On torque and tumbling in swimming Escherichia coli

Interfacial Stresses within Droplets and Channels Influence Bacterial Physiology: A Perspective

Bacterial cells frequently experience fluid motion in their natural environments, like water bodies, aerosols, fomites, human capillaries, etc., a phenomenon that researchers have largely overlooked. Nevertheless, some reports have suggested that the interfacial stresses caused by fluid motion inside evaporating droplets or shear flows within capillaries may trigger physiological and morphological changes in the bacterial cells. Remarkably, the virulence of bacterial cells exhibits significant alterations in response to fluctuations in stress levels and external environmental factors. The dynamics of bacterial systems are analogous to colloidal systems but with the distinction that bacterial systems exhibit responsiveness, necessitating thorough exploration in dynamic environments. In this perspective, we discuss the important issue pertaining to bacterial survival, virulence, and disease transmission. Furthermore, we delineate a pathway and underscore emerging opportunities that demand exploration to unveil new avenues in the domains of bacterial pathogenicity, drug development, and strategies for disease mitigation.

Collective behavior of squirmers in thin films

Bacteria in biofilms form complex structures and can collectively migrate within mobile aggregates, which is referred to as swarming. This behavior is influenced by a combination of various factors, including morphological characteristics and propulsive forces of swimmers, their volume fraction within a confined environment, and hydrodynamic and steric interactions between them. In our study, we employ the squirmer model for microswimmers and the dissipative particle dynamics method for fluid modeling to investigate the collective motion of swimmers in thin films. The film thickness permits a free orientation of non-spherical squirmers, but constraints them to form a two-layered structure at maximum. Structural and dynamic properties of squirmer suspensions confined within the slit are analyzed for different volume fractions of swimmers, motility types (e.g., pusher, neutral squirmer, puller), and the presence of a rotlet dipolar flow field, which mimics the counter-rotating flow generated by flagellated bacteria. Different states are characterized, including a gas-like phase, swarming, and motility-induced phase separation, as a function of increasing volume fraction. Our study highlights the importance of an anisotropic swimmer shape, hydrodynamic interactions between squirmers, and their interaction with the walls for the emergence of different collective behaviors. Interestingly, the formation of collective structures may not be symmetric with respect to the two walls. Furthermore, the presence of a rotlet dipole significantly mitigates differences in the collective behavior between various swimmer types. These results contribute to a better understanding of the formation of bacterial biofilms and the emergence of collective states in confined active matter.

Reassessing the Standard Chemotaxis Framework for Understanding Biased Migration in Helicobacter pylori

Helicobacter pylori infections are a major cause of peptic ulcers and gastric cancers. The development of robust inflammation in response to these flagellated, motile bacteria is correlated with poor prognosis. Chemotaxis plays a crucial role in H. pylori colonization, enabling the bacteria to swim toward favorable chemical environments. Unlike the model species of bacterial chemotaxis, Escherichia coli, H. pylori cells possess polar flagella. They run forward by rotating their flagella counterclockwise, whereas backward runs are achieved by rotating their flagella clockwise. We delve into the implications of certain features of the canonical model of chemotaxis on our understanding of biased migration in polarly flagellated bacteria such as H. pylori. In particular, we predict how the translational displacement of H. pylori cells during a backward run could give rise to chemotaxis errors within the canonical framework. Also, H. pylori lack key chemotaxis enzymes found in E. coli, without which sensitive detection of ligands with a wide dynamic range seems unlikely. Despite these problems, H. pylori exhibit robust ability to migrate toward urea-rich sources. We emphasize various unresolved questions regarding the biophysical mechanisms of chemotaxis in H. pylori, shedding light on potential directions for future research. Understanding the intricacies of biased migration in H. pylori could offer valuable insights into how pathogens breach various protective barriers in the human host.

Bacterial motility depends on a critical flagellum length and energy-optimised assembly

The flagellum is the most complex macromolecular structure known in bacteria and comprised of around two dozen distinct proteins. The main building block of the long, external flagellar filament, flagellin, is secreted through the flagellar type-III secretion system at a remarkable rate of several tens of thousands amino acids per second, significantly surpassing the rates achieved by other pore-based protein secretion systems. The evolutionary implications and potential benefits of this high secretion rate for flagellum assembly and function, however, have remained elusive. In this study, we provide both experimental and theoretical evidence that the flagellar secretion rate has been evolutionarily optimized to facilitate rapid and efficient construction of a functional flagellum. By synchronizing flagellar assembly, we found that a minimal filament length of 2.5 µm was required for swimming motility. Biophysical modelling revealed that this minimal filament length threshold resulted from an elasto-hydrodynamic instability of the whole swimming cell, dependent on the filament length. Furthermore, we developed a stepwise filament labeling method combined with electron microscopy visualization to validate predicted flagellin secretion rates of up to 10,000 amino acids per second. A biophysical model of flagellum growth demonstrates that the observed high flagellin secretion rate efficiently balances filament elongation and energy consumption, thereby enabling motility in the shortest amount of time. Taken together, these insights underscore the evolutionary pressures that have shaped the development and optimization of the flagellum and type-III secretion system, illuminating the intricate interplay between functionality and efficiency in assembly of large macromolecular structures.

Significance statement

Our study demonstrates how protein secretion of the bacterial flagellum is finely tuned to optimize filament assembly rate and flagellum function while minimizing energy consumption. By measuring flagellar filament lengths and bacterial swimming after initiation of flag-ellum assembly, we were able to establish the minimal filament length necessary for swimming motility, which we rationalized physically as resulting from an elasto-hydrodynamic instability of the swimming cell. Our bio-physical model of flagellum growth further illustrates how the physiological flagellin secretion rate is optimized to maximize filament elongation while conserving energy. These findings illuminate the evolutionary pressures that have shaped the function of the bacterial flagellum and type-III secretion system, driving improvements in bacterial motility and overall fitness.

Speed-dependent bacterial surface swimming

Solid surfaces submerged in liquid in natural environments alter bacterial swimming behavior and serve as platforms for bacteria to form biofilms. In the initial stage of biofilm formation, bacteria detect surfaces and increase the intracellular level of the second messenger c-di-GMP, leading to a reduction in swimming speed. The impact of this speed reduction on bacterial surface swimming remains unclear. In this study, we utilized advanced microscopy techniques to examine the effect of swimming speed on bacterial surface swimming behavior. We found that a decrease in swimming speed reduces the cell-surface distance and prolongs the surface trapping time. Both these effects would enhance bacterial surface sensing and increase the likelihood of cells adhering to the surface, thereby promoting biofilm formation. We also examined the surface-escaping behavior of wild-type Escherichia coli and Pseudomonas aeruginosa, noting distinct surface-escaping mechanisms between the two bacterial species.

IMPORTANCE

In the early phase of biofilm formation, bacteria identify surfaces and increase the intracellular level of the second messenger c-di-GMP, resulting in a decrease in swimming speed. Here, we utilized advanced microscopy techniques to investigate the impact of swimming speed on bacterial surface swimming, focusing on Escherichia coli and Pseudomonas aeruginosa. We found that an increase in swimming speed led to an increase in the radius of curvature and a decrease in surface detention time. These effects were explained through hydrodynamic modeling as a result of an increase in the cell-surface distance with increasing swimming speed. We also observed distinct surface-escaping mechanisms between the two bacterial species. Our study suggests that a decrease in swimming speed could enhance the likelihood of cells adhering to the surface, promoting biofilm formation. This sheds light on the role of reduced swimming speed in the transition from motile to sedentary bacterial lifestyles.

Thermodynamic Effects Are Essential for Surface Entrapment of Bacteria

The entrapment of bacteria near boundary surfaces is of biological and practical importance, yet the underlying physics is not well understood. We demonstrate that it is crucial to include a commonly neglected thermodynamic effect related to the spatial variation of hydrodynamic interactions, through a model that provides analytic explanation of bacterial entrapment in two dimensionless parameters: α_{1} the ratio of thermal energy to self-propulsion, and α_{2} an intrinsic shape factor. For α_{1} and α_{2} that match an Escherichia coli at room temperature, our model quantitatively reproduces existing experimental observations, including two key features that have not been previously resolved: The bacterial "nose-down" configuration, and the anticorrelation between the pitch angle and the wobbling angle. Furthermore, our model analytically predicts the existence of an entrapment zone in the parameter space defined by {α_{1},α_{2}}.

Run-and-tumble kinematics of Enterobacter Sp. SM3

The recent discovery of the peritrichous, swarm-competent bacterium Enterobacter sp. SM3 has offered a new opportunity to investigate the connection between bacterial swimming and swarming. Here, we report the run-and-tumble behavior of SM3 as planktonic swimming cells and as swarming cells diluted in liquid medium, drawing comparison between the two states. Swimming cells of SM3 run for an average of 0.77 s with a speed of approximately 30µm/s before tumbling. Tumbles last for a duration of 0.12 s on average and cause changes in direction averaging 69^{∘}. Swimming cells exposed to the common chemoattractant serine in bulk solution suppress the frequency of tumbles in the steady state, lengthening the average run duration and decreasing the average tumble angle. When exposed to aspartate, cells do not demonstrate a notable change in run-and-tumble parameters in the steady state. For swarming cells of SM3, the frequency of tumbles is reduced, with the average run duration being 50% longer on average than that of swimming cells in the same liquid medium. Additionally, the average tumble angle of swarming cells is smaller by 35%. These findings reveal that the newly identified species, SM3, performs run-and-tumble motility similar to other species of peritrichous bacteria such as E. coli, both in the swimming and swarming states. We present a simple mechanical model, which provides a physical understanding of the run-and-tumble behavior of peritrichous bacteria.

The swimming defect caused by the absence of the transcriptional regulator LdtR in Sinorhizobium meliloti is restored by mutations in the motility genes motA and motS

The flagellar motor is a powerful macromolecular machine used to propel bacteria through various environments. We determined that flagellar motility of the alpha-proteobacterium Sinorhizobium meliloti is nearly abolished in the absence of the transcriptional regulator LdtR, known to influence peptidoglycan remodeling and stress response. LdtR does not regulate motility gene transcription. Remarkably, the motility defects of the ΔldtR mutant can be restored by secondary mutations in the motility gene motA or a previously uncharacterized gene in the flagellar regulon, which we named motS. MotS is not essential for S. meliloti motility and may serve an accessory role in flagellar motor function. Structural modeling predicts that MotS comprised an N-terminal transmembrane segment, a long-disordered region, and a conserved β-sandwich domain. The C terminus of MotS is localized in the periplasm. Genetics based substitution of MotA with MotAG12S also restored the ΔldtR motility defect. The MotAG12S variant protein features a local polarity shift at the periphery of the MotAB stator units. We propose that MotS may be required for optimal alignment of stators in wild-type flagellar motors but becomes detrimental in cells with altered peptidoglycan. Similarly, the polarity shift in stator units composed of MotB/MotAG12S might stabilize its interaction with altered peptidoglycan.

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.

Bacterial surface swimming states revealed by TIRF microscopy

Motility near solid surfaces plays a key role in the life cycle of bacteria and is essential for biofilm formation, biofilm dispersal, and virulence. The alignment of the cell body with the surface during surface swimming impacts bacterial surface sensing. Here, we developed a high-throughput method for characterizing the orientation of the cell body relative to the surface using total internal reflection fluorescence (TIRF) microscopy. The angle between the cell body and the surface was determined by maximizing image cross-correlations between the TIRF image of the cell and a reference library. Utilizing this technique, we surprisingly identified six distinct surface swimming states of Pseudomonas aeruginosa according to the body alignment and the flagellar position. Furthermore, we observed that the near-surface swimming speed is greater in the pull state than in the push state, attributed to hydrodynamic effects near the liquid-solid interface. Hydrodynamic force analysis of the swimming states provided rich insights into the mechanics of bacterial surface swimming. Our technique is readily applicable to the study of surface motility across a wide spectrum of bacterial species.

Flagellar dynamics reveal fluctuations and kinetic limit in the Escherichia coli chemotaxis network

The Escherichia coli chemotaxis network, by which bacteria modulate their random run/tumble swimming pattern to navigate their environment, must cope with unavoidable number fluctuations ("noise") in its molecular constituents like other signaling networks. The probability of clockwise (CW) flagellar rotation, or CW bias, is a measure of the chemotaxis network's output, and its temporal fluctuations provide a proxy for network noise. Here we quantify fluctuations in the chemotaxis signaling network from the switching statistics of flagella, observed using time-resolved fluorescence microscopy of individual optically trapped E. coli cells. This approach allows noise to be quantified across the dynamic range of the network. Large CW bias fluctuations are revealed at steady state, which may play a critical role in driving flagellar switching and cell tumbling. When the network is stimulated chemically to higher activity, fluctuations dramatically decrease. A stochastic theoretical model, inspired by work on gene expression noise, points to CheY activation occurring in bursts, driving CW bias fluctuations. This model also shows that an intrinsic kinetic ceiling on network activity places an upper limit on activated CheY and CW bias, which when encountered suppresses network fluctuations. This limit may also prevent cells from tumbling unproductively in steep gradients.

The common origin and degenerative evolution of flagella in Actinobacteria

IMPORTANCE

Flagellar motility plays an important role in the environmental adaptation of bacteria and is found in more than 50% of known bacterial species. However, this important characteristic is sparsely distributed within members of the phylum Actinobacteria, which constitutes one of the largest bacterial groups. It is unclear why this important fitness organelle is absent in most actinobacterial species and the origin of flagellar genes in other species. Here, we present detailed analyses of the evolution of flagellar genes in Actinobacteria, in conjunction with the ecological distribution and cell biological features of major actinobacterial lineages, and the co-evolution of signal transduction systems. The results presented in addition to clarifying the puzzle of sporadic distribution of flagellar motility in Actinobacteria, also provide important insights into the evolution of major lineages within this phylum.

Multiflagellarity leads to the size-independent swimming speed of peritrichous bacteria

To swim through a viscous fluid, a flagellated bacterium must overcome the fluid drag on its body by rotating a flagellum or a bundle of multiple flagella. Because the drag increases with the size of bacteria, it is expected theoretically that the swimming speed of a bacterium inversely correlates with its body length. Nevertheless, despite extensive research, the fundamental size-speed relation of flagellated bacteria remains unclear with different experiments reporting conflicting results. Here, by critically reviewing the existing evidence and synergizing our own experiments of large sample sizes, hydrodynamic modeling, and simulations, we demonstrate that the average swimming speed of Escherichia coli, a premier model of peritrichous bacteria, is independent of their body length. Our quantitative analysis shows that such a counterintuitive relation is the consequence of the collective flagellar dynamics dictated by the linear correlation between the body length and the number of flagella of bacteria. Notably, our study reveals how bacteria utilize the increasing number of flagella to regulate the flagellar motor load. The collective load sharing among multiple flagella results in a lower load on each flagellar motor and therefore faster flagellar rotation, which compensates for the higher fluid drag on the longer bodies of bacteria. Without this balancing mechanism, the swimming speed of monotrichous bacteria generically decreases with increasing body length, a feature limiting the size variation of the bacteria. Altogether, our study resolves a long-standing controversy over the size-speed relation of flagellated bacteria and provides insights into the functional benefit of multiflagellarity in bacteria.

Flagellar motors of swimming bacteria contain an incomplete set of stator units to ensure robust motility

Flagellated bacteria, like Escherichia coli, swim by rotating helical flagellar filaments powered by rotary flagellar motors at their base. Motor dynamics are sensitive to the load it drives. It was previously thought that motor load was high when driving filament rotation in free liquid environments. However, torque measurements from swimming bacteria revealed substantially lower values compared to single-motor studies. We addressed this inconsistency through motor resurrection experiments, abruptly attaching a 1-micrometer-diameter bead to the filament to ensure high load. Unexpectedly, we found that the motor works with only half the complement of stator units when driving filament rotation. This suggests that the motor is not under high load during bacterial swimming, which we confirmed by measuring the torque-speed relationship by varying media viscosity. Therefore, the motor operates in an intermediate-load region, adaptively regulating its stator number on the basis of external load conditions. This ensures the robustness of bacterial motility when swimming in diverse load conditions and varying flagella numbers.

Atomic-level architecture of Caulobacter crescentus flagellar filaments provide evidence for multi-flagellin filament stabilization

Flagella are dynamic, ion-powered machines with assembly pathways that are optimized for efficient flagella production. In bacteria, dozens of genes are coordinated at specific times in the cell lifecycle to generate each component of the flagellum. This is the case for Caulobacter crescentus, but little is known about why this species encodes six different flagellin genes. Furthermore, little is known about the benefits multi-flagellin species possess over single flagellin species, if any, or what molecular properties allow for multi-flagellin filaments to assemble. Here we present an in-depth analysis of several single flagellin filaments from C. crescentus, including an extremely well-resolved structure of a bacterial flagellar filament. We highlight key molecular interactions that differ between each bacterial strain and speculate how these interactions may alleviate or impose helical strain on the overall architecture of the filament. We detail conserved residues within the flagellin subunit that allow for the synthesis of multi-flagellin filaments. We further comment on how these molecular differences impact bacterial motility and highlight how no single flagellin filament achieves wild-type levels of motility, suggesting C. crescentus has evolved to produce a filament optimized for motility comprised of six flagellins. Finally, we highlight an ordered arrangement of glycosylation sites on the surface of the filaments and speculate how these sites may protect the β-hairpin located on the surface exposed domain of the flagellin subunit.

Field-Controlled Microrobots Fabricated by Photopolymerization

Field-controlled microrobots have attracted extensive research in the biological and medical fields due to the prominent characteristics including high flexibility, small size, strong controllability, remote manipulation, and minimal damage to living organisms. However, the fabrication of these field-controlled microrobots with complex and high-precision 2- or 3-dimensional structures remains challenging. The photopolymerization technology is often chosen to fabricate field-controlled microrobots due to its fast-printing velocity, high accuracy, and high surface quality. This review categorizes the photopolymerization technologies utilized in the fabrication of field-controlled microrobots into stereolithography, digital light processing, and 2-photon polymerization. Furthermore, the photopolymerized microrobots actuated by different field forces and their functions are introduced. Finally, we conclude the future development and potential applications of photopolymerization for the fabrication of field-controlled microrobots.

Mechanobiology as a tool for addressing the genotype-to-phenotype problem in microbiology

The central hypothesis of the genotype-phenotype relationship is that the phenotype of a developing organism (i.e., its set of observable attributes) depends on its genome and the environment. However, as we learn more about the genetics and biochemistry of living systems, our understanding does not fully extend to the complex multiscale nature of how cells move, interact, and organize; this gap in understanding is referred to as the genotype-to-phenotype problem. The physics of soft matter sets the background on which living organisms evolved, and the cell environment is a strong determinant of cell phenotype. This inevitably leads to challenges as the full function of many genes, and the diversity of cellular behaviors cannot be assessed without wide screens of environmental conditions. Cellular mechanobiology is an emerging field that provides methodologies to understand how cells integrate chemical and physical environmental stress and signals, and how they are transduced to control cell function. Biofilm forming bacteria represent an attractive model because they are fast growing, genetically malleable and can display sophisticated self-organizing developmental behaviors similar to those found in higher organisms. Here, we propose mechanobiology as a new area of study in prokaryotic systems and describe its potential for unveiling new links between an organism's genome and phenome.

Decoding the hydrodynamic properties of microscale helical propellers from Brownian fluctuations

The complex motility of bacteria, ranging from single-swimmer behaviors such as chemotaxis to collective dynamics, including biofilm formation and active matter phenomena, is driven by their microscale propellers. Despite extensive study of swimming flagellated bacteria, the hydrodynamic properties of their helical-shaped propellers have never been directly measured. The primary challenges to directly studying microscale propellers are 1) their small size and fast, correlated motion, 2) the necessity of controlling fluid flow at the microscale, and 3) isolating the influence of a single propeller from a propeller bundle. To solve the outstanding problem of characterizing the hydrodynamic properties of these propellers, we adopt a dual statistical viewpoint that connects to the hydrodynamics through the fluctuation-dissipation theorem (FDT). We regard the propellers as colloidal particles and characterize their Brownian fluctuations, described by 21 diffusion coefficients for translation, rotation, and correlated translation-rotation in a static fluid. To perform this measurement, we applied recent advances in high-resolution oblique plane microscopy to generate high-speed volumetric movies of fluorophore-labeled, freely diffusing Escherichia coli flagella. Analyzing these movies with a bespoke helical single-particle tracking algorithm, we extracted trajectories, calculated the full set of diffusion coefficients, and inferred the average propulsion matrix using a generalized Einstein relation. Our results provide a direct measurement of a microhelix's propulsion matrix and validate proposals that the flagella are highly inefficient propellers, with a maximum propulsion efficiency of less than 3%. Our approach opens broad avenues for studying the motility of particles in complex environments where direct hydrodynamic approaches are not feasible.

Bacteria-inspired robotic propulsion from bundling of soft helical filaments at low Reynolds number

The bundling of flagella is known to create a "run" phase, where the bacteria moves in a nearly straight line rather than making changes in direction. Historically, mechanical explanations for the bundling phenomenon intrigued many researchers, and significant advances were made in physical models and experimental methods. Contributing to the field of research, we present a bacteria-inspired centimeter-scale soft robotic hardware platform and a computational framework for a physically plausible simulation model of the multi-flagellated robot under low Reynolds number (∼10^-1). The fluid-structure interaction simulation couples the discrete elastic rods algorithm with the method of regularized Stokeslet segments. Contact between two flagella is handled by a penalty-based method. We present a comparison between our experimental and simulation results and verify that the simulation tool can capture the essential physics of this problem. Preliminary findings on robustness to buckling provided by the bundling phenomenon and the efficiency of a multi-flagellated soft robot are compared with the single-flagellated counterparts. Observations were made on the coupling between geometry and elasticity, which manifests itself in the propulsion of the robot by nonlinear dependency on the rotational speed of the flagella.

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.

Frustrated 'run and tumble' of swimming Escherichia coli bacteria in nematic liquid crystals

In many situations, bacteria move in complex environments, as soils, oceans or the human gut-track, where carrier fluids show complex structures associated with non-Newtonian rheology. Many fundamental questions concerning the ability to navigate in such environments remain unsolved. Recently, it has been shown that the kinetics of bacterial motion in structured fluids as liquid crystals (LCs) is constrained by the orientational molecular order (or director field) and that novel spatio-temporal patterns arise. A question unaddressed so far is how bacteria change swimming direction in such an environment. In this work, we study the swimming mechanism of a single bacterium, Esherichia coli, constrained to move along the director field of a lyotropic chromonic liquid crystal confined to a planar cell. Here, the spontaneous 'run and tumble' motion of the bacterium gets frustrated: the elasticity of the LC prevents flagella from unbundling. Interestingly, to change direction, bacteria execute a reversal motion along the director field, driven by the relocation of a single flagellum, a 'frustrated tumble'. We characterize this phenomenon in detail experimentally, exploiting exceptional spatial and temporal resolution of bacterial and flagellar dynamics, using a two colour Lagrangian tracking technique. We suggest a possible mechanism accounting for these observations.

Individual-Based Modeling of Spatial Dynamics of Chemotactic Microbial Populations

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

Convergent evolution in the supercoiling of prokaryotic flagellar filaments

The supercoiling of bacterial and archaeal flagellar filaments is required for motility. Archaeal flagellar filaments have no homology to their bacterial counterparts and are instead homologs of bacterial type IV pili. How these prokaryotic flagellar filaments, each composed of thousands of copies of identical subunits, can form stable supercoils under torsional stress is a fascinating puzzle for which structural insights have been elusive. Advances in cryoelectron microscopy (cryo-EM) make it now possible to directly visualize the basis for supercoiling, and here, we show the atomic structures of supercoiled bacterial and archaeal flagellar filaments. For the bacterial flagellar filament, we identify 11 distinct protofilament conformations with three broad classes of inter-protomer interface. For the archaeal flagellar filament, 10 protofilaments form a supercoil geometry supported by 10 distinct conformations, with one inter-protomer discontinuity creating a seam inside of the curve. Our results suggest that convergent evolution has yielded stable superhelical geometries that enable microbial locomotion.

Kinematics of persistent random walkers with two distinct modes of motion

We study the stochastic motion of active particles that undergo spontaneous transitions between two distinct modes of motion. Each mode is characterized by a velocity distribution and an arbitrary (anti)persistence. We present an analytical formalism to provide a quantitative link between these two microscopic statistical properties of the trajectory and macroscopically observable transport quantities of interest. For exponentially distributed residence times in each state, we derive analytical expressions for the initial anomalous exponent, the characteristic crossover time to the asymptotic diffusive dynamics, and the long-term diffusion constant. We also obtain an exact expression for the time evolution of the mean square displacement over all timescales and provide a recipe to obtain higher displacement moments. Our approach enables us to disentangle the combined effects of velocity, persistence, and switching probabilities between the two states on the kinematics of particles in a wide range of stochastic active or passive processes and to optimize the transport quantities of interest with respect to any of the particle dynamics properties.

Experimental determination of the propulsion matrix of the body of helical Magnetospirillum magneticum cells

Helical-shaped magnetotactic bacteria provide a rare opportunity to precisely measure both the translational and rotational friction coefficients of micron-sized chiral particles. The possibility to align these cells with a uniform magnetic field allows clearly separating diffusion along and perpendicular to their longitudinal axis. Meanwhile, their corkscrew shape allows detecting rotations around their longitudinal axis, after which orientation correlation analysis can be used to retrieve rotational diffusion coefficients in the two principal directions. Using light microscopy, we measured the four principal friction coefficients of deflagellated Magnetospirillum magneticum cells, and compared our results to that expected for cylinders of comparable size. We show that for rotational motions, the overall dimensions of the cell body are what matters most, while the exact body shape has a larger influence on translational motions. To obtain a full characterization of the friction matrix of these elongated chiral particles, we also quantified the coupling between the rotation around and translation along the longitudinal axis of the cell. Our results suggest that for this bacterial species cell body rotation could significantly contribute to cellular propulsion.

Fluid-driven bacterial accumulation in proximity of laser-textured surfaces

In this work we investigated the role of fluid in the initial phase of bacterial adhesion on textured surfaces, focusing onto the approach of the bacterial cells towards the surface. In particular, stainless steel surfaces textured via femtosecond laser interaction have been considered. The method combined a simulation routine, based on the numerical solution of Navier-Stokes equations, and the use of a theoretical model, based on the Smoluchowski's equation. Results highlighted a slowdown of the fluid velocity field in correspondence of the surface dales. In addition, a shear induced accumulation on the top of the surface protrusions was predicted for motile bacterial species, E. coli. In particular, we observed a role of the surface protrusions in increasing the range over which motile bacterial species are attracted towards the surface through a rheotactic mechanism. In other words, we found that, in certain conditions of fluid flow and textured surface morphology, surface protrusions act as a sort of "rheotactic antennas".

Wrapped Up: The Motility of Polarly Flagellated Bacteria

A huge number of bacterial species are motile by flagella, which allow them to actively move toward favorable environments and away from hazardous areas and to conquer new habitats. The general perception of flagellum-mediated movement and chemotaxis is dominated by the Escherichia coli paradigm, with its peritrichous flagellation and its famous run-and-tumble navigation pattern, which has shaped the view on how bacteria swim and navigate in chemical gradients. However, a significant amount-more likely the majority-of bacterial species exhibit a (bi)polar flagellar localization pattern instead of lateral flagella. Accordingly, these species have evolved very different mechanisms for navigation and chemotaxis. Here, we review the earlier and recent findings on the various modes of motility mediated by polar flagella. Expected final online publication date for the Annual Review of Microbiology, Volume 76 is September 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Elastohydrodynamic Synchronization of Rotating Bacterial Flagella

To rotate continuously without jamming, the flagellar filaments of bacteria need to be locked in phase. While several models have been proposed for eukaryotic flagella, the synchronization of bacterial flagella is less well understood. Starting from a reduced model of flexible and hydrodynamically coupled bacterial flagella, we rigorously coarse grain the equations of motion using the method of multiple scales, and hence show that bacterial flagella generically synchronize to zero phase difference via an elastohydrodynamic mechanism. Remarkably, the far-field rate of synchronization is maximized at an intermediate value of elastic compliance, with surprising implications for bacteria.

Observation of broken detailed balance in polymorphic transformation of bacterial flagellar filament

Living systems operate far from thermodynamic equilibrium, which usually manifests as broken detailed balance at the molecular scale. At larger scales with collective function of many molecules, the presence of non-equilibrium thermodynamics may not be evident. In bacterial motility, the switching dynamics of the flagellar rotary motor was recently discovered to be operating in non-equilibrium. However, the resulting motility pattern at the mesoscale, the run-and-tumble behavior, was normally considered to be a Poisson process that can be described by a two-state equilibrium model. Here, we studied the details of the run-and-tumble behavior by following the polymorphic transformation of the flagellar filaments, observing broken detailed balance that reveals its non-equilibrium nature. Evaluation of entropy production provided a direct measure of the lack of detailed balance, and a quantification of the rate of energy dissipation for bacterial run-and-tumble regulation.

Bending stiffness characterization of Bacillus subtilis' flagellar filament

The filament of a bacterial flagellum is a tube-like organelle made of single protein - flagellin, and assembled into multiple polymorphic forms. The filament can be further discretized into four subunit domains (D0, D1, D2 and D3) along the radial direction. However, it remains unclear which subunit domain plays an important role in regulating the rigidity of the filament. In this article, we address how the absence of two outer subunit domains (D2 and D3) affects the bending stiffness of the bacterium B. subtilis' flagellar filament. We first shear off flagellar filaments from the cell body, anchor one of its ends to the wall of a microfluidic channel, and correlate the elongation of the filament with the driving background flow. A numerical model is then applied to determine the bending stiffness of the filament. We find that the bending stiffness does not change drastically when the filament transforms from normal to hyperextended forms, which is estimated to be 2-3 pN.μm². Furthermore, B. subtilis' flagellar filament has similar bending stiffness to Salmonella's, though the radius of the former is almost half of that of the latter, suggesting that the rigidity comes from the inner D0 and D1 subunit domains.

Indole modulates cooperative protein-protein interactions in the flagellar motor

Indole is a major component of the bacterial exometabolome, and the mechanisms for its wide-ranging effects on bacterial physiology are biomedically significant, although they remain poorly understood. Here, we determined how indole modulates the functions of a widely conserved motility apparatus, the bacterial flagellum. Our experiments in Escherichia coli revealed that indole influences the rotation rates and reversals in the flagellum’s direction of rotation via multiple mechanisms. At concentrations higher than 1 mM, indole decreased the membrane potential to dissipate the power available for the rotation of the motor that operates the flagellum. Below 1 mM, indole did not dissipate the membrane potential. Instead, experiments and modeling indicated that indole weakens cooperative protein interactions within the flagellar complexes to inhibit motility. The metabolite also induced reversals in the rotational direction of the motor to promote a weak chemotactic response, even when the chemotaxis response regulator, CheY, was lacking. Experiments further revealed that indole does not require the transporter Mtr to cross the membrane and influence motor functions. Based on these findings, we propose that indole modulates intra- and inter-protein interactions in the cell to influence several physiological functions.

Modeling of lophotrichous bacteria reveals key factors for swimming reorientation

Lophotrichous bacteria swim through fluid by rotating their flagellar bundle extended collectively from one pole of the cell body. Cells experience modes of motility such as push, pull, and wrapping, accompanied by pauses of motor rotation in between. We present a mathematical model of a lophotrichous bacterium and investigate the hydrodynamic interaction of cells to understand their swimming mechanism. We classify the swimming modes which vary depending on the bending modulus of the hook and the magnitude of applied torques on the motor. Given the hook’s bending modulus, we find that there exist corresponding critical thresholds of the magnitude of applied torques that separate wrapping from pull in CW motor rotation, and overwhirling from push in CCW motor rotation, respectively. We also investigate reoriented directions of cells in three-dimensional perspectives as the cell experiences different series of swimming modes. Our simulations show that the transition from a wrapping mode to a push mode and pauses in between are key factors to determine a new path and that the reoriented direction depends upon the start time and duration of the pauses. It is also shown that the wrapping mode may help a cell to escape from the region where the cell is trapped near a wall.

A physical mechanism underlying the torque generation of the bacterial flagellar motor

This study proposes a physical mechanism underlying the torque generation of a bacterial flagellar motor (BFM), in which the torque for the rotation of the rotor can be generated from impulsive forces resulting from collisions between the randomly moving stator and rotor. The torque required for the rotation of the rotor may be generated through two coexisting mechanisms: mechanism (A), in which the stator collides with the rotor, whose rotation axis fluctuates asymmetrically, generating a torque in the direction of the rod, and mechanism (B), in which physical collisions between the stator and the asymmetric [Formula: see text]and [Formula: see text] generate the torque in the direction of the rod. Mechanism (A) might be related the bidirectional rotation and the tumbling of the motion of the cell. Mechanism (B) might be related to occurrence of the steps in the time traces of the rotational angle, backward stepping or switching of the rotational direction, and the knee-shaped [Formula: see text]-[Formula: see text] relation. The above-mentioned characteristics of the rotation of BFM are reproduced in a model device designed to confirm the applicability of the proposed concept to real BFM. Moreover, a prediction of the disappearance of the knee-shaped [Formula: see text]-[Formula: see text] relation of the actual BFM at a high temperature is proposed.

The colloidal nature of complex fluids enhances bacterial motility

The natural habitats of microorganisms in the human microbiome, ocean and soil ecosystems are full of colloids and macromolecules. Such environments exhibit non-Newtonian flow properties, drastically affecting the locomotion of microorganisms^1-5. Although the low-Reynolds-number hydrodynamics of swimming flagellated bacteria in simple Newtonian fluids has been well developed^6-9, our understanding of bacterial motility in complex non-Newtonian fluids is less mature^10,11. Even after six decades of research, fundamental questions about the nature and origin of bacterial motility enhancement in polymer solutions are still under debate^12-23. Here we show that flagellated bacteria in dilute colloidal suspensions display quantitatively similar motile behaviours to those in dilute polymer solutions, in particular a universal particle-size-dependent motility enhancement up to 80% accompanied by a strong suppression of bacterial wobbling^18,24. By virtue of the hard-sphere nature of colloids, whose size and volume fraction we vary across experiments, our results shed light on the long-standing controversy over bacterial motility enhancement in complex fluids and suggest that polymer dynamics may not be essential for capturing the phenomenon^12-23. A physical model that incorporates the colloidal nature of complex fluids quantitatively explains bacterial wobbling dynamics and mobility enhancement in both colloidal and polymeric fluids. Our findings contribute to the understanding of motile behaviours of bacteria in complex fluids, which are relevant for a wide range of microbiological processes²⁵ and for engineering bacterial swimming in complex environments^26,27.

Coordination of two opposite flagella allows high-speed swimming and active turning of individual zoospores

Phytophthora species cause diseases in a large variety of plants and represent a serious agricultural threat, leading, every year, to multibillion dollar losses. Infection occurs when their biflagellated zoospores move across the soil at their characteristic high speed and reach the roots of a host plant. Despite the relevance of zoospore spreading in the epidemics of plant diseases, individual swimming of zoospores have not been fully investigated. It remains unknown about the characteristics of two opposite beating flagella during translation and turning, and the roles of each flagellum on zoospore swimming. Here, combining experiments and modeling, we show how these two flagella contribute to generate thrust when beating together, and identify the mastigonemes-attached anterior flagellum as the main source of thrust. Furthermore, we find that turning involves a complex active process, in which the posterior flagellum temporarily stops, while the anterior flagellum keeps on beating and changes its gait from sinusoidal waves to power and recovery strokes, similar to Chlamydomonas's breaststroke, to reorient its body to a new direction. Our study is a fundamental step toward a better understanding of the spreading of plant pathogens' motile forms, and shows that the motility pattern of these biflagellated zoospores represents a distinct eukaryotic version of the celebrated 'run-and-tumble' motility class exhibited by peritrichous bacteria.

Flagellin outer domain dimerization modulates motility in pathogenic and soil bacteria from viscous environments

Flagellar filaments function as the propellers of the bacterial flagellum and their supercoiling is key to motility. The outer domains on the surface of the filament are non-critical for motility in many bacteria and their structures and functions are not conserved. Here, we show the atomic cryo-electron microscopy structures for flagellar filaments from enterohemorrhagic Escherichia coli O157:H7, enteropathogenic E. coli O127:H6, Achromobacter, and Sinorhizobium meliloti, where the outer domains dimerize or tetramerize to form either a sheath or a screw-like surface. These dimers are formed by 180° rotations of half of the outer domains. The outer domain sheath (ODS) plays a role in bacterial motility by stabilizing an intermediate waveform and prolonging the tumbling of E. coli cells. Bacteria with these ODS and screw-like flagellar filaments are commonly found in soil and human intestinal environments of relatively high viscosity suggesting a role for the dimerization in these environments.

It has been suggested that the outer domains of bacterial flagellins are not needed for motility. Here, the authors show that flagellar filament outer domains from some bacteria have unique structures which can alter the motility of the bacteria.

The ecological roles of bacterial chemotaxis

How bacterial chemotaxis is performed is much better understood than why. Traditionally, chemotaxis has been understood as a foraging strategy by which bacteria enhance their uptake of nutrients and energy, yet it has remained puzzling why certain less nutritious compounds are strong chemoattractants and vice versa. Recently, we have gained increased understanding of alternative ecological roles of chemotaxis, such as navigational guidance in colony expansion, localization of hosts or symbiotic partners and contribution to microbial diversity by the generation of spatial segregation in bacterial communities. Although bacterial chemotaxis has been observed in a wide range of environmental settings, insights into the phenomenon are mostly based on laboratory studies of model organisms. In this Review, we highlight how observing individual and collective migratory behaviour of bacteria in different settings informs the quantification of trade-offs, including between chemotaxis and growth. We argue that systematically mapping when and where bacteria are motile, in particular by transgenerational bacterial tracking in dynamic environments and in situ approaches from guts to oceans, will open the door to understanding the rich interplay between metabolism and growth and the contribution of chemotaxis to microbial life.

Materials science and mechanosensitivity of living matter

Living systems are composed of molecules that are synthesized by cells that use energy sources within their surroundings to create fascinating materials that have mechanical properties optimized for their biological function. Their functionality is a ubiquitous aspect of our lives. We use wood to construct furniture, bacterial colonies to modify the texture of dairy products and other foods, intestines as violin strings, bladders in bagpipes, and so on. The mechanical properties of these biological materials differ from those of other simpler synthetic elastomers, glasses, and crystals. Reproducing their mechanical properties synthetically or from first principles is still often unattainable. The challenge is that biomaterials often exist far from equilibrium, either in a kinetically arrested state or in an energy consuming active state that is not yet possible to reproduce de novo. Also, the design principles that form biological materials often result in nonlinear responses of stress to strain, or force to displacement, and theoretical models to explain these nonlinear effects are in relatively early stages of development compared to the predictive models for rubberlike elastomers or metals. In this Review, we summarize some of the most common and striking mechanical features of biological materials and make comparisons among animal, plant, fungal, and bacterial systems. We also summarize some of the mechanisms by which living systems develop forces that shape biological matter and examine newly discovered mechanisms by which cells sense and respond to the forces they generate themselves, which are resisted by their environment, or that are exerted upon them by their environment. Within this framework, we discuss examples of how physical methods are being applied to cell biology and bioengineering.

Recent Progress of Magnetically Actuated DNA Micro/Nanorobots

In the past few decades, the field of DNA origami-based micro/nanotechnology has developed dramatically and spawned attention increasingly, as its high integrality, rigid structure, and excellent resistance ability to enzyme digestion. Many two-dimensional and three-dimensional DNA nanostructures coordinated with optical, chemical, or magnetic triggers have been designed and assembled, extensively used as versatile templates for molecular robots, nanosensors, and intracellular drug delivery. The magnetic field has been widely regarded as an ideal driving and operating system for micro/nanomaterials, as it does not require high-intensity lasers like light control, nor does it need to change the chemical composition similar to chemical activation. Herein, we review the recent achievements in the induction and actuation of DNA origami-based nanodevices that respond to magnetic fields. These magnetic actuation-based DNA nanodevices were regularly combined with magnetic beads or gold nanoparticles and applied to generate single-stranded scaffolds, assemble various DNA nanostructures, and purify specific DNA nanostructures. Moreover, they also produced artificial magnetism or moved regularly driven by external magnetic fields to explain deeper scientific issues.

Serial passage in an insect host indicates genetic stability of the human probiotic Escherichia coli Nissle 1917

Background and objectives

The probiotic Escherichia coli strain Nissle 1917 (EcN) has been shown to effectively prevent and alleviate intestinal diseases. Despite the widespread medical application of EcN, we still lack basic knowledge about persistence and evolution of EcN outside the human body. Such knowledge is important also for public health aspects, as in contrast to abiotic therapeutics, probiotics are living organisms that have the potential to evolve. This study made use of experimental evolution of EcN in an insect host, the red flour beetle Tribolium castaneum, and its flour environment.

Methodology

Using a serial passage approach, we orally introduced EcN to larvae of T.castaneum as a new host, and also propagated it in the flour environment. After eight propagation cycles, we analyzed phenotypic attributes of the passaged replicate EcN lines, their effects on the host in the context of immunity and infection with the entomopathogen Bacillus thuringiensis, and potential genomic changes using WGS of three of the evolved lines.

Results

We observed weak phenotypic differences between the ancestral EcN and both, beetle and flour passaged EcN lines, in motility and growth at 30°C, but neither any genetic changes, nor the expected increased persistence of the beetle-passaged lines. One of these lines displayed distinct morphological and physiological characteristics.

Conclusions and implications

Our findings suggest that EcN remains rather stable during serial passage in an insect. Weak phenotypic changes in growth and motility combined with a lack of genetic changes indicate a certain degree of phenotypic plasticity of EcN.

Lay Summary

For studying adaptation of the human probiotic Escherichia coli strain Nissle 1917, we introduced it to a novel insect host system and its environment using a serial passage approach. After passage, we observed weak phenotypic changes in growth and motility but no mutations or changes in persistence inside the host.

Upcoming flow promotes the bundle formation of bacterial flagella

Flagellated bacteria swim by rotating a bundle of helical flagella and commonly explore the surrounding environment in a "run-and-tumble" motility mode. Here, we show that the upcoming flow could impact the bacterial run-and-tumble behavior by affecting the formation and dispersal of the flagellar bundle. Using a dual optical tweezers setup to trap individual bacteria, we characterized the effects of the imposed fluid flow and cell body rotation on the run-and-tumble behavior. We found that the two factors affect the behavior differently, with the imposed fluid flow increasing the running time and decreasing the tumbling time and the cell body rotation decreasing the tumbling time only. Using numerical simulations, we computed the flagellar bundling time as a function of flow velocity, which agrees well with our experimental observations. The mechanical effects we characterized here provide novel, to our knowledge, ingredients for further studies of bacterial chemotaxis in complex environments such as dynamic fluid environments.

Direct dynamic read-out of molecular chirality with autonomous enzyme-driven swimmers

A key approach for designing bioinspired machines is to transfer concepts from nature to man-made structures by integrating biomolecules into artificial mechanical systems. This strategy allows the conversion of molecular information into macroscopic action. Here, we describe the design and dynamic behaviour of hybrid bioelectrochemical swimmers that move spontaneously at the air-water interface. Their motion is governed by the diastereomeric interactions between immobilized enantiopure oligomers and the enantiomers of a chiral probe molecule present in solution. These dynamic bipolar systems are able to convert chiral information present at the molecular level into enantiospecific macroscopic trajectories. Depending on the enantiomer in solution, the swimmers will move clockwise or anticlockwise; the concept can also be used for the direct visualization of the degree of enantiomeric excess by analysing the curvature of the trajectories. Deciphering in such a straightforward way the enantiomeric ratio could be useful for biomedical applications, for the read-out of food quality or as a more general analogue of polarimetric measurements.

Bacterial motility: machinery and mechanisms

Bacteria have developed a large array of motility mechanisms to exploit available resources and environments. These mechanisms can be broadly classified into swimming in aqueous media and movement over solid surfaces. Swimming motility involves either the rotation of rigid helical filaments through the external medium or gyration of the cell body in response to the rotation of internal filaments. On surfaces, bacteria swarm collectively in a thin layer of fluid powered by the rotation of rigid helical filaments, they twitch by assembling and disassembling type IV pili, they glide by driving adhesins along tracks fixed to the cell surface and, finally, non-motile cells slide over surfaces in response to outward forces due to colony growth. Recent technological advances, especially in cryo-electron microscopy, have greatly improved our knowledge of the molecular machinery that powers the various forms of bacterial motility. In this Review, we describe the current understanding of the physical and molecular mechanisms that allow bacteria to move around.

Swimming behavior of the multicellular magnetotactic prokaryote 'Candidatus Magnetoglobus multicellularis' near solid boundaries and natural magnetic grains

The magnetotactic yet uncultured species 'Candidatus Magnetoglobus multicellularis' is a spherical, multicellular ensemble of bacterial cells able to align along magnetic field lines while swimming propelled by flagella. Magnetotaxis is due to intracytoplasmic, membrane-bound magnetic crystals called magnetosomes. The net magnetic moment of magnetosomes interacts with local magnetic fields, imparting the whole microorganism a torque. Previous works investigated 'Ca. M. multicellularis' behavior when free swimming in water; however, they occur in sediments where bumping into solid particles must be routine. In this work, we investigate the swimming trajectories of 'Ca. M. multicellularis' close to solid boundaries using video microscopy. We applied magnetic fields 0.25-8.0 mT parallel to the optical axis of a light microscope, such that microorganisms were driven upwards towards a coverslip. Because their swimming trajectories approach cylindrical helixes, circular profiles would be expected. Nevertheless, at fields 0.25-1.1 mT, most trajectory projections were roughly sinusoidal, and net movements were approximately perpendicular to applied magnetic fields. Closed loops appeared in some trajectory projections at 1.1 mT, which could indicate a transition to the loopy profiles observed at magnetic fields ≥ 2.15 mT. The behavior of 'Ca. M. multicellularis' near natural magnetic grains showed that they were temporarily trapped by the particle's magnetic field but could reverse the direction of movement to flee away. Our results show that interactions of 'Ca. M. multicellularis with solid boundaries and magnetic grains are complex and possibly involve mechano-taxis.

Hydrodynamics and direction change of tumbling bacteria

The bacterium Escherichia coli (E. coli) swims in viscous fluids by rotating several helical flagellar filaments, which are gathered in a bundle behind the cell during ‘runs’ wherein the cell moves steadily forward. In between runs, the cell undergoes quick ‘tumble’ events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place and a random reorientation of the cell. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. The change of direction during a tumble is not uniformly distributed but is skewed towards smaller angles with an average of about 62°–68°, as first measured by Berg and Brown (1972). Here we develop a theoretical approach to model the angular distribution of swimming E. coli cells during tumbles. We first use past experimental imaging results to construct a kinematic description of the dynamics of the flagellar filaments during a tumble. We then employ low-Reynolds number hydrodynamics to compute the consequences of the kinematic model on the force and torque balance of the cell and to deduce the overall change in orientation. The results of our model are in good agreement with experimental observations. We find that the main change of direction occurs during the ‘bundling’ part of the process wherein, at the end of a tumble, the dispersed flagellar filaments are brought back together in the helical bundle, which we confirm using a simplified forced-sphere model.

The bank of swimming organisms at the micron scale (BOSO-Micro)

Unicellular microscopic organisms living in aqueous environments outnumber all other creatures on Earth. A large proportion of them are able to self-propel in fluids with a vast diversity of swimming gaits and motility patterns. In this paper we present a biophysical survey of the available experimental data produced to date on the characteristics of motile behaviour in unicellular microswimmers. We assemble from the available literature empirical data on the motility of four broad categories of organisms: bacteria (and archaea), flagellated eukaryotes, spermatozoa and ciliates. Whenever possible, we gather the following biological, morphological, kinematic and dynamical parameters: species, geometry and size of the organisms, swimming speeds, actuation frequencies, actuation amplitudes, number of flagella and properties of the surrounding fluid. We then organise the data using the established fluid mechanics principles for propulsion at low Reynolds number. Specifically, we use theoretical biophysical models for the locomotion of cells within the same taxonomic groups of organisms as a means of rationalising the raw material we have assembled, while demonstrating the variability for organisms of different species within the same group. The material gathered in our work is an attempt to summarise the available experimental data in the field, providing a convenient and practical reference point for future studies.

Design of nematic liquid crystals to control microscale dynamics

The dynamics of small particles, both living such as swimming bacteria and inanimate, such as colloidal spheres, has fascinated scientists for centuries. If one could learn how to control and streamline their chaotic motion, that would open technological opportunities in the transformation of stored or environmental energy into systematic motion, with applications in micro-robotics, transport of matter, guided morphogenesis. This review presents an approach to command microscale dynamics by replacing an isotropic medium with a liquid crystal. Orientational order and associated properties, such as elasticity, surface anchoring, and bulk anisotropy, enable new dynamic effects, ranging from the appearance and propagation of particle-like solitary waves to self-locomotion of an active droplet. By using photoalignment, the liquid crystal can be patterned into predesigned structures. In the presence of the electric field, these patterns enable the transport of solid and fluid particles through nonlinear electrokinetics rooted in anisotropy of conductivity and permittivity. Director patterns command the dynamics of swimming bacteria, guiding their trajectories, polarity of swimming, and distribution in space. This guidance is of a higher level of complexity than a simple following of the director by rod-like microorganisms. Namely, the director gradients mediate hydrodynamic interactions of bacteria to produce an active force and collective polar modes of swimming. The patterned director could also be engraved in a liquid crystal elastomer. When an elastomer coating is activated by heat or light, these patterns produce a deterministic surface topography. The director gradients define an activation force that shapes the elastomer in a manner similar to the active stresses triggering flows in active nematics. The patterned elastomer substrates could be used to define the orientation of cells in living tissues. The liquid-crystal guidance holds a major promise in achieving the goal of commanding microscale active flows.

Deep neural net tracking of human pluripotent stem cells reveals intrinsic behaviors directing morphogenesis

Lineage tracing is a powerful tool in developmental biology to interrogate the evolution of tissue formation, but the dense, three-dimensional nature of tissue limits the assembly of individual cell trajectories into complete reconstructions of development. Human induced pluripotent stem cells (hiPSCs) can recapitulate aspects of developmental processes, providing an in vitro platform to assess the dynamic collective behaviors directing tissue morphogenesis. Here, we trained an ensemble of neural networks to track individual hiPSCs in time-lapse microscopy, generating longitudinal measures of cell and cellular neighborhood properties on timescales from minutes to days. Our analysis reveals that, while individual cell parameters are not strongly affected by pluripotency maintenance conditions or morphogenic cues, regional changes in cell behavior predict cell fate and colony organization. By generating complete multicellular reconstructions of hiPSC behavior, our tracking pipeline enables fine-grained understanding of morphogenesis by elucidating the role of regional behavior in early tissue formation.

Locomotion of Miniature Soft Robots

Miniature soft robots are mobile devices, which are made of smart materials that can be actuated by external stimuli to realize their desired functionalities. Here, the key advancements and challenges of the locomotion producible by miniature soft robots in micro- to centimeter length scales are highlighted. It is highly desirable to endow these small machines with dexterous locomotive gaits as it enables them to easily access highly confined and enclosed spaces via a noninvasive manner. If miniature soft robots are able to capitalize this unique ability, they will have the potential to transform a vast range of applications, including but not limited to, minimally invasive medical treatments, lab-on-chip applications, and search-and-rescue missions. The gaits of miniature soft robots are categorized into terrestrial, aquatic, and aerial locomotion. Except for the centimeter-scale robots that can perform aerial locomotion, the discussions in this report are centered around soft robots that are in the micro- to millimeter length scales. Under each category of locomotion, prospective methods and strategies that can improve their gait performances are also discussed. This report provides critical analyses and discussions that can inspire future strategies to make miniature soft robots significantly more agile.