Flexibility of bacterial flagella in external shear results in complex swimming trajectories

Bacterial active matter

Bacteria are among the oldest and most abundant species on Earth. Bacteria successfully colonize diverse habitats and play a significant role in the oxygen, carbon, and nitrogen cycles. They also form human and animal microbiota and may become sources of pathogens and a cause of many infectious diseases. Suspensions of motile bacteria constitute one of the most studied examples of active matter: a broad class of non-equilibrium systems converting energy from the environment (e.g., chemical energy of the nutrient) into mechanical motion. Concentrated bacterial suspensions, often termed active fluids, exhibit complex collective behavior, such as large-scale turbulent-like motion (so-called bacterial turbulence) and swarming. The activity of bacteria also affects the effective viscosity and diffusivity of the suspension. This work reports on the progress in bacterial active matter from the physics viewpoint. It covers the key experimental results, provides a critical assessment of major theoretical approaches, and addresses the effects of visco-elasticity, liquid crystallinity, and external confinement on collective behavior in bacterial suspensions.

Force and torque-free helical tail robot to study low Reynolds number micro-organism swimming

Helical propulsion is used by many micro-organisms to swim in viscous-dominated environments. Their swimming dynamics are relatively well understood, but a detailed study of the flow fields is still needed to understand wall effects and hydrodynamic interactions among swimmers. In this letter, we describe the development of an autonomous swimming robot with a helical tail that operates in the Stokes regime. The device uses a battery-based power system with a miniature motor that imposes a rotational speed on a helical tail. The speed, direction, and activation are controlled electronically using an infrared remote control. Since the robot is about 5 cm long, we use highly viscous fluids to match the Reynolds number, Re, to be less than 0.1. Measurements of swimming speeds are conducted for a range of helical wavelengths, λ, head geometries, and rotation rates, ω. We provide comparisons of the experimental measurements with analytical predictions derived from resistive force theory. This force and torque-free neutrally buoyant swimmer mimics the swimming strategy of bacteria more closely than previously used designs and offers a lot of potential for future applications.

Migration of active filaments under Poiseuille flow in a microcapillary tube

We present a comprehensive study of active filaments confined in a cylindrical channel under Poiseuille flow. The activity drives the filament towards the channel boundary, whereas external fluid flow migrates the filament away from the boundary. This migration further shifts towards the centre for higher flow strength. The migration behaviour of the filaments is presented in terms of the alignment order parameter that shows the alignment grows with shear and activity. Further, we have also addressed the role of length of filament on the migration behaviour, which suggests higher migration for larger filaments. Moreover, we discuss the polar ordering of filaments as a function of distance from the centre of channel that displays upstream motion near the boundary and downstream motion at the centre of the tube.

Effect of external shear flow on sperm motility

The trajectory of sperm in the presence of background flow is of utmost importance for the success of fertilization, as sperm encounter background flow of different magnitude and direction on their way to the egg. Here, we have studied the effect of an unbounded simple shear flow as well as a Poiseuille flow on the sperm trajectory. In the presence of a simple shear flow, the sperm moves on an elliptical trajectory in the reference frame advecting with the local background flow. The length of the major-axis of this elliptical trajectory decreases with the shear rate. The flexibility of the flagellum and consequently the length of the major axis of the elliptical trajectories increases with the sperm number. The sperm number is a dimensionless number representing the ratio of viscous force to elastic force. The sperm moves downstream or upstream depending on the strength of background Poiseuille flow. In contrast to the simple shear flow, the sperm also moves toward the centerline in a Poiseuille flow. Far away from the centerline, the cross-stream migration velocity of the sperm increases as the transverse distance of the sperm from the centerline decreases. Close to the centerline, on the other hand, the cross-stream migration velocity decreases as the sperm further approaches the center. The cross-stream migration velocity of the sperm also increases with the sperm number.

Mechanical shear controls bacterial penetration in mucus

Mucus plays crucial roles in higher organisms, from aiding fertilization to protecting the female reproductive tract. Here, we investigate how anisotropic organization of mucus affects bacterial motility. We demonstrate by cryo electron micrographs and elongated tracer particles imaging, that mucus anisotropy and heterogeneity depend on how mechanical stress is applied. In shallow mucus films, we observe bacteria reversing their swimming direction without U-turns. During the forward motion, bacteria burrowed tunnels that last for several seconds and enable them to swim back faster, following the same track. We elucidate the physical mechanism of direction reversal by fluorescent visualization of the flagella: when the bacterial body is suddenly stopped by the mucus structure, the compression on the flagellar bundle causes buckling, disassembly and reorganization on the other side of the bacterium. Our results shed light into motility of bacteria in complex visco-elastic fluids and can provide clues in the propagation of bacteria-born diseases in mucus.

Behavior of active filaments near solid-boundary under linear shear flow

The steady-state behavior of a dilute suspension of self-propelled filaments confined between planar walls subjected to Couette-flow is reported herein. The effect of hydrodynamics has been taken into account using a mesoscale simulation approach. We present a detailed analysis of positional and angular probability distributions of filaments with varying propulsive force and shear-flow. The distribution of the centre-of-mass of the filament shows adsorption near the surfaces, which diminishes with the flow. The excess density of filaments decreases with Weissenberg number as Wi-β with an exponent β ≈ 0.8, in the intermediate shear range (1 < Wi < 30). The angular orientational moment also decreases near the wall as Wi-δ with δ ≈ 1/5; the variation in orientational moment near the wall is relatively slower than the bulk. It shows a strong dependence on the propulsive force near the wall, with variation on force as Pe-1/3 for large Pe ≥ 1. The active filament shows orientational preference with flow near the surfaces, which splits into upstream and downstream swimming. The population splitting from a unimodal (propulsive force dominated regime) to bimodal phase (shear dominated regime) is identified in the parameter space of propulsive force and shear flow.

Random sets of stadiums in square and collective behavior of bacteria

Collective motion of swimmers can be detected by hydrodynamic interactions through the eective (macroscopic) viscosity. It follows form the general hydrodynamics that the eective viscosity of non-dilute random suspensions depends on the shape of particles and of their spacial probabilistic distribution. Therefore, a comparative analysis of disordered and collectively interacting particles of the bacteria shape can be done in terms of the probabilistic geometric parameters which determine the eective viscosity. In this paper, we develop a quantitative criterion to detect the collective behavior of bacteria. This criterion is based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums) which characterize the high-order correlation functions. The locations and the shape of bacteria are modeled by stadiums randomly embedded in medium without overlapping. This shape models can be considered as improvement of the previous segment model.We calculate the e-sums of the simulated disordered sets and of the observed experimental locations of bacteria subtilis. The obtained results show a dierence between these two sets that demonstrates the collective motion of bacteria.

Flagella bending affects macroscopic properties of bacterial suspensions

To survive in harsh conditions, motile bacteria swim in complex environments and respond to the surrounding flow. Here, we develop a mathematical model describing how flagella bending affects macroscopic properties of bacterial suspensions. First, we show how the flagella bending contributes to the decrease in the effective viscosity observed in dilute suspension. Our results do not impose tumbling (random reorientation) as was previously done to explain the viscosity reduction. Second, we demonstrate how a bacterium escapes from wall entrapment due to the self-induced buckling of flagella. Our results shed light on the role of flexible bacterial flagella in interactions of bacteria with shear flow and walls or obstacles.

A criterion of collective behavior of bacteria

It was established in the previous works that hydrodynamic interactions between the swimmers can lead to collective motion. Its implicit evidences were confirmed by reduction in the effective viscosity. We propose a new quantitative criterion to detect such a collective behavior. Our criterion is based on a new computationally effective RVE (representative volume element) theory based on the basic statistic moments (e-sums or generalized Eisenstein-Rayleigh sums). The criterion can be applied to various two-phase dispersed media (biological systems, composites etc). The locations of bacteria are modeled by short segments having a small width randomly embedded in medium without overlapping. We compute the e-sums of the simulated disordered sets and of the observed experimental locations of Bacillus subtilis. The obtained results show a difference between these two sets that demonstrates the collective motion of bacteria.

Perspectives in flow-based microfluidic gradient generators for characterizing bacterial chemotaxis

Chemotaxis is a phenomenon which enables cells to sense concentrations of certain chemical species in their microenvironment and move towards chemically favorable regions. Recent advances in microbiology have engineered the chemotactic properties of bacteria to perform novel functions, but traditional methods of characterizing chemotaxis do not fully capture the associated cell motion, making it difficult to infer mechanisms that link the motion to the microbiology which induces it. Microfluidics offers a potential solution in the form of gradient generators. Many of the gradient generators studied to date for this application are flow-based, where a chemical species diffuses across the laminar flow interface between two solutions moving through a microchannel. Despite significant research efforts, flow-based gradient generators have achieved mixed success at accurately capturing the highly subtle chemotactic responses exhibited by bacteria. Here we present an analysis encompassing previously published versions of flow-based gradient generators, the theories that govern their gradient-generating properties, and new, more practical considerations that result from experimental factors. We conclude that flow-based gradient generators present a challenge inherent to their design in that the residence time and gradient decay must be finely balanced, and that this significantly narrows the window for reliable observation and quantification of chemotactic motion. This challenge is compounded by the effects of shear on an ellipsoidal bacterium that causes it to preferentially align with the direction of flow and subsequently suppresses the cross-flow chemotactic response. These problems suggest that a static, non-flowing gradient generator may be a more suitable platform for chemotaxis studies in the long run, despite posing greater difficulties in design and fabrication.

Succeed escape: Flow shear promotes tumbling of Escherichia colinear a solid surface

Understanding how bacteria move close to a surface under various stimuli is crucial for a broad range of microbial processes including biofilm formation, bacterial transport and migration. While prior studies focus on interactions between single stimulus and bacterial suspension, we emphasize on compounding effects of flow shear and solid surfaces on bacterial motility, especially reorientation and tumble. We have applied microfluidics and digital holographic microscopy to capture a large number (>10⁵) of 3D Escherichia coli trajectories near a surface under various flow shear. We find that near-surface flow shear promotes cell reorientation and mitigates the tumble suppression and re-orientation confinement found in a quiescent flow, and consequently enhances surface normal bacterial dispersion. Conditional sampling suggests that two complimentary hydrodynamic mechanisms, Jeffrey Orbit and shear-induced flagella unbundling, are responsible for the enhancement in bacterial tumble motility. These findings imply that flow shear may mitigate cell trapping and prevent biofilm initiation.

Shear-induced orientational dynamics and spatial heterogeneity in suspensions of motile phytoplankton

Fluid flow, ubiquitous in natural and man-made environments, has the potential to profoundly impact the transport of microorganisms, including phytoplankton in aquatic habitats and bioreactors. Yet, the effect of ambient flow on the swimming behaviour of phytoplankton has remained poorly understood, largely owing to the difficulty of observing cell-flow interactions at the microscale. Here, we present microfluidic experiments where we tracked individual cells for four species of motile phytoplankton exposed to a spatially non-uniform fluid shear rate, characteristic of many flows in natural and artificial environments. We observed that medium-to-high mean shear rates (1-25 s(-1)) produce heterogeneous cell concentrations in the form of regions of accumulation and regions of depletion. The location of these regions relative to the flow depends on the cells' propulsion mechanism, body shape and flagellar arrangement, as captured by an effective aspect ratio. Species having a large effective aspect ratio accumulated in the high-shear regions, owing to shear-induced alignment of the swimming orientation with the fluid streamlines. Species having an effective aspect ratio close to unity exhibited little preferential accumulation at low-to-moderate flow rates, but strongly accumulated in the low-shear regions under high flow conditions, potentially owing to an active, behavioural response of cells to shear. These observations demonstrate that ambient fluid flow can strongly affect the motility and spatial distribution of phytoplankton and highlight the rich dynamics emerging from the interaction between motility, morphology and flow.

Effective Rheological Properties in Semi-dilute Bacterial Suspensions

Interactions between swimming bacteria have led to remarkable experimentally observable macroscopic properties such as the reduction in the effective viscosity, enhanced mixing, and diffusion. In this work, we study an individual-based model for a suspension of interacting point dipoles representing bacteria in order to gain greater insight into the physical mechanisms responsible for the drastic reduction in the effective viscosity. In particular, asymptotic analysis is carried out on the corresponding kinetic equation governing the distribution of bacteria orientations. This allows one to derive an explicit asymptotic formula for the effective viscosity of the bacterial suspension in the limit of bacterium non-sphericity. The results show good qualitative agreement with numerical simulations and previous experimental observations. Finally, we justify our approach by proving existence, uniqueness, and regularity properties for this kinetic PDE model.

Modelling the mechanics and hydrodynamics of swimming E. coli

The swimming properties of an E. coli-type model bacterium are investigated by mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the bacterium with the multiparticle particle collision dynamics method for the embedding fluid. The bacterium is composed of a spherocylindrical body with attached helical flagella, built up from discrete particles for an efficient coupling with the fluid. We measure the hydrodynamic friction coefficients of the bacterium and find quantitative agreement with experimental results of swimming E. coli. The flow field of the bacterium shows a force-dipole-like pattern in the swimming plane and two vortices perpendicular to its swimming direction arising from counterrotation of the cell body and the flagella. By comparison with the flow field of a force dipole and rotlet dipole, we extract the force-dipole and rotlet-dipole strengths for the bacterium and find that counterrotation of the cell body and the flagella is essential for describing the near-field hydrodynamics of the bacterium.

Microbes in flow

Microbes often live in moving fluids. Despite the multitude of implications that flow has on microbial ecology and environmental microbiology, only recently have experimental tools and conceptual frameworks from fluid physics been applied systematically to further our knowledge of the behavior of microbes in flow. This nascent research field, which truly straddles biology and physics, has already produced important contributions to our understanding of the physical interaction between microbes and flow, both in bulk fluid and close to surfaces, at the same time revealing the richness and complexity of the resulting dynamics.