Bacterial active matter

Active nematics in corrugated channels

Active nematic fluids exhibit complex dynamics in both bulk and in simple confining geometries. However, complex confining geometries could have substantial impact on active spontaneous flows. Using multiparticle collision dynamics simulations adapted for active nematic particles, we study the dynamic behaviour of an active nematic fluid confined in a corrugated channel. The transition from a quiescent state to a spontaneous flow state occurs from a weak swirling flow to a strong coherent flow due to the presence of curved-wall induced active flows. We show that the active nematic fluid flows in corrugated channels can be understood in two different ways: (i) as the result of an early or delayed flow transition when compared with that in a flat-walled channel of appropriate width and (ii) boundary-induced active flows in the corrugations providing an effective slip velocity to the coherent flows in the bulk. Thus, our work illustrates the crucial role of corrugations of the confining boundary in dictating the flow transition and flow states of active fluids.

Where physics and biology meet

As part of this special issue on physics and biology, we invited several leading experts that bridge these disciplines to provide their views on the reciprocal contributions of each field and the benefits and challenges of working across physics and biology: introduction provided by Wallace Marshall.

Controlled stigmergy in quasi-one-dimensional active particle systems

In quasi-one-dimensional circularly symmetric systems of active particles, experiments and simulations reveal an indirect interplay between particles and environmental drag effects, proving crucial in the realm of generalized parametrically controlled stigmergy. Our investigation goes deeper into understanding how stigmergy manifests itself, closely examining unconventional, more physically grounded interpretations in contrast to established concepts. Deeper insights into the complex dynamics of stigmergically interacting particle systems are gained by systematically studying the transition regions between short- and long-term stigmergic effects. Mechanical and computational modeling techniques complement each other to provide a comprehensive understanding of various clustering patterns, oscillatory modes, and system dynamics, where hysteresis may occur depending on the conditions.

Emergence of bacterial glass

Densely packed, motile bacteria can adopt collective states not seen in conventional, passive materials. These states remain in many ways mysterious, and their physical characterization can aid our understanding of natural bacterial colonies and biofilms as well as materials in general. Here, we overcome challenges associated with generating uniformly growing, large, quasi-two-dimensional bacterial assemblies by a membrane-based microfluidic device and report the emergence of glassy states in two-dimensional suspension of Escherichia coli. As the number density increases by cell growth, populations of motile bacteria transition to a glassy state, where cells are packed and unable to move. This takes place in two steps, the first one suppressing only the orientational modes and the second one vitrifying the motion completely. Characterizing each phase through statistical analyses and investigations of individual motion of bacteria, we find not only characteristic features of glass such as rapid slowdown, dynamic heterogeneity, and cage effects, but also a few properties distinguished from those of thermal glass. These distinctive properties include the spontaneous formation of micro-domains of aligned cells with collective motion, the appearance of an unusual signal in the dynamic susceptibility, and the dynamic slowdown with a density dependence generally forbidden for thermal systems. Our results are expected to capture general characteristics of such active rod glass, which may serve as a physical mechanism underlying dense bacterial aggregates.

Harnessing density to control the duration of intermittent Lévy walks in bacterial turbulence

Dense bacterial suspensions display collective motion exhibiting coherent flow structures reminiscent of turbulent flows. However, in contrast to inertial turbulence, the microscopic dynamics underlying bacterial turbulence is only beginning to be understood. Here, we report experiments revealing correlations between microscopic dynamics and the emergence of collective motion in bacterial suspensions. Our results demonstrate the existence of three microscopic dynamical regimes: initial ballistic dynamics followed by an intermittent Lévy walk before the intriguing decay to random Gaussian fluctuations. Our experiments capture that the fluid correlation time earmarks the transition from Lévy to Gaussian fluctuations demonstrating the microscopic reason underlying the observation. By harnessing the flow activity via bacterial concentration, we reveal systematic control over the flow correlation timescales, which, in turn, allows controlling the duration of the Lévy walk.

Microswimmers Knead Nematics into Cholesterics

The hydrodynamic stresses created by active particles can destabilize orientational order present in the system. This is manifested, for example, by the appearance of a bend instability in active nematics or in quasi-two-dimensional living liquid crystals consisting of swimming bacteria in thin nematic films. Using large-scale hydrodynamics simulations, we study a system consisting of spherical microswimmers within a three-dimensional nematic liquid crystal. We observe a spontaneous chiral symmetry breaking, where the uniform nematic state is kneaded into a continuously twisting state, corresponding to a helical director configuration akin to a cholesteric liquid crystal. The transition arises from the hydrodynamic coupling between the liquid crystalline elasticity and the swimmer flow fields, leading to a twist-bend instability of the nematic order. It is observed for both pusher (extensile) and puller (contractile) swimmers. Further, we show that the liquid crystal director and particle trajectories are connected: in the cholesteric state the particle trajectories become helicoidal.

Topological defects in multi-layered swarming bacteria

Topological defects, which are singular points in a director field, play a major role in shaping active systems. Here, we experimentally study topological defects and the flow patterns around them, that are formed during the highly rapid dynamics of swarming bacteria. The results are compared to the predictions of two-dimensional active nematics. We show that, even though some of the assumptions underlying the theory do not hold, the swarm dynamics is in agreement with two-dimensional nematic theory. In particular, we look into the multi-layered structure of the swarm, which is an important feature of real, natural colonies, and find a strong coupling between layers. Our results suggest that the defect-charge density is hyperuniform, i.e., that long range density-fluctuations are suppressed.

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.

Novel turbulence and coarsening arrest in active-scalar fluids

We uncover a new type of turbulence - activity-induced homogeneous and isotropic turbulence - in a model that has been employed to investigate motility-induced phase separation (MIPS) in a system of microswimmers. The active Cahn-Hilliard-Navier-Stokes (CHNS) equations, also called active model H, provide a natural theoretical framework for our study. In this CHNS model, a single scalar order parameter ϕ, positive (negative) in regions of high (low) microswimmer density, is coupled with the velocity field u. The activity of the microswimmers is governed by an activity parameter ζ that is positive for extensile swimmers and negative for contractile swimmers. With extensile swimmers, this system undergoes complete phase separation, which is similar to that in binary-fluid mixtures. By carrying out pseudospectral direct numerical simulations (DNSs), we show, for the first time, that (a) this model develops an emergent nonequilibrium, but statistically steady, state (NESS) of active turbulence, for the case of contractile swimmers, if ζ is sufficiently large and negative, and (b) this turbulence arrests the phase separation. We quantify this suppression by showing how the coarsening-arrest length scale does not grow indefinitely, with time t, but saturates at a finite value at large times. We characterise the statistical properties of this active-scalar turbulence by employing energy spectra and fluxes and the spectrum of ϕ. For sufficiently high Reynolds numbers, the energy spectrum (k) displays an inertial range, with a power-law dependence on the wavenumber k. We demonstrate that, in this range, the flux Π(k) assumes a nearly constant, negative value, which indicates that the system shows an inverse cascade of energy, even though energy injection occurs over a wide range of wavenumbers in our active-CHNS model.

The motion of micro-swimmers over a cavity in a micro-channel

This article combines the lattice Boltzmann method (LBM) with the squirmer model to investigate the motion of micro-swimmers in a channel-cavity system. The study analyses various influential factors, including the value of the squirmer-type factor (β), the swimming Reynolds number (Rep), the size of the cavity, initial position and particle size on the movement of micro-swimmers within the channel-cavity system. We simultaneously studied three types of squirmer models, Puller (β > 0), Pusher (β < 0), and Neutral (β = 0) swimmers. The findings reveal that the motion of micro-swimmers is determined by the value of β and Rep, which can be classified into six distinct motion modes. For Puller and Pusher, when the β value is constant, an increase in Rep will lead to transition in the motion mode. Moreover, the appropriate depth of cavity within the channel-cavity system plays a crucial role in capturing and separating Neutral swimmers. This study, for the first time, explores the effect of complex channel-cavity systems on the behaviour of micro-swimmers and highlights their separation and capture ability. These findings offer novel insights for the design and enhancement of micro-channel structures in achieving efficient separation and capture of micro-swimmers.

Self-enhanced mobility enables vortex pattern formation in living matter

Ranging from subcellular organelle biogenesis to embryo development, the formation of self-organized structures is a hallmark of living systems. Whereas the emergence of ordered spatial patterns in biology is often driven by intricate chemical signalling that coordinates cellular behaviour and differentiation1-4, purely physical interactions can drive the formation of regular biological patterns such as crystalline vortex arrays in suspensions of spermatozoa5 and bacteria6. Here we discovered a new route to self-organized pattern formation driven by physical interactions, which creates large-scale regular spatial structures with multiscale ordering. Specifically we found that dense bacterial living matter spontaneously developed a lattice of mesoscale, fast-spinning vortices; these vortices each consisted of around 104-105 motile bacterial cells and were arranged in space at greater than centimetre scale and with apparent hexagonal order, whereas individual cells in the vortices moved in coordinated directions with strong polar and vortical order. Single-cell tracking and numerical simulations suggest that the phenomenon is enabled by self-enhanced mobility in the system-that is, the speed of individual cells increasing with cell-generated collective stresses at a given cell density. Stress-induced mobility enhancement and fluidization is prevalent in dense living matter at various scales of length7-9. Our findings demonstrate that self-enhanced mobility offers a simple physical mechanism for pattern formation in living systems and, more generally, in other active matter systems10 near the boundary of fluid- and solid-like behaviours11-17.

Phase behaviour and dynamics of three-dimensional active dumbbell systems

We present a comprehensive numerical study of the phase behavior and dynamics of a three-dimensional active dumbbell system with attractive interactions. We demonstrate that attraction is essential for the system to exhibit nontrivial phases. We construct a detailed phase diagram by exploring the effects of the system's activity, density, and attraction strength. We identify several distinct phases, including a disordered, a gel, and a completely phase-separated phase. Additionally, we discover a novel dynamical phase, that we name percolating network, which is characterized by the presence of a spanning network of connected dumbbells. In the phase-separated phase we characterize numerically and describe analytically the helical motion of the dense cluster.

Nonequilibrium structure formation in electrohydrodynamic emulsions

Application of an electric field across the interface of two fluids with low, but non-zero, conductivities gives rise to a sustained electrohydrodynamic (EHD) fluid flow. In the presence of neighboring drops, drops interact via the EHD flows of their neighbors, as well as through a dielectrophoretic (DEP) force, a consequence of drops encountering disturbance electric fields around their neighbors. We explore the collective dynamics of emulsions with drops undergoing EHD and DEP interactions. The interplay between EHD and DEP results in a rich set of emergent behaviors. We simulate the collective behavior of large numbers of drops; in two dimensions, where drops are confined to a plane; and three dimensions. In monodisperse emulsions, drops in two dimensions cluster or crystallize depending on the relative strengths of EHD and DEP, and form spaced clusters when EHD and DEP balance. In three dimensions, chain formation observed under DEP alone is suppressed by EHD, and lost entirely when EHD dominates. When a second population of drops are introduced, such that the electrical conductivity, permittivity, or viscosity are different from the first population of drops, the interaction between the drops becomes non-reciprocal, an apparent violation of Newton's Third Law. The breadth of consequences due to these non-reciprocal interactions are vast: we show selected cases in two dimensions, where drops cluster into active dimers, trimers, and larger clusters that continue to translate and rotate over long timescales; and three dimensions, where drops form stratified chains, or combine into a single dynamic sheet.

Motility-Induced Phase Separation Mediated by Bacterial Quorum Sensing

We study motility-induced phase separation (MIPS) in living active matter, in which cells interact through chemical signaling, or quorum sensing. In contrast to previous theories of MIPS, our multiscale continuum model accounts explicitly for genetic regulation of signal production and motility. Through analysis and simulations, we derive a new criterion for the onset of MIPS that depends on features of the genetic network. Furthermore, we identify and characterize a new type of oscillatory instability that occurs when gene regulation inside cells promotes motility in higher signal concentrations.

Shape-Tension Coupling Produces Nematic Order in an Epithelium Vertex Model

We study the vertex model for epithelial tissue mechanics extended to include coupling between the cell shapes and tensions in cell-cell junctions. This coupling represents an active force which drives the system out of equilibrium and leads to the formation of nematic order interspersed with prominent, long-lived +1 defects. The defects in the nematic ordering are coupled to the shape of the cell tiling, affecting cell areas and coordinations. This intricate interplay between cell shape, size, and coordination provides a possible mechanism by which tissues could spontaneously develop long-range polarity through local mechanical forces without resorting to long-range chemical patterning.

50-year history and perspective on biomechanics of swimming microorganisms: Part II. Collective behaviours

The paired review papers in Parts I and II describe the 50-year history of research on the biomechanics of swimming microorganisms and its prospects in the next 50 years. Parts I and II are divided not by the period covered, but by the content of the research: Part I explains the behaviours of individual microorganisms, and Part II explains collective behaviour. In the 1990s, the description of microbial suspensions as a continuum progressed, and macroscopic flow structures such as bioconvection were analysed. The continuum model was later extended to analyse various phenomena such as flow induced trapping of microorganisms and accumulation of cells at interfaces. In the 2000s, the collective behaviour of swimming microorganisms came into the limelight, and physicists as well as biomechanics researchers carried out many studies probing microorganism collectivity. In particular, research on the turbulence-like flow structure of dense bacterial suspensions has led to dramatic developments in the field of microbial biomechanics. Efforts to bridge the cellular scale to the macroscopic scale by extracting macroscopic physical quantities from the microstructure of cell suspensions are also underway. This Part II reviews these collective behaviours of swimming microorganisms and discusses future prospects of the field.

Viscoelasticity enhances collective motion of bacteria

Bacteria form human and animal microbiota. They are the leading causes of many infections and constitute an important class of active matter. Concentrated bacterial suspensions exhibit large-scale turbulent-like locomotion and swarming. While the collective behavior of bacteria in Newtonian fluids is relatively well understood, many fundamental questions remain open for complex fluids. Here, we report on the collective bacterial motion in a representative biological non-Newtonian viscoelastic environment exemplified by mucus. Experiments are performed with synthetic porcine gastric mucus, natural cow cervical mucus, and a Newtonian-like polymer solution. We have found that an increase in mucin concentration and, correspondingly, an increase in the suspension's elasticity monotonously increases the length scale of collective bacterial locomotion. On the contrary, this length remains practically unchanged in Newtonian polymer solution in a wide range of concentrations. The experimental observations are supported by computational modeling. Our results provide insight into how viscoelasticity affects the spatiotemporal organization of bacterial active matter. They also expand our understanding of bacterial colonization of mucosal surfaces and the onset of antibiotic resistance due to swarming.

Liquid Crystalline Systems from Nature and Interaction of Living Organisms with Liquid Crystals

Biomaterials, which are substances interacting with biological systems, have been extensively explored to understand living organisms and obtain scientific inspiration (such as biomimetics). However, many aspects of biomaterials have yet to be fully understood. Because liquid crystalline phases are ubiquitously found in biomaterials (e.g., cholesterol, amphiphile, DNA, cellulose, bacteria), therefore, a wide range of research has made attempts to approach unresolved issues with the concept of liquid crystals (LCs). This review presents these studies that address the interactive correlation between biomaterials and LCs. Specifically, intrinsic LC behavior of various biomaterials such as DNA, cellulose nanocrystals, and bacteriaare first introduced. Second, the dynamics of bacteria in LC media are addressed, with focus on how bacteria interact with LCs, and how dynamics of bacteria can be controlled by exploiting the characteristics of LCs. Lastly, how the strong correlation between LCs and biomaterials has been leveraged to design a new class of biosensors with additional functionalities (e.g., self-regulated drug release) that are not available in previous systems is reviewed. Examples addressed in this review convey the message that the intersection between biomaterials and LCs offers deep insights into fundamental understanding of biomaterials, and provides resources for development of transformative technologies.

Multi-scale organization in communicating active matter

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

Tubulation and dispersion of oil by bacterial growth on droplets

Bacteria on surfaces exhibit collective behaviors, such as active turbulence and active stresses, which result from their motility, growth, and interactions with their local surroundings. However, interfacial deformations on soft surfaces and liquid interfaces caused by active growth, particularly over long time scales, are not well understood. Here, we describe experimental observations on the emergence of tubular structures arising from the growth of rod-shaped bacteria at the interface of oil droplets in water. Using microfluidics and timelapse microscopy, the dimensions and extension rates of individual tubular structures as well as bulk bio-aggregate formation are quantified for hundreds of droplets over 72 hours. Tubular structures are comparable in length to the initial droplet radius and are composed of an outer shell of bacteria that stabilize an inner filament of oil. The oil filament breaks up into smaller microdroplets dispersed within the bacterial shell. This work provides insight into active stresses at deformable interfaces and improves our understanding of microbial oil biodegradation and its potential influence on the transport of droplets in the ocean water column.

Motion of a swimming droplet under external perturbations: A model-based approach

Microdroplets driven by the Marangoni effect are known to continue to swim for hours despite their simple composition. This swimming microdroplet changes its motion from straight to curvilinear and further to chaotic as the Péclet number increases. In this study, we investigate the effect of external perturbations on the three-dimensional axis-asymmetric model of a droplet driven by the Marangoni effect. The aim here is to elucidate the contribution of external perturbation to the complex motion of the droplet and the change in its effect according to the droplet size. In this paper, first we provide a detailed explanation on the derivation of the model introduced in our previous work, which is next used to describe the motion of the droplet in the numerical study of the angular response to random perturbations. The numerical simulation of droplet motion with different types of noise indicates that the model does not converge them into a certain type of motion but rather helps to reflect the external perturbations. The obtained results suggest that the types and properties of external perturbation have a considerable effect on the droplet motion.