological properties, under different amounts of external forcing imposed by mechanical shaking, and in both aerobic and anaerobic conditions. Our experiments establish a general principle: that the balance between the yield stress of the environment that the cells inhabit, σy, and the external stress imposed on the environment, σ, modulates bacterial growth by altering transport of essential nutrients to the cells. In particular, when σy<σ, the environment is easily fluidized and mixed over large scales, providing nutrients to the cells and sustaining complete cellular growth. By contrast, when σy>σ, the elasticity of the environment suppresses large-scale fluid mixing, limiting nutrient availability and arresting cellular growth. Our work thus reveals a new mechanism, beyond effects that change cellular behavior via local forcing, by which the rheology of the environment may modulate microbial physiology in diverse natural and industrial settings.

Microbes in porous environments: from active interactions to emergent feedback

Microbes thrive in diverse porous environments-from soil and riverbeds to human lungs and cancer tissues-spanning multiple scales and conditions. Short- to long-term fluctuations in local factors induce spatio-temporal heterogeneities, often leading to physiologically stressful settings. How microbes respond and adapt to such biophysical constraints is an active field of research where considerable insight has been gained over the last decades. With a focus on bacteria, here we review recent advances in self-organization and dispersal in inorganic and organic porous settings, highlighting the role of active interactions and feedback that mediates microbial survival and fitness. We discuss open questions and opportunities for using integrative approaches to advance our understanding of the biophysical strategies which microbes employ at various scales to make porous settings habitable.

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.

Spatial structure, chemotaxis and quorum sensing shape bacterial biomass accumulation in complex porous media

Biological tissues, sediments, or engineered systems are spatially structured media with a tortuous and porous structure that host the flow of fluids. Such complex environments can influence the spatial and temporal colonization patterns of bacteria by controlling the transport of individual bacterial cells, the availability of resources, and the distribution of chemical signals for communication. Yet, due to the multi-scale structure of these complex systems, it is hard to assess how different biotic and abiotic properties work together to control the accumulation of bacterial biomass. Here, we explore how flow-mediated interactions allow the gut commensal Escherichia coli to colonize a porous structure that is composed of heterogenous dead-end pores (DEPs) and connecting percolating channels, i.e. transmitting pores (TPs), mimicking the structured surface of mammalian guts. We find that in presence of flow, gradients of the quorum sensing (QS) signaling molecule autoinducer-2 (AI-2) promote E. coli chemotactic accumulation in the DEPs. In this crowded environment, the combination of growth and cell-to-cell collision favors the development of suspended bacterial aggregates. This results in hot-spots of resource consumption, which, upon resource limitation, triggers the mechanical evasion of biomass from nutrients and oxygen depleted DEPs. Our findings demonstrate that microscale medium structure and complex flow coupled with bacterial quorum sensing and chemotaxis control the heterogenous accumulation of bacterial biomass in a spatially structured environment, such as villi and crypts in the gut or in tortuous pores within soil and filters.

Kinetic temperature and pressure of an active Tonks gas

Using computer simulation and analytical theory, we study an active analog of the well-known Tonks gas, where active Brownian particles are confined to a periodic one-dimensional (1D) channel. By introducing the notion of a kinetic temperature, we derive an accurate analytical expression for the pressure and clarify the paradoxical behavior where active Brownian particles confined to 1D exhibit anomalous clustering but no motility-induced phase transition. More generally, this work provides a deeper understanding of pressure in active systems as we uncover a unique link between the kinetic temperature and swim pressure valid for active Brownian particles in higher dimensions.

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.

Structure and dynamics of an active polymer chain inside a nanochannel grafted with polymers

We use computer simulations to investigate the complex dynamics of a polymer, made of active Brownian particles, inside a channel grafted internally with passive polymer chains. Our simulations reveal that this probe-polymer, if passive, exhibits a compact structure when its interaction is repulsive with the grafted chains as it tends to stay within the hollow space created along the axis of the channel. On increasing the attractive interaction, the passive probe-polymer is pulled towards the grafted polymeric region and adopts an extended structure. By contrast, switching on the activity helps the probe-polymer to escape from the local traps caused by the sticky grafted chains. The interplay between the activity of the probe-polymer and its sticky interaction with the grafted chains results in shrinking, followed by swelling as the activity is increased. To elucidate the dynamics we compute the mean square displacement (MSD) of the center of mass of the probe-polymer, which increases monotonically with activity and displays superdiffusive behavior at an intermediate time and enhanced diffusion at a long time period. In addition, compared with the attractive interaction, the active probe-polymer shows faster dynamics when the interaction is repulsive to the grafted polymers. We believe that our current study will provide insights into the structural changes and dynamics of active polymers in heterogeneous media and will be useful in designing polymer-based drug delivery vehicles.

Multiplexed microfluidic screening of bacterial chemotaxis

Microorganism sensing of and responding to ambient chemical gradients regulates a myriad of microbial processes that are fundamental to ecosystem function and human health and disease. The development of efficient, high-throughput screening tools for microbial chemotaxis is essential to disentangling the roles of diverse chemical compounds and concentrations that control cell nutrient uptake, chemorepulsion from toxins, and microbial pathogenesis. Here, we present a novel microfluidic multiplexed chemotaxis device (MCD) which uses serial dilution to simultaneously perform six parallel bacterial chemotaxis assays that span five orders of magnitude in chemostimulant concentration on a single chip. We first validated the dilution and gradient generation performance of the MCD, and then compared the measured chemotactic response of an established bacterial chemotaxis system (Vibrio alginolyticus) to a standard microfluidic assay. Next, the MCD's versatility was assessed by quantifying the chemotactic responses of different bacteria (Psuedoalteromonas haloplanktis, Escherichia coli) to different chemoattractants and chemorepellents. The MCD vastly accelerates the chemotactic screening process, which is critical to deciphering the complex sea of chemical stimuli underlying microbial responses.

Biphasic Chemokinesis of Mammalian Sperm

The female reproductive tract (FRT) continuously modulates mammalian sperm motion by releasing various clues as sperm migrate toward the fertilization site. An existing gap in our understanding of sperm migration within the FRT is a quantitative picture of how sperm respond to and navigate the biochemical clues within the FRT. In this experimental study, we have found that in response to biochemical clues, mammalian sperm display two distinct chemokinetic behaviors which are dependent upon the rheological properties of the media: chiral, characterized by swimming in circles; and hyperactive, characterized by random reorientation events. We used minimal theoretical modeling, along with statistical characterization of the chiral and hyperactive trajectories, to show that the effective diffusivity of these motion phases decreases with increasing concentration of chemical stimulant. In the context of navigation this concentration dependent chemokinesis suggests that the chiral or hyperactive motion refines the sperm search area within different FRT functional regions. Further, the ability to switch between phases indicates that sperm may use various stochastic navigational strategies, such as run and tumble or intermittent search, within the fluctuating and spatially heterogeneous environment of the FRT.

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.

Directed colloidal assembly and banding via DC electrokinetics

Manipulating the transport and assembly of colloidal particles to form segregated bands or ordered supracolloidal structures plays an important role in many aspects of science and technology, from understanding the origin of life to synthesizing new materials for next-generation manufacturing, electronics, and therapeutics. One commonly used method to direct colloidal transport and assembly is the application of electric fields, either AC or DC, due to its feasibility. However, as colloidal segregation and assembly both require active redistribution of colloidal particles across multiple length scales, it is not apparent at first sight how a DC electric field, either externally applied or internally induced, can lead to colloidal structuring. In this Perspective, we briefly review and highlight recent advances and standing challenges in colloidal transport and assembly enabled by DC electrokinetics.

Surface tension coupled non-uniformly imposed flows modulate the activity of reproducing chemotactic bacteria in porous media

This paper investigates a non-homogeneous two-dimensional model for reproducing chemotactic bacteria, immersed in a porous medium that experiences non-uniformly imposed flows. It is shown that independently of the form of the fluid velocity field, the compressible/incompressible nature of the fluid significantly shifts the Turing stability-instability transition line. In dry media, Gaussian perturbations travel faster than the hyperbolic secant ones, yet the latter exhibit better stability properties. The system becomes highly unstable under strong flows and high surface tension. Approximated solutions recovered by injecting Gaussian perturbations overgrow, in addition to triggering concentric breathing features that split the medium into high and low-density domains. Secant perturbations on the other hand scatter slowly and form patterns of non-uniformly distributed peaks for strong flows and high surface tension. These results emphasize that Gaussian perturbations strongly modulate the activity of bacteria, hence can be exploited to perform fast spreading in environments with changing properties. In this sense, Gaussian profiles are better candidates to explain quick bacterial responses to external factors. Secant-type approximated solutions slowly modulate the bacterial activity, hence are better alternatives to dive into weak bacterial progressions in heterogeneous media.

Lab on a chip for a low-carbon future

Transitioning our society to a sustainable future, with low or net-zero carbon emissions to the atmosphere, will require a wide-spread transformation of energy and environmental technologies. In this perspective article, we describe how lab-on-a-chip (LoC) systems can help address this challenge by providing insight into the fundamental physical and geochemical processes underlying new technologies critical to this transition, and developing the new processes and materials required. We focus on six areas: (I) subsurface carbon sequestration, (II) subsurface hydrogen storage, (III) geothermal energy extraction, (IV) bioenergy, (V) recovering critical materials, and (VI) water filtration and remediation. We hope to engage the LoC community in the many opportunities within the transition ahead, and highlight the potential of LoC approaches to the broader community of researchers, industry experts, and policy makers working toward a low-carbon future.

Morphological instability and roughening of growing 3D bacterial colonies

The morphogenesis of two-dimensional bacterial colonies has been well studied. However, little is known about the colony morphologies of bacteria growing in three dimensions, despite the prevalence of three-dimensional environments (e.g., soil, inside hosts) as natural bacterial habitats. Using experiments on bacteria in granular hydrogel matrices, we find that dense multicellular colonies growing in three dimensions undergo a common morphological instability and roughen, adopting a characteristic broccoli-like morphology when they exceed a critical size. Analysis of a continuum “active fluid” model of the expanding colony reveals that this behavior originates from an interplay of competition for nutrients with growth-driven colony expansion, both of which vary spatially. These results shed light on the fundamental biophysical principles underlying growth in three dimensions.

How do growing bacterial colonies get their shapes? While colony morphogenesis is well studied in two dimensions, many bacteria grow as large colonies in three-dimensional (3D) environments, such as gels and tissues in the body or subsurface soils and sediments. Here, we describe the morphodynamics of large colonies of bacteria growing in three dimensions. Using experiments in transparent 3D granular hydrogel matrices, we show that dense colonies of four different species of bacteria generically become morphologically unstable and roughen as they consume nutrients and grow beyond a critical size—eventually adopting a characteristic branched, broccoli-like morphology independent of variations in the cell type and environmental conditions. This behavior reflects a key difference between two-dimensional (2D) and 3D colonies; while a 2D colony may access the nutrients needed for growth from the third dimension, a 3D colony inevitably becomes nutrient limited in its interior, driving a transition to unstable growth at its surface. We elucidate the onset of the instability using linear stability analysis and numerical simulations of a continuum model that treats the colony as an “active fluid” whose dynamics are driven by nutrient-dependent cellular growth. We find that when all dimensions of the colony substantially exceed the nutrient penetration length, nutrient-limited growth drives a 3D morphological instability that recapitulates essential features of the experimental observations. Our work thus provides a framework to predict and control the organization of growing colonies—as well as other forms of growing active matter, such as tumors and engineered living materials—in 3D environments.

Three-dimensional bioprinting: A cutting-edge tool for designing and fabricating engineered living materials

The design of engineered living materials (ELMs) is an emerging field developed from synthetic biology and materials science principles. ELMs are multi-scale bulk materials that combine the properties of self-healing and organism adaptability with the designed physicochemical or mechanical properties for functional applications in various fields, including therapy, electronics, and architecture. Among the many ELM design and manufacturing methods, three-dimensional (3D) bioprinting stands out for its precise control over the structure of the fabricated constructs and the spatial distribution of cells. In this review, we summarize the progress in the field, cell type and material selection, and the latest applications of 3D bioprinting to manufacture ELMs, as well as their advantages and limitations, hoping to deepen our understanding and provide new insights into ELM design. We believe that 3D bioprinting will become an important development direction and provide more contributions to this field.

Leveraging ultra-low interfacial tension and liquid-liquid phase separation in embedded 3D bioprinting

Many recently developed 3D bioprinting strategies operate by extruding aqueous biopolymer solutions directly into a variety of different support materials constituted from swollen, solvated, aqueous, polymer assemblies. In developing these 3D printing methods and materials, great care is often taken to tune the rheological behaviors of both inks and 3D support media. By contrast, much less attention has been given to the physics of the interfaces created when structuring one polymer phase into another in embedded 3D printing applications. For example, it is currently unclear whether a dynamic interfacial tension between miscible phases stabilizes embedded 3D bioprinted structures as they are shaped while in a liquid state. Interest in the physics of interfaces between complex fluids has grown dramatically since the discovery of liquid-liquid phase separation (LLPS) in living cells. We believe that many new insights coming from this burst of investigation into LLPS within biological contexts can be leveraged to develop new materials and methods for improved 3D bioprinting that leverage LLPS in mixtures of biopolymers, biocompatible synthetic polymers, and proteins. Thus, in this review article, we highlight work at the interface between recent LLPS research and embedded 3D bioprinting methods and materials, and we introduce a 3D bioprinting method that leverages LLPS to stabilize printed biopolymer inks embedded in a bioprinting support material.

Direct measurement of the aerotactic response in a bacterial suspension

Aerotaxis is the ability of motile cells to navigate toward oxygen. A key question is the dependence of the aerotactic velocity with the local oxygen concentration c. Here we combine simultaneous bacteria tracking and local oxygen concentration measurements using Ruthenium encapsulated in micelles to characterize the aerotactic response of Burkholderia contaminans, a motile bacterium ubiquitous in the environment. In our experiments, an oxygen gradient is produced by the bacterial respiration in a sealed glass capillary permeable to oxygen at one end, producing a bacterial band traveling toward the oxygen source. We compute the aerotactic response χ(c) both at the population scale, from the drift velocity in the bacterial band, and at the bacterial scale, from the angular modulation of the run times. Both methods are consistent with a power-law χ∝c^{-2}, in good agreement with existing models based on the biochemistry of bacterial membrane receptors.

Role of tactic response on the mobilization of motile bacteria through micrometer-sized pores

A major cause of high bioremediation endpoints is the limited bioaccessibility to residual contaminants resting in soil pores with diameters close to the size exclusion limit of bacterial cells. Under nongrowing conditions and in the absence of hydraulic flow, we examined how the tactic behavior of motile, contaminant-degrading Pseudomonas putida G7 cells (2 × 1 μm) influenced passage through membranes with pores ranging in size from 1 μm to 12 μm. The bacteria were spontaneously retained by the membranes - even those with the largest pore size. However, the cells were mobilized through 5 μm and 12 μm pores after the application of an attractant (salicylate). Mobilization also occurred by attraction to the common root exudate constituents γ-aminobutyric acid and citrate and repellence (or negative taxis) to zero-valent iron nanoparticles. The observed pore size threshold for tactic mobilization (5 μm) and unaltered cell fluxes and effective cell diffusion against different chemoeffector strengths and concentrations suggest that there is a physical constraint on the gradient sensing mechanism at the pores that drives the tactic response. Our results indicate that chemically mediated, small-scale tactic reactions of motile bacteria may become relevant to enhance the bioaccessibility of the residual contaminants present in micrometer-sized soil pores.

Transitioning to confined spaces impacts bacterial swimming and escape response

Symbiotic bacteria often navigate complex environments before colonizing privileged sites in their host organism. Chemical gradients are known to facilitate directional taxis of these bacteria, guiding them toward their eventual destination. However, less is known about the role of physical features in shaping the path the bacteria take and defining how they traverse a given space. The flagellated marine bacterium Vibrio fischeri, which forms a binary symbiosis with the Hawaiian bobtail squid, Euprymna scolopes, must navigate tight physical confinement during colonization, squeezing through a tissue bottleneck constricting to ∼2 μm in width on the way to its eventual home. Using microfluidic in vitro experiments, we discovered that V. fischeri cells alter their behavior upon entry into confined space, straightening their swimming paths and promoting escape from confinement. Using a computational model, we attributed this escape response to two factors: reduced directional fluctuation and a refractory period between reversals. Additional experiments in asymmetric capillary tubes confirmed that V. fischeri quickly escape from confined ends, even when drawn into the ends by chemoattraction. This avoidance was apparent down to a limit of confinement approaching the diameter of the cell itself, resulting in a balance between chemoattraction and evasion of physical confinement. Our findings demonstrate that nontrivial distributions of swimming bacteria can emerge from simple physical gradients in the level of confinement. Tight spaces may serve as an additional, crucial cue for bacteria while they navigate complex environments to enter specific habitats.

Migration of active rings in porous media

Inspired by how the shape deformations in active organisms help them to migrate through disordered porous environments, we simulate active ring polymers in two-dimensional random porous media. Flexible and inextensible active ring polymers navigate smoothly through the disordered media. In contrast, semiflexible rings undergo transient trapping inside the pore space; the degree of trapping is inversely correlated with the increase in activity. We discover that flexible rings swell while inextensible and semiflexible rings monotonically shrink upon increasing the activity. Together, our findings identify the optimal migration of active ring polymers through porous media.

Collective behavior and nongenetic inheritance allow bacterial populations to adapt to changing environments

Collective behaviors require coordination among a group of individuals. As a result, individuals that are too phenotypically different from the rest of the group can be left out, reducing heterogeneity, but increasing coordination. If individuals also reproduce, the offspring can have different phenotypes from their parent(s). This raises the question of how these two opposing processes-loss of diversity by collective behaviors and generation of it through growth and inheritance-dynamically shape the phenotypic composition of an isogenic population. We examine this question theoretically using collective migration of chemotactic bacteria as a model system, where cells of different swimming phenotypes are better suited to navigate in different environments. We find that the differential loss of phenotypes caused by collective migration is environment-dependent. With cell growth, this differential loss enables migrating populations to dynamically adapt their phenotype compositions to the environment, enhancing migration through multiple environments. Which phenotypes are produced upon cell division depends on the level of nongenetic inheritance, and higher inheritance leads to larger composition adaptation and faster migration at steady state. However, this comes at the cost of slower responses to new environments. Due to this trade-off, there is an optimal level of inheritance that maximizes migration speed through changing environments, which enables a diverse population to outperform a nondiverse one. Growing populations might generally leverage the selection-like effects provided by collective behaviors to dynamically shape their own phenotype compositions, without mutations.

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.

A biophysical threshold for biofilm formation

Bacteria are ubiquitous in our daily lives, either as motile planktonic cells or as immobilized surface-attached biofilms. These different phenotypic states play key roles in agriculture, environment, industry, and medicine; hence, it is critically important to be able to predict the conditions under which bacteria transition from one state to the other. Unfortunately, these transitions depend on a dizzyingly complex array of factors that are determined by the intrinsic properties of the individual cells as well as those of their surrounding environments, and are thus challenging to describe. To address this issue, here, we develop a generally-applicable biophysical model of the interplay between motility-mediated dispersal and biofilm formation under positive quorum sensing control. Using this model, we establish a universal rule predicting how the onset and extent of biofilm formation depend collectively on cell concentration and motility, nutrient diffusion and consumption, chemotactic sensing, and autoinducer production. Our work thus provides a key step toward quantitatively predicting and controlling biofilm formation in diverse and complex settings.

Influence of confinement on the spreading of bacterial populations

The spreading of bacterial populations is central to processes in agriculture, the environment, and medicine. However, existing models of spreading typically focus on cells in unconfined settings—despite the fact that many bacteria inhabit complex and crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and thereby strongly regulate population spreading. Here, we develop an extended version of the classic Keller-Segel model of bacterial spreading via motility that also incorporates cellular growth and division, and explicitly considers the influence of confinement in promoting both cell-solid and cell-cell collisions. Numerical simulations of this extended model demonstrate how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations, in good agreement with recent experimental results. In particular, with increasing confinement, we find that cell-cell collisions increasingly hinder the initial formation and the long-time propagation speed of chemotactic pulses. Moreover, also with increasing confinement, we find that cellular growth and division plays an increasingly dominant role in driving population spreading—eventually leading to a transition from chemotactic spreading to growth-driven spreading via a slower, jammed front. This work thus provides a theoretical foundation for further investigations of the influence of confinement on bacterial spreading. More broadly, these results help to provide a framework to predict and control the dynamics of bacterial populations in complex and crowded environments.

The spreading of bacteria through their environments critically impacts our everyday lives; it can be harmful, underlying the progression of infections and spoilage of foods, or can be beneficial, enabling the delivery of therapeutics, sustaining plant growth, and remediating polluted terrain. In all these cases, bacteria typically inhabit crowded environments, such as soils, sediments, and biological tissues/gels, in which solid obstacles confine the cells and regulate their spreading. However, existing models of spreading typically focus on cells in unconfined settings, and thus are frequently not applicable to cells in more complex environments. Here, we address this gap in knowledge by extending the classic Keller-Segel model of bacterial spreading via motility to also incorporate cellular growth and division, and explicitly consider the influence of confinement. Through numerical simulations of this extended model, we show how confinement fundamentally alters the dynamics and morphology of spreading bacterial populations—in particular, driving a transition from chemotactic spreading of motile cells to growth-driven spreading via a slower, jammed front. These results provide a foundation for further investigations of the influence of confinement on bacterial spreading, both by yielding testable predictions for future experiments, and by providing guidelines to predict and control the dynamics of bacterial populations in complex and crowded environments.

Dynamics of Bacteria Scanning a Porous Environment

It has recently been reported that bacteria, such as Escherichia coli Bhattacharjee and Datta, Nat. Commun. 10, 2075 (2019).NCAOBW2041-172310.1038/s41467-019-10115-1 and Pseudomonas putida Alirezaeizanjani et al., Sci. Adv. 6, eaaz6153 (2020).SACDAF2375-254810.1126/sciadv.aaz6153, perform distinct modes of motion when placed in porous media as compared to dilute regions or free space. This has led us to suggest an efficient strategy for active particles in a disordered environment: reorientations are suppressed in locally dilute regions and intensified in locally dense ones. Thereby the local geometry determines the optimal path of the active agent and substantially accelerates the dynamics for up to 2 orders of magnitude. We observe a nonmonotonic behavior of the diffusion coefficient in dependence on the tumbling rate and identify a localization transition, either by increasing the density of obstacles or by decreasing the reorientation rate.

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.

Partitioning of active particles into porous media

Passive Brownian particles partition homogeneously between a porous medium and an adjacent fluid reservoir. In contrast, active particles accumulate near boundaries and can therefore preferentially partition into the porous medium. Understanding how active particles interact with and partition into such an environment is important for optimizing particle transport. In this work, both the initial transient and steady behavior as active swimmers partition into a porous medium from a bulk fluid reservoir are investigated. At short times, the particle number density in the porous medium exhibits an oscillatory behavior due to the particles' ballistic motion when time t < τ_R, where τ_R is the reorientation time of the active particles. At longer times, t > L²/D^swim, the particles diffuse from the reservoir into the porous medium, leading to a steady state concentration partitioning. Here, L is the characteristic length scale of the porous medium and D^swim = U₀/d(d - 1), where U₀ is the intrinsic swim speed of the particles,  = U₀τ_R is the particles' run, or persistence, length, and d is the dimension of the reorientation process. An analytical prediction is developed for this partitioning for spherical obstacles connected to a fluid reservoir in both two and three dimensions based on the Smoluchowski equation and a macroscopic mechanical momentum balance. The analytical prediction agrees well with Brownian dynamics simulations.

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.

E. coli aggregation and impaired cell division after terahertz irradiation

In this study we demonstrated that exposure of Escherichia coli (E. coli) to terahertz (THz) radiation resulted in a change in the activities of the tdcABCDEFGR and matA–F genes (signs of cell aggregation), gene yjjQ (signs of suppression of cell motility), dicABCF, FtsZ, and minCDE genes (signs of suppression of cell division), sfmACDHF genes (signs of adhesin synthesis), yjbEFGH and gfcA genes (signs of cell envelope stabilization). Moreover, THz radiation induced E. coli csg operon genes of amyloid biosynthesis. Electron microscopy revealed that the irradiated bacteria underwent increased aggregation; 20% of them formed bundle-like structures consisting of two to four pili clumped together. This could be the result of changes in the adhesive properties of the pili. We also found aberrations in cell wall structure in the middle part of the bacterial cell; these aberrations impaired the cell at the initial stages of division and resulted in accumulation of long rod-like cells. Overall, THz radiation was shown to have adverse effects on bacterial populations resulting in cells with abnormal morphology.