Confinement and activity regulate bacterial motion in porous media

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.

Collective dynamics of active dumbbells near a circular obstacle

In this article, we present the collective dynamics of active dumbbells in the presence of a static circular obstacle using Brownian dynamics simulation. The active dumbbells aggregate on the surface of a circular obstacle beyond a critical radius. The aggregation is non-uniform along the circumference, and the aggregate size increases with the activity (Pe) and the curvature radius (Ro). The dense aggregate of active dumbbells displays persistent rotational motion with a certain angular speed, which linearly increases with activity. Furthermore, we show a strong polar ordering of the active dumbbells within the aggregate. The polar ordering exhibits long-range correlation, with the correlation length corresponding to the aggregate size. Additionally, we show that the residence time of an active dumbbell on the obstacle surface increases rapidly with area fraction due to many-body interactions that lead to a slowdown of the rotational diffusion. This article further considers the dynamical behavior of a tracer particle in the solution of active dumbbells. Interestingly, the speed of the passive tracer particle displays a crossover from monotonically decreasing to increasing with the size of the tracer particle upon increasing the dumbbells' speed. Furthermore, the effective diffusion of the tracer particle displays non-monotonic behavior with the area fraction; the initial increase in diffusivity is followed by a decrease for a larger area fraction.

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.

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.

Learning dynamical models of single and collective cell migration: a review

Single and collective cell migration are fundamental processes critical for physiological phenomena ranging from embryonic development and immune response to wound healing and cancer metastasis. To understand cell migration from a physical perspective, a broad variety of models for the underlying physical mechanisms that govern cell motility have been developed. A key challenge in the development of such models is how to connect them to experimental observations, which often exhibit complex stochastic behaviours. In this review, we discuss recent advances in data-driven theoretical approaches that directly connect with experimental data to infer dynamical models of stochastic cell migration. Leveraging advances in nanofabrication, image analysis, and tracking technology, experimental studies now provide unprecedented large datasets on cellular dynamics. In parallel, theoretical efforts have been directed towards integrating such datasets into physical models from the single cell to the tissue scale with the aim of conceptualising the emergent behaviour of cells. We first review how this inference problem has been addressed in both freely migrating and confined cells. Next, we discuss why these dynamics typically take the form of underdamped stochastic equations of motion, and how such equations can be inferred from data. We then review applications of data-driven inference and machine learning approaches to heterogeneity in cell behaviour, subcellular degrees of freedom, and to the collective dynamics of multicellular systems. Across these applications, we emphasise how data-driven methods can be integrated with physical active matter models of migrating cells, and help reveal how underlying molecular mechanisms control cell behaviour. Together, these data-driven approaches are a promising avenue for building physical models of cell migration directly from experimental data, and for providing conceptual links between different length-scales of description.

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.

Transition from active motion to anomalous diffusion for Bacillus subtilis confined in hydrogel matrices

We investigate the motility of B. subtilis under different degrees of confinement induced by transparent porous hydrogels. The dynamical behavior of the bacteria at short times is linked to characteristic parameters describing the hydrogel porosity. Mean squared displacements (MSDs) reveal that the run-and-tumble dynamics of unconfined B. subtilis progressively turns into sub-diffusive motion with increasing confinement. Correspondingly, the median instantaneous velocity of bacteria decreases and becomes more narrowly distributed, while the reorientation rate increases and reaches a plateau value. Analyzing single-trajectories, we show that the average dynamical behavior is the result of complex displacements, in which active, diffusive and sub-diffusive segments coexist. For small and moderate confinements, the number of active segments reduces, while the diffusive and sub-diffusive segments increase. The alternation of sub-diffusion, diffusion and active motion along the same trajectory can be described as a hopping ad trapping motion, in which hopping events correspond to displacements with an instantaneous velocity exceeding the corresponding mean value along a trajectory. Different from previous observations, escape from local trapping occurs for B. subtilis through active runs but also diffusion. Interestingly, the contribution of diffusion is maximum at intermediate confinements. At sufficiently long times transport coefficients estimated from the experimental MSDs under different degrees of confinement can be reproduced using a recently proposed hopping and trapping model. Finally, we propose a quantitative relationship linking the median velocity of confined and unconfined bacteria through the characteristic confinement length of the hydrogel matrix. Our work provides new insights for the bacterial motility in complex media that mimic natural environments and are relevant to important problems like sterilization, water purification, biofilm formation, membrane permeation and bacteria separation.

Chiral active particles are sensitive reporters to environmental geometry

Chiral active particles (CAPs) are self-propelling particles that break time-reversal symmetry by orbiting or spinning, leading to intriguing behaviors. Here, we examined the dynamics of CAPs moving in 2D lattices of disk obstacles through active Brownian dynamics simulations and granular experiments with grass seeds. We find that the effective diffusivity of the CAPs is sensitive to the structure of the obstacle lattice, a feature absent in achiral active particles. We further studied the transport of CAPs in obstacle arrays under an external field and found a reentrant directional locking effect, which can be used to sort CAPs with different activities. Finally, we demonstrated that parallelogram lattices of obstacles without mirror symmetry can separate clockwise and counter-clockwise CAPs. The mechanisms of the above three novel phenomena are qualitatively explained. As such, our work provides a basis for designing chirality-based tools for single-cell diagnosis and separation, and active particle-based environmental sensors.

Motility-induced phase separation and frustration in active matter swarmalators

We introduce a two dimensional system of active matter swarmalators composed of elastically interacting run-and-tumble active disks with an internal parameter ϕ_{i}. The disks experience an additional attractive or repulsive force with neighboring disks depending upon their relative difference in ϕ_{i}, making them similar to swarmalators used in robotic systems. In the absence of the internal parameter, the system forms a motility-induced phase separated (MIPS) state, but when the swarmalator interactions are present, a wide variety of other active phases appear depending upon whether the interaction is attractive or repulsive and whether the particles act to synchronize or ant-synchronize their internal parameter values. These phases include a gas-free gel regime, arrested clusters, a labyrinthine state, a regular MIPS state, a frustrated MIPS state for attractive antisynchronization, and a superlattice MIPS state for attractive synchronization.

Forced and spontaneous translocation dynamics of a semiflexible active polymer in two dimensions

Polymer translocation is a fundamental topic in non-equilibrium physics and is crucially important to many biological processes in life. In the present work, we adopt two-dimensional Langevin dynamics simulations to study the forced and spontaneous translocation dynamics of an active filament. The influence of polymer stiffness on the underlying dynamics is explicitly analyzed. For the forced translocation, the results show a robust stiffness-induced inhibition, and the translocation time exhibits a dual-exponent scaling relationship with the bending modulus. Tension propagation (TP) is also examined, where we find prominent modifications in terms of both activity and stiffness. For spontaneous translocation into a pure solvent, the translocation time is almost independent of the polymer stiffness. However, when the polymer is translocated into a porous medium, an intriguing non-monotonic alteration of translocation time with increasing chain stiffness is demonstrated. The semiflexible chain is beneficial for translocation while the rigid chain is not conducive. Stiffness regulation on the diffusion dynamics of the polymer in porous media shows a consistent scenario. The interplay of activity, stiffness, and porous crowding provides a new mechanism for understanding the non-trivial translocation dynamics of an active filament in complex environments.

Dispersion of run-and-tumble microswimmers through disordered media

Understanding the transport properties of microorganisms and self-propelled particles in porous media has important implications for human health as well as microbial ecology. In free space, most microswimmers perform diffusive random walks as a result of the interplay of self-propulsion and orientation decorrelation mechanisms such as run-and-tumble dynamics or rotational diffusion. In an unstructured porous medium, collisions with the microstructure result in a decrease in the effective spatial diffusivity of the particles from its free-space value. Here, we analyze this problem for a simple model system consisting of noninteracting point particles performing run-and-tumble dynamics through a two-dimensional disordered medium composed of a random distribution of circular obstacles, in the absence of Brownian diffusion or hydrodynamic interactions. The particles are assumed to collide with the obstacles as hard spheres and subsequently slide on the obstacle surface with no frictional resistance while maintaining their orientation, until they either escape or tumble. We show that the variations in the long-time diffusivity can be described by a universal dimensionless hindrance function f(ϕ,Pe) of the obstacle area fraction ϕ and Péclet number Pe, or ratio of the swimmer run length to the obstacle size. We analytically derive an asymptotic expression for the hindrance function valid for dilute media (Peϕ≪1), and its extension to denser media is obtained using stochastic simulations. As we explain, the model is also easily generalized to describe dispersion in three dimensions.

Optimal motility strategies for self-propelled agents to explore porous media

Microrobots for, e.g., biomedical applications, need to be equipped with motility strategies that enable them to navigate through complex environments. Inspired by biological microorganisms we re-create motility patterns such as run-and-reverse, run-and-tumble, or run-reverse-flick applied to active rodlike particles in silico. We investigate their capability to efficiently explore disordered porous environments with various porosities and mean pore sizes ranging down to the scale of the active particle. By calculating the effective diffusivity for the different patterns, we can predict the optimal one for each porous sample geometry. We find that providing the agent with very basic sensing and decision-making capabilities yields a motility pattern outperforming the biologically inspired patterns for all investigated porous samples.

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.

Conformation and dynamics of an active filament in crowded media

The structural and dynamical properties of active filamentous objects under macromolecular crowding have a great relevance in biology. By means of Brownian dynamics simulations, we perform a comparative study for the conformational change and diffusion dynamics of an active chain in pure solvents and in crowded media. Our result shows a robust compaction-to-swelling conformational change with the augment of the Péclet number. The presence of crowding facilitates self-trapping of monomers and, thus, reinforces the activity mediated compaction. In addition, the efficient collisions between the self-propelled monomers and crowders induce a coil-to-globulelike transition, indicated by a marked change of the Flory scaling exponent of the gyration radius. Moreover, the diffusion dynamics of the active chain in crowded solutions demonstrates activity-enhanced subdiffusion. The center of mass diffusion manifests rather new scaling relations with respect to both the chain length and Péclet number. The interplay of chain activity and medium crowding provides a new mechanism to understand the non-trivial properties of active filaments in complex environments.

Bacterial mobility and motility in porous media mimicked by microspheres

Bacterial motion in porous media is essential for their survival, proper functioning, and various applications. Here we investigated the motion of Escherichia coli bacteria in microsphere-mimicked porous media. We observed reduced bacterial velocity and enhanced directional changes of bacteria as the density of microspheres increased, while such changes happened mostly around the microspheres and due to the collisions with the microspheres. More importantly, we established and quantified the correlation between the bacterial trapping in porous media and the geometric confinement imposed by the microspheres. In addition, numerical simulations showed that the active Brownian motion model in the presence of microspheres resulted in bacterial motion that are consistent with the experimental observations. Our study suggested that it is important to distinguish the ability of bacteria to move easily - bacterial mobility - from the ability of bacteria to move independently - bacteria motility. Our results showed that bacterial motility remains similar in porous media, but bacterial mobility was significantly affected by the pore-scale confinement.

Role of the Two Flagellar Stators in Swimming Motility of Pseudomonas putida

In the soil bacterium Pseudomonas putida, the motor torque for flagellar rotation is generated by the two stators MotAB and MotCD. Here, we construct mutant strains in which one or both stators are knocked out and investigate their swimming motility in fluids of different viscosity and in heterogeneous structured environments (semisolid agar). Besides phase-contrast imaging of single-cell trajectories and spreading cultures, dual-color fluorescence microscopy allows us to quantify the role of the stators in enabling P. putida's three different swimming modes, where the flagellar bundle pushes, pulls, or wraps around the cell body. The MotAB stator is essential for swimming motility in liquids, while spreading in semisolid agar is not affected. Moreover, if the MotAB stator is knocked out, wrapped mode formation under low-viscosity conditions is strongly impaired and only partly restored for increased viscosity and in semisolid agar. In contrast, when the MotCD stator is missing, cells are indistinguishable from the wild type in fluid experiments but spread much more slowly in semisolid agar. Analysis of the microscopic trajectories reveals that the MotCD knockout strain forms sessile clusters, thereby reducing the number of motile cells, while the swimming speed is unaffected. Together, both stators ensure a robust wild type that swims efficiently under different environmental conditions. IMPORTANCE Because of its heterogeneous habitat, the soil bacterium Pseudomonas putida needs to swim efficiently under very different environmental conditions. In this paper, we knocked out the stators MotAB and MotCD to investigate their impact on the swimming motility of P. putida. While the MotAB stator is crucial for swimming in fluids, in semisolid agar, both stators are sufficient to sustain a fast-swimming phenotype and increased frequencies of the wrapped mode, which is known to be beneficial for escaping mechanical traps. However, in contrast to the MotAB knockout, a culture of MotCD knockout cells spreads much more slowly in the agar, as it forms nonmotile clusters that reduce the number of motile cells.

Escaping speed of bacteria from confinement

Microswimmers such as bacteria exhibit large speed fluctuation when exploring their living environment. Here, we show that the bacterium Escherichia coli with a wide range of length speeds up beyond its free-swimming speed when passing through narrow and short confinement. The speedup is observed in two modes: for short bacteria with L <20 μm, the maximum speed occurs when the cell body leaves the confinement, but a flagellar bundle is still confined. For longer bacteria (L ≥ 20 μm), the maximum speed occurs when the middle of the cell, where the maximum number of flagellar bundles locate, is confined. The two speed-up modes are explained by a vanishing body drag and an increased flagella drag-a universal property of an "ideal swimmer." The spatial variance of speed can be quantitatively explained by a simple model based on the resistance matrix of a partially confined bacterium. The speed change depends on the distribution of motors, and the latter is confirmed by fluorescent imaging of flagellar hooks. By measuring the duration of slowdown and speedup, we find that the effective chemotaxis is biased in filamentous bacteria, which might benefit their survival. The experimental setup can be useful to study the motion of microswimmers near surfaces with different surface chemistry.

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.

Unjamming and emergent nonreciprocity in active ploughing through a compressible viscoelastic fluid

A dilute suspension of active Brownian particles in a dense compressible viscoelastic fluid, forms a natural setting to study the emergence of nonreciprocity during a dynamical phase transition. At these densities, the transport of active particles is strongly influenced by the passive medium and shows a dynamical jamming transition as a function of activity and medium density. In the process, the compressible medium is actively churned up - for low activity, the active particle gets self-trapped in a cavity of its own making, while for large activity, the active particle ploughs through the medium, either accompanied by a moving anisotropic wake, or leaving a porous trail. A hydrodynamic approach makes it evident that the active particle generates a long-range density wake which breaks fore-aft symmetry, consistent with the simulations. Accounting for the back-reaction of the compressible medium leads to (i) dynamical jamming of the active particle, and (ii) a dynamical non-reciprocal attraction between two active particles moving along the same direction, with the trailing particle catching up with the leading one in finite time. We emphasize that these nonreciprocal effects appear only when the active particles are moving and so manifest in the vicinity of the jamming-unjamming transition.

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.

Engineered Living Hydrogels

Living biological systems, ranging from single cells to whole organisms, can sense, process information, and actuate in response to changing environmental conditions. Inspired by living biological systems, engineered living cells and nonliving matrices are brought together, which gives rise to the technology of engineered living materials. By designing the functionalities of living cells and the structures of nonliving matrices, engineered living materials can be created to detect variability in the surrounding environment and to adjust their functions accordingly, thereby enabling applications in health monitoring, disease treatment, and environmental remediation. Hydrogels, a class of soft, wet, and biocompatible materials, have been widely used as matrices for engineered living cells, leading to the nascent field of engineered living hydrogels. Here, the interactions between hydrogel matrices and engineered living cells are described, focusing on how hydrogels influence cell behaviors and how cells affect hydrogel properties. The interactions between engineered living hydrogels and their environments, and how these interactions enable versatile applications, are also discussed. Finally, current challenges facing the field of engineered living hydrogels for their applications in clinical and environmental settings are highlighted.

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.

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.

Phase separation of self-propelled disks with ferromagnetic and nematic alignment

We present a comprehensive study of a model system of repulsive self-propelled disks in two dimensions with ferromagnetic and nematic velocity alignment interactions. We characterize the phase behavior of the system as a function of the alignment and self-propulsion strength, featuring orientational order for strong alignment and motility-induced phase separation (MIPS) at moderate alignment but high enough self-propulsion. We derive a microscopic theory for these systems yielding a closed set of hydrodynamic equations from which we perform a linear stability analysis of the homogenous disordered state. This analysis predicts MIPS in the presence of aligning torques. The nature of the continuum theory allows for an explicit quantitative comparison with particle-based simulations, which consistently shows that ferromagnetic alignment fosters phase separation, while nematic alignment does not alter either the nature or the location of the instability responsible for it. In the ferromagnetic case, such behavior is due to an increase of the imbalance of the number of particle collisions along different orientations, giving rise to the self-trapping of particles along their self-propulsion direction. On the contrary, the anisotropy of the pair correlation function, which encodes this self-trapping effect, is not significantly affected by nematic torques. Our work shows the predictive power of such microscopic theories to describe complex active matter systems with different interaction symmetries and sheds light on the impact of velocity-alignment interactions in motility-induced phase separation.

A geometric criterion for the optimal spreading of active polymers in porous media

Efficient navigation through disordered, porous environments poses a major challenge for swimming microorganisms and future synthetic cargo-carriers. We perform Brownian dynamics simulations of active stiff polymers undergoing run-reverse dynamics, and so mimic bacterial swimming, in porous media. In accord with experiments of Escherichia coli, the polymer dynamics are characterized by trapping phases interrupted by directed hopping motion through the pores. Our findings show that the spreading of active agents in porous media can be optimized by tuning their run lengths, which we rationalize using a coarse-grained model. More significantly, we discover a geometric criterion for the optimal spreading, which emerges when their run lengths are comparable to the longest straight path available in the porous medium. Our criterion unifies results for porous media with disparate pore sizes and shapes and for run-and-tumble polymers. It thus provides a fundamental principle for optimal transport of active agents in densely-packed biological and environmental settings.

Active matter shepherding and clustering in inhomogeneous environments

We consider a mixture of active and passive run-and-tumble disks in an inhomogeneous environment where only half of the sample contains quenched disorder or pinning. The disks are initialized in a fully mixed state of uniform density. We identify several distinct dynamical phases as a function of motor force and pinning density. At high pinning densities and high motor forces, there is a two-step process initiated by a rapid accumulation of both active and passive disks in the pinned region, which produces a large density gradient in the system. This is followed by a slower species phase separation process where the inactive disks are shepherded by the active disks into the pin-free region, forming a nonclustered fluid and producing a more uniform density with species phase separation. For higher pinning densities and low motor forces, the dynamics becomes very slow and the system maintains a strong density gradient. For weaker pinning and large motor forces, a floating clustered state appears, and the time-averaged density of the system is uniform. We illustrate the appearance of these phases in a dynamic phase diagram.

Mechanisms of transport enhancement for self-propelled nanoswimmers in a porous matrix

Micro/nanoswimmers convert diverse energy sources into directional movement, demonstrating significant promise for biomedical and environmental applications, many of which involve complex, tortuous, or crowded environments. Here, we investigated the transport behavior of self-propelled catalytic Janus particles in a complex interconnected porous void space, where the rate-determining step involves the escape from a cavity and translocation through holes to adjacent cavities. Surprisingly, self-propelled nanoswimmers escaped from cavities more than 20× faster than passive (Brownian) particles, despite the fact that the mobility of nanoswimmers was less than 2× greater than that of passive particles in unconfined bulk liquid. Combining experimental measurements, Monte Carlo simulations, and theoretical calculations, we found that the escape of nanoswimmers was enhanced by nuanced secondary effects of self-propulsion which were amplified in confined environments. In particular, active escape was facilitated by anomalously rapid confined short-time mobility, highly efficient surface-mediated searching for holes, and the effective abolition of entropic and/or electrostatic barriers at the exit hole regions by propulsion forces. The latter mechanism converted the escape process from barrier-limited to search-limited. These findings provide general and important insights into micro/nanoswimmer mobility in complex environments.

Non-Genetic Diversity in Chemosensing and Chemotactic Behavior

Non-genetic phenotypic diversity plays a significant role in the chemotactic behavior of bacteria, influencing how populations sense and respond to chemical stimuli. First, we review the molecular mechanisms that generate phenotypic diversity in bacterial chemotaxis. Next, we discuss the functional consequences of phenotypic diversity for the chemosensing and chemotactic performance of single cells and populations. Finally, we discuss mechanisms that modulate the amount of phenotypic diversity in chemosensory parameters in response to changes in the environment.

Chemotactic migration of bacteria in porous media

Chemotactic migration of bacteria-their ability to direct multicellular motion along chemical gradients-is central to processes in agriculture, the environment, and medicine. However, current understanding of migration is based on studies performed in bulk liquid, despite the fact that many bacteria inhabit tight porous media such as soils, sediments, and biological gels. Here, we directly visualize the chemotactic migration of Escherichia coli populations in well-defined 3D porous media in the absence of any other imposed external forcing (e.g., flow). We find that pore-scale confinement is a strong regulator of migration. Strikingly, cells use a different primary mechanism to direct their motion in confinement than in bulk liquid. Furthermore, confinement markedly alters the dynamics and morphology of the migrating population-features that can be described by a continuum model, but only when standard motility parameters are substantially altered from their bulk liquid values to reflect the influence of pore-scale confinement. Our work thus provides a framework to predict and control the migration of bacteria, and active matter in general, in complex environments.

Tunable depletion force in active and crowded environments

We adopt two-dimensional Langevin dynamics simulations to study the effective interactions between two passive colloids in a bath crowded with active particles. We mainly pay attention to the significant effects of active particle size, crowding-activity coupling, and chirality. First, a transition of depletion force from repulsion to attraction is revealed by varying particle size. Moreover, larger active crowders with sufficient activity can generate strong attractive force, which is in contrast to the cage effect in passive media. It is interesting that the attraction induced by large active crowders follows a linear scaling with the persistence length of active particles. Second, the effective force also experiences a transition from repulsion to attraction as volume fraction increases, as a consequence of the competition between the two contrastive factors of activity and crowding. As bath volume fraction is relatively small, activity generates a dominant repulsion force, while as the bath becomes concentrated, crowding-induced attraction becomes overwhelming. Lastly, in a chiral bath, we observe a very surprising oscillation phenomenon of active depletion force, showing an evident quasiperiodic variation with increasing chirality. Aggregation of active particles in the vicinity of the colloids is carefully examined, which serves as a reasonable picture for our observations. Our findings provide an inspiring strategy for the tunable active depletion force by crowding, activity, and chirality.

Active matter commensuration and frustration effects on periodic substrates

We show that self-driven particles coupled to a periodic obstacle array exhibit active matter commensuration effects that are absent in the Brownian limit. As the obstacle size is varied for sufficiently large activity, a series of commensuration effects appear in which the motility induced phase separation produces commensurate crystalline states, while for other obstacle sizes we find frustrated or amorphous states. The commensuration effects are associated with peaks in the amount of sixfold ordering and the maximum cluster size. When a drift force is added to the system, the mobility contains peaks and dips similar to those found in transport studies for commensuration effects in superconducting vortices and colloidal particles.

Disorder-Induced Long-Ranged Correlations in Scalar Active Matter

We study the impact of quenched random potentials and torques on scalar active matter. Microscopic simulations reveal that motility-induced phase separation is replaced in two dimensions by an asymptotically homogeneous phase with anomalous long-ranged correlations and nonvanishing steady-state currents. Using a combination of phenomenological models and a field-theoretical treatment, we show the existence of a lower-critical dimension d_{c}=4, below which phase separation is only observed for systems smaller than an Imry-Ma length scale. We identify a weak-disorder regime in which the structure factor scales as S(q)∼1/q^{2}, which accounts for our numerics. In d=2, we predict that, at larger scales, the behavior should cross over to a strong-disorder regime. In d>2, these two regimes exist separately, depending on the strength of the potential.

The influence of motility on bacterial accumulation in a microporous channel

We study the transport of bacteria in a porous media modeled by a square channel containing one cylindrical obstacle via molecular dynamics simulations coupled to a lattice Boltzmann fluid. Our bacteria model is a rod-shaped rigid body which is propelled by a force-free mechanism. To account for the behavior of living bacteria, the model also incorporates a run-and-tumble process. The model bacteria are capable of hydrodynamically interacting with both of the channel walls and the obstacle. This enables the bacteria to get reoriented when experiencing a shear-flow. We demonstrate that this model is capable of reproducing the bacterial accumulation on the rear side of an obstacle, as has recently been experimentally observed by [G. L. Miño, et al., Adv. Microbiol., 2018, 8, 451] using E. coli bacteria. By systematically varying the external flow strength and the motility of the bacteria, we resolve the interplay between the local flow strength and the swimming characteristics that lead to the accumulation. Moreover, by changing the geometry of the channel, we also reveal the important role of the interactions between the bacteria and the confining walls for the accumulation process.

Impact of confined geometries on hopping and trapping of motile bacteria in porous media

We use a random walk particle-tracking (RWPT) approach to elucidate the impact of porous media confinement and cell-cell interactions on bacterial transport. The model employs stochastic alternating motility states consisting of hopping movement and trapping reorientation. The stochastic motility patterns are defined based on direct visualization of individual trajectory data. We validate our model against experimental data, at single-cell resolution, of bacterial E. coli motion in three-dimensional confined porous media. Results show that the model is able to efficiently simulate the spreading dynamics of motile bacteria as it captures the impact of cell-cell interaction and pore confinement, which marks the transition to a late-time subdiffusive regime. Furthermore, the model is able to qualitatively reproduce the observed directional persistence. Our RWPT model constitutes a meshless simple method which is easy to implement and does not invoke ad hoc assumptions but represents the basis for a multiscale approach to the study of bacterial dispersal in porous systems.

Active Brownian and inertial particles in disordered environments: Short-time expansion of the mean-square displacement

We consider an active Brownian particle moving in a disordered two-dimensional energy or motility landscape. The averaged mean-square displacement (MSD) of the particle is calculated analytically within a systematic short-time expansion. As a result, for overdamped particles, both an external random force field and disorder in the self-propulsion speed induce ballistic behavior adding to the ballistic regime of an active particle with sharp self-propulsion speed. Spatial correlations in the force and motility landscape contribute only to the cubic and higher-order powers in time for the MSD. Finally, for inertial particles two superballistic regimes are found where the scaling exponent of the MSD with time is α=3 and α=4. We confirm our theoretical predictions by computer simulations. Moreover, they are verifiable in experiments on self-propelled colloids in random environments.

Directional locking effects for active matter particles coupled to a periodic substrate

Directional locking occurs when a particle moving over a periodic substrate becomes constrained to travel along certain substrate symmetry directions. Such locking effects arise for colloids and superconducting vortices moving over ordered substrates when the direction of the external drive is varied. Here we study the directional locking of run-and-tumble active matter particles interacting with a periodic array of obstacles. In the absence of an external biasing force, we find that the active particle motion locks to various symmetry directions of the substrate when the run time between tumbles is large. The number of possible locking directions depends on the array density and on the relative sizes of the particles and the obstacles. For a square array of large obstacles, the active particle only locks to the x, y, and 45^{∘} directions, while for smaller obstacles, the number of locking angles increases. Each locking angle satisfies θ=arctan(p/q), where p and q are integers, and the angle of motion can be measured using the ratio of the velocities or the velocity distributions in the x and y directions. When a biasing driving force is applied, the directional locking behavior is affected by the ratio of the self-propulsion force to the biasing force. For large biasing, the behavior resembles that found for directional locking in passive systems. For large obstacles under biased driving, a trapping behavior occurs that is nonmonotonic as a function of increasing run length or increasing self-propulsion force, and the trapping diminishes when the run length is sufficiently large.

Translational and rotational dynamics of a self-propelled Janus probe in crowded environments

We computationally investigate the dynamics of a self-propelled Janus probe in crowded environments. The crowding is caused by the presence of viscoelastic polymers or non-viscoelastic disconnected monomers. Our simulations show that the translational as well as rotational mean square displacements have a distinctive three-step growth for fixed values of self-propulsion force, and steadily increase with self-propulsion, irrespective of the nature of the crowder. On the other hand, in the absence of crowders, the rotational dynamics of the Janus probe is independent of self-propulsion force. On replacing the repulsive polymers with sticky ones, translational and rotational mean square displacements of the Janus probe show a sharp drop. Since different faces of a Janus particle interact differently with the environment, we show that the direction of self-propulsion also affects its dynamics. The ratio of long-time translational and rotational diffusivities of the self-propelled probe with a fixed self-propulsion, when plotted against the area fraction of the crowders, passes through a minimum and at higher area fraction merges to its value in the absence of the crowder. This points towards the decoupling of the translational and rotational dynamics of the self-propelled probe at an intermediate area fraction of the crowders. However, such translational-rotational decoupling is absent for passive probes.

3D aggregation of cells in packed microgel media

In both natural and applied contexts, investigating cell self-assembly and aggregation within controlled 3D environments leads to improved understanding of how structured cell assemblies emerge, what determines their shapes and sizes, and whether their structural features are stable. However, the inherent limits of using solid scaffolding or liquid spheroid culture for this purpose restrict experimental freedom in studies of cell self-assembly. Here we investigate multi-cellular self-assembly using a 3D culture medium made from packed microgels as a bridge between the extremes of solid scaffolds and liquid culture. We find that cells dispersed at different volume fractions in this microgel-based 3D culture media aggregate into clusters of different sizes and shapes, forming large system-spanning networks at the highest cell densities. We find that the transitions between different states of assembly can be controlled by the level of cell-cell cohesion and by the yield stress of the packed microgel environment. Measurements of aggregate fractal dimension show that those with increased cell-cell cohesion are less sphere-like and more irregularly shaped, indicating that cell stickiness inhibits rearrangements in aggregates, in analogy to the assembly of colloids with strong cohesive bonds. Thus, the effective surface tension often expected to emerge from increased cell cohesion is suppressed in this type of cell self-assembly.

Pinning dislocations in colloidal crystals with active particles that seek stacking faults

There is growing interest in functional, adaptive devices built from colloidal subunits of micron size or smaller. A colloidal material with dynamic mechanical properties could facilitate such microrobotic machines. Here we study via computer simulation how active interstitial particles in small quantities can be used to modify the bulk mechanical properties of a colloidal crystal. Passive interstitial particles are known to pin dislocations in metals, thereby increasing resistance to plastic deformation. We extend this tactic by employing anisotropic active interstitials that travel super-diffusively and bind strongly to stacking faults associated with partial dislocations. We find that: (1) interstitials that are effective at reducing plasticity compromise between strong binding to stacking faults and high mobility in the crystal bulk. (2) Reorientation of active interstitials in the crystal depends upon rotational transitions between high-symmetry crystal directions. (3) The addition of certain active interstitial shapes at concentrations as low as 60 per million host particles (0.006%) can create a shear threshold for dislocation migration. This work demonstrates how active materials in a dense matrix can locally sense their environment and lead to bulk property changes.