Characterization of hydrodynamic surface interactions of Escherichia coli cell bodies in shear flow

AI-aided geometric design of anti-infection catheters

Bacteria can swim upstream in a narrow tube and pose a clinical threat of urinary tract infection to patients implanted with catheters. Coatings and structured surfaces have been proposed to repel bacteria, but no such approach thoroughly addresses the contamination problem in catheters. Here, on the basis of the physical mechanism of upstream swimming, we propose a novel geometric design, optimized by an artificial intelligence model. Using Escherichia coli, we demonstrate the anti-infection mechanism in microfluidic experiments and evaluate the effectiveness of the design in three-dimensionally printed prototype catheters under clinical flow rates. Our catheter design shows that one to two orders of magnitude improved suppression of bacterial contamination at the upstream end, potentially prolonging the in-dwelling time for catheter use and reducing the overall risk of catheter-associated urinary tract infection.

Confined active matter in external fields

We analyze a dilute suspension of active particles confined between walls and subjected to fields that can modulate particle speed as well as orientation. Generally, the particle distribution is different in the bulk compared to near the walls. In the bulk, particles tend to accumulate in the regions of low speed, but in the presence of an orienting field normal to the walls, particles rotate to align with the field and accumulate in the field direction. At the walls, particles tend to accumulate pointing into the walls and thereby exert pressure on walls. But the presence of strong orienting fields can cause the particles to reorient away from the walls, and hence shows a possible mechanism for preventing contamination of surfaces. The pressure at the walls depends on the wall separation and the field strengths. This work demonstrates how multiple fields with different functionalities can be used to control active matter under confinement.

Shear-enhanced sorting of ovoid and filamentous bacterial cells using pinch flow fractionation

In this paper, we experimentally investigate the influence of the flow rate on the trajectory of ovoid and filamentous bacterial cells of E. coli in a low aspect ratio pinch flow fractionation device. To that aim, we vary the Reynolds number over two orders of magnitude, while monitoring the dynamics of the cells across our device. At low flow rates, filamentous cells adopt several rotational motions in the pinched segment, which are induced both by the shear rate and by their close interactions with the nearest wall. As a result, the geometrical centre of the filamentous cells deviates towards the centre of the channel, which increases their effective sorting diameter depending on the length of their major axis as well as on the rotational mode they adopt in the pinch. As the flow rate increases, particles are forced to align vertically in the pinch, in the direction of the main shear gradient, which reduces the amplitude of the lateral deviation generated by their rotation. The trajectory of the particles in the expansion is directly determined by their position at the pinch outlet. As a consequence, the position of the filamentous cells at the outlet of the device strongly depends on the flow rate as well as on the length of their major axis. Based on these observations we optimized the flow conditions to successfully extract an ultra high purity sample of filamentous cells from a solution containing mainly ovoid cells.

Active particles crossing sharp viscosity gradients

Active particles (living or synthetic) often move through inhomogeneous environments, such as gradients in light, heat or nutrient concentration, that can lead to directed motion (or taxis). Recent research has explored inhomogeneity in the rheological properties of a suspending fluid, in particular viscosity, as a mechanical (rather than biological) mechanism for taxis. Theoretical and experimental studies have shown that gradients in viscosity can lead to reorientation due to asymmetric viscous forces. In particular, recent experiments with Chlamydomonas Reinhardtii algae swimming across sharp viscosity gradients have observed that the microorganisms are redirected and scattered due to the viscosity change. Here we develop a simple theoretical model to explain these experiments. We model the swimmers as spherical squirmers and focus on small, but sharp, viscosity changes. We derive a law, analogous to Snell's law of refraction, that governs the orientation of active particles in the presence of a viscosity interface. Theoretical predictions show good agreement with experiments and provide a mechanistic understanding of the observed reorientation process.

Microswimmers in vortices: dynamics and trapping

Biological and artificial microswimmers often self-propel in external flows of vortical nature; relevant examples include algae in small-scale ocean eddies, spermatozoa in uterine peristaltic flows and bacteria in microfluidic devices. A recent experiment has shown that swimming bacteria in model vortices are expelled from the vortex all the way to a well-defined depletion zone (A. Sokolov and I. S. Aranson, Rapid expulsion of microswimmers by a vortical flow. Nat. Commun., 2016, 7, 11114). In this paper, we propose a theoretical model to investigate the dynamics of elongated microswimmers in elementary vortices, namely active particles in two- and three-dimensional rotlets. A deterministic model first reveals the existence of bounded orbits near the centre of the vortex and unbounded orbits elsewhere. We further discover a conserved quantity of motion that allows us to map the phase space according to the type of the orbit (bounded vs unbounded). We next introduce translational and rotational noise into the system. Using a Fokker-Planck formalism, we quantify the quality of trapping near the centre of the vortex by examining the probability of escape and the mean time of escape from the region of deterministically bounded orbits. We finally show how to use these findings to formulate a prediction for the radius of the depletion zone, which compares favourably with the experiments (A. Sokolov and I. S. Aranson, Rapid expulsion of microswimmers by a vortical flow. Nat. Commun., 2016, 7, 11114).

Interplay of physico-chemical and mechanical bacteria-surface interactions with transport processes controls early biofilm growth: A review

Biofilms initiate when bacteria encounter and are retained on surfaces. The surface orchestrates biofilm growth through direct physico-chemical and mechanical interactions with different structures on bacterial cells and, in turn, through its influence on cell-cell interactions. Individual cells respond directly to a surface through mechanical or chemical means, initiating "surface sensing" pathways that regulate gene expression, for instance producing extra cellular matrix or altering phenotypes. The surface can also physically direct the evolving colony morphology as cells divide and grow. In either case, the physico-chemistry of the surface influences cells and cell communities through mechanisms that involve additional factors. For instance the numbers of cells arriving on a surface from solution relative to the generation of new cells by division depends on adhesion and transport kinetics, affecting early colony density and composition. Separately, the forces experienced by adhering cells depend on hydrodynamics, gravity, and the relative stiffnesses and viscoelasticity of the cells and substrate materials, affecting mechanosensing pathways. Physical chemistry and surface functionality, along with interfacial mechanics also influence cell-surface friction and control colony morphology, in particular 2D and 3D shape. This review focuses on the current understanding of the mechanisms in which physico-chemical interactions, deriving from surface functionality, impact individual cells and cell community behavior through their coupling with other interfacial processes.

Diffusion of chiral active particles in a Poiseuille flow

We study the diffusive behavior of chiral active (self-propelled) Brownian particles in a two-dimensional microchannel with a Poiseuille flow. Using numerical simulations, we show that the behavior of the transport coefficients of particles, for example, the average velocity v and the effective diffusion coefficient D_{eff}, strongly depends on flow strength u_{0}, translational diffusion constant D_{0}, rotational diffusion rate D_{θ}, and chirality of the active particles Ω. It is demonstrated that the particles can exhibit upstream drift, resulting in a negative v, for the optimal parameter values of u_{0}, D_{θ}, and Ω. Interestingly, the direction of v can be controlled by tuning these parameters. We observe that for some optimal values of u_{0} and Ω, the chiral particles aggregate near a channel wall and the corresponding D_{eff} are enhanced. However, for the nonchiral particles (Ω=0), D_{eff} is suppressed by the presence of Poiseuille flow. It is expected that these findings have a great potential for developing microfluidic and lab-on-a-chip devices for separating the active particles.

Surface Chemistry Guides the Orientations of Adhering E. coli Cells Captured from Flow

Motivated by observations of cell orientation at biofilm-substrate interfaces and reports that cell orientation and adhesion play important roles in biofilm evolution and function, we investigated the influence of surface chemistry on the orientation of Escherichia coli cells captured from flow onto surfaces that were cationic, hydrophobic, or anionic. We characterized the initial orientations of nonmotile cells captured from gentle shear relative to the surface and flow directions. The broad distribution of captured cell orientations observed on cationic surfaces suggests that rapid electrostatic attractions of cells to oppositely charged surfaces preserve the instantaneous orientations of cells as they rotate in the near-surface shearing flow. By contrast, on hydrophobic and anionic surfaces, cells were oriented slightly more in the plane of the surface and in the flow direction compared with that on the cationic surface. This suggests slower development of adhesion at hydrophobic and anionic surfaces, allowing cells to tip toward the surface as they adhere. Once cells were captured, the flow was increased by 20-fold. Cells did not reorient substantially on the cationic surface, suggesting a strong cell-surface bonding. By contrast, on hydrophobic and anionic surfaces, increased shear forced cells to tip toward the surface and align in the flow direction, a process that was reversible upon reducing the shear. These findings suggest mechanisms by which surface chemistry may play a role in the evolving structure and function of microbial communities.

Active particles with polar alignment in ring-shaped confinement

We study steady-state properties of active, nonchiral and chiral Brownian particles with polar alignment and steric interactions confined within a ring-shaped confinement (annulus) in two dimensions. Exploring possible interplays between polar interparticle alignment, geometric confinement and the surface curvature, being incorporated here on minimal levels, we report a surface-population reversal effect, whereby active particles migrate from the outer concave boundary of the annulus to accumulate on its inner convex boundary. This contrasts the conventional picture, implying stronger accumulation of active particles on concave boundaries relative to the convex ones. The population reversal is caused by both particle alignment and surface curvature, disappearing when either of these factors is absent. We explore the ensuing consequences for the chirality-induced current and swim pressure of active particles and analyze possible roles of system parameters, such as the mean number density of particles and particle self-propulsion, chirality, and alignment strengths.

Confined Bubble-Propelled Microswimmers in Capillaries: Wall Effect, Fuel Deprivation, and Exhaust Product Excess

Self-propelled autonomous nano/microswimmers are at the forefront of materials science. These swimmers are expected to operate in highly confined environments, such as between the grains of soil or in the capillaries of the human organism. To date, little attention is paid to the problem that in such a confined environment the fuel powering catalytic nano/microswimmers can be exhausted quickly and the space can be polluted with the product of the catalytic reaction. In addition, the motion of the nano/microswimmers may be influenced by the confinement. These issues are addressed here, showing the influence of the size of the capillary and length of the micromotor on the motion and the influence of the depletion of the fuel and excess of the exhaust products. Theoretical modeling is provided as well to bring further insight into the observations. This article shows challenges that these systems face and stimulates research to overcome them.

Active dipolar spheroids in shear flow and transverse field: Population splitting, cross-stream migration, and orientational pinning

We study the steady-state behavior of active, dipolar, Brownian spheroids in a planar channel subjected to an imposed Couette flow and an external transverse field, applied in the "downward" normal-to-flow direction. The field-induced torque on active spheroids (swimmers) is taken to be of magnetic form by assuming that they have a permanent magnetic dipole moment, pointing along their self-propulsion (swim) direction. Using a continuum approach, we show that a host of behaviors emerges over the parameter space spanned by the particle aspect ratio, self-propulsion and shear/field strengths, and the channel width. The cross-stream migration of the model swimmers is shown to involve a regime of linear response (quantified by a linear-response factor) in weak fields. For prolate swimmers, the weak-field behavior crosses over to a regime of full swimmer migration to the bottom half of the channel in strong fields. For oblate swimmers, a counterintuitive regime of reverse migration arises in intermediate fields, where a macroscopic fraction of swimmers reorient and swim to the top channel half at an acute "upward" angle relative to the field axis. The diverse behaviors reported here are analyzed based on the shear-induced population splitting (bimodality) of the swim orientation, giving two distinct, oppositely polarized, swimmer subpopulations (albeit very differently for prolate/oblate swimmers) in each channel half. In strong fields, swimmers of both types exhibit net upstream currents relative to the laboratory frame. The onsets of full migration and net upstream current depend on the aspect ratio, enabling efficient particle separation strategies in microfluidic setups.

Growth of microorganisms in an interfacially driven space bioreactor analog

Fluid bioreactors in microgravity environments may utilize alternative methods of containment and mixing. The ring-sheared drop (RSD) is a containerless mixing device which functions in microgravity using surface tension for containment and mixes through interfacially-driven flow. To assess the feasibility of using interfacially driven flow devices, such as the RSD, as bioreactors, Escherichia coli growth and recombinant protein expression were analyzed in a ground-based analog of the RSD called the knife edge surface viscometer (KEV). Results demonstrated that the KEV can facilitate the growth of E. coli and that growth rate increases logarithmically with increasing knife edge rotation rate, similar to the standard growth method on Earth (orbital shaker). Furthermore, the KEV was shown to be viable for supporting recombinant protein expression in E. coli at levels comparable to those achieved using standard growth methods.

Rapid Electrostatic Capture of Rod-Shaped Particles on Planar Surfaces: Standing up to Shear

We compare the electrostatically driven capture of flowing rod-shaped and spherical silica particles from dilute solutions onto a flow chamber wall that carries the opposite electrostatic charge from the particles. Particle accumulation and orientation are measured in time at a fixed region on the wall of a shear flow chamber. Rod-shaped particle aspect ratios are 2.5-3.2 and particle lengths are 1.3 and 2.67 μm for two samples, while sphere diameters were 0.72, 0.96, and 2.0 μm for three samples. At a moderate wall shear rate of 22 s^-1, the particle accumulation for both rods and spheres is well described by diffusion-limited kinetics, demonstrating the limiting effect of particle diffusion in the near-wall boundary layer for electrostatically driven capture in this particle shape and size range. The significance of this finding is demonstrated in a calculation that shows that for delivery applications, nearly the same (within 10%) particle volume or mass is delivered to a surface at the diffusion-limited rate by rods and spheres. Therefore, in the absence of other motivating factors, the expense of developing rod-shaped microscale delivery packages to enhance capture from flow in the diffusion-limited simple shear regime is unwarranted. It is also interesting that the captured orientations of the larger rods, 2.6 μm in average length, were highly varied and insensitive to flow: a substantial fraction of rods were trapped in standing and slightly leaning orientations, touching the surface by their ends. Additionally, for particles that were substantially tipped over, there was only modest orientation in the flow direction. Taken together, these findings suggest that on the time scale of near-surface particle rotations, adhesion events are fast, trapping particles in orientations that do not necessarily maximize their favored adhesive contact or reduce hydrodynamic drag.

Reassessment of the Basis of Cell Size Control Based on Analysis of Cell-to-Cell Variability

Fundamental mechanisms governing cell size control and homeostasis are still poorly understood. The relationship between sizes at division and birth in single cells is used as a metric to categorize the basis of size homeostasis. Cells dividing at a fixed size regardless of birth size (sizer) are expected to show a division-birth slope of zero, whereas cells dividing after growing for a fixed size increment (adder) have an expected slope of +1. These two theoretical values are, however, rarely experimentally observed. For example, rod-shaped fission yeast Schizosaccharomyces pombe cells, which divide at a fixed surface area, exhibit a division-birth slope for cell lengths of 0.25 ± 0.02, significantly different from the expected sizer value of zero. Here, we investigate possible reasons for this discrepancy by developing a mathematical model of sizer control including the relevant sources of variation. Our results support pure sizer control and show that deviation from zero slope is exaggerated by measurement of an inappropriate geometrical quantity (e.g., length instead of area), combined with cell-to-cell radius variability. The model predicts that mutants with greater errors in size sensing or septum positioning paradoxically appear to behave as better sizers. Furthermore, accounting for cell width variability, we show that pure sizer control can in some circumstances reproduce the apparent adder behavior observed in Escherichia coli. These findings demonstrate that analysis of geometric variation can lead to new insights into cell size control.

Oscillatory surface rheotaxis of swimming E. coli bacteria

Bacterial contamination of biological channels, catheters or water resources is a major threat to public health, which can be amplified by the ability of bacteria to swim upstream. The mechanisms of this 'rheotaxis', the reorientation with respect to flow gradients, are still poorly understood. Here, we follow individual E. coli bacteria swimming at surfaces under shear flow using 3D Lagrangian tracking and fluorescent flagellar labelling. Three transitions are identified with increasing shear rate: Above a first critical shear rate, bacteria shift to swimming upstream. After a second threshold, we report the discovery of an oscillatory rheotaxis. Beyond a third transition, we further observe coexistence of rheotaxis along the positive and negative vorticity directions. A theoretical analysis explains these rheotaxis regimes and predicts the corresponding critical shear rates. Our results shed light on bacterial transport and reveal strategies for contamination prevention, rheotactic cell sorting, and microswimmer navigation in complex flow environments.

Dynamics of individual Brownian rods in a microchannel flow

We study the orientational dynamics of heavy silica microrods flowing through a microfluidic channel. Comparing experiments and Brownian dynamics simulations we identify different particle orbits, in particular in-plane tumbling behavior, which cannot be explained by classical Jeffery theory, and we relate this behavior to the rotational diffusion of the rods. By constructing the full, three-dimensional, orientation distribution, we describe the rod trajectories and quantify the persistence of Jeffery orbits using temporal correlation functions of the Jeffery constant. We find that our colloidal rods lose memory of their initial configuration in about a second, corresponding to half a Jeffery period.

Separation of spermatozoa from erythrocytes using their tumbling mechanism in a pinch flow fractionation device

Men suffering from azoospermia can father a child, by extracting spermatozoa from a testicular biopsy sample. The main complication in this procedure is the presence of an abundance of erythrocytes. Currently, the isolation of the few spermatozoa from the sample is manually performed due to ineffectiveness of filtering methods, making it time consuming and labor intensive. The spermatozoa are smaller in both width and height than any other cell type found in the sample, with a very small difference compared with the erythrocyte for the smallest, making this not the feature to base the extraction on. However, the length of the spermatozoon is 5× larger than the diameter of an erythrocyte and can be utilized. Here we propose a microfluidic chip, in which the tumbling behavior of spermatozoa in pinched flow fractionation is utilized to separate them from the erythrocytes. We show that we can extract 95% of the spermatozoa from a sample containing 2.5% spermatozoa, while removing around 90% of the erythrocytes. By adjusting the flow rates, we are able to increase the collection efficiency while slightly sacrificing the purity, tuning the solution for the available sample in the clinic.

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.

Spatial Cross-Correlated Diffusion of Colloids under Shear Flow

The spatial cross-correlated diffusion of colloidal particles is often used as an essential tool to study the dynamic properties of a fluid because it directly describes the hydrodynamic interaction between two particles in a fluid. However, the experimental measurement of cross-correlated diffusion can be substantially modified by even a weak shear flow. In this work, the effect of a shear flow on spatial cross-correlated diffusion is demonstrated using experimental measurements that show a clear dependence on pair angles. An analytical solution is proposed to explain the experimental observations. A numerical simulation is performed to systemically demonstrate the influence of shear flow on spatial cross-correlated diffusion. The results of the experiment, theoretical analysis, and numerical simulation agree well with each other. Therefore, this research provides a sensitive experimental method to determine the weak shear flow in any quasi-two-dimensional fluid systems.

Confined Flow: Consequences and Implications for Bacteria and Biofilms

Bacteria overwhelmingly live in geometrically confined habitats that feature small pores or cavities, narrow channels, or nearby interfaces. Fluid flows through these confined habitats are ubiquitous in both natural and artificial environments colonized by bacteria. Moreover, these flows occur on time and length scales comparable to those associated with motility of bacteria and with the formation and growth of biofilms, which are surface-associated communities that house the vast majority of bacteria to protect them from host and environmental stresses. This review describes the emerging understanding of how flow near surfaces and within channels and pores alters physical processes that control how bacteria disperse, attach to surfaces, and form biofilms. This understanding will inform the development and deployment of technologies for drug delivery, water treatment, and antifouling coatings and guide the structuring of bacterial consortia for production of chemicals and pharmaceuticals.

Re-entrant bimodality in spheroidal chiral swimmers in shear flow

We use a continuum model to report on the behavior of a dilute suspension of chiral swimmers subject to externally imposed shear in a planar channel. Swimmer orientation in response to the imposed shear can be characterized by two distinct phases of behavior, corresponding to unimodal or bimodal distribution functions for swimmer orientation along the channel. These phases indicate the occurrence (or not) of a population splitting phenomenon changing the swimming direction of a macroscopic fraction of active particles to the exact opposite of that dictated by the imposed flow. We present a detailed quantitative analysis elucidating the complexities added to the population splitting behavior of swimmers when they are chiral. In particular, the transition from unimodal to bimodal and vice versa are shown to display a re-entrant behavior across the parameter space spanned by varying the chiral angular speed. We also present the notable effects of particle aspect ratio and self-propulsion speed on system phase behavior and discuss potential implications of our results in applications such as swimmer separation/sorting.

The Effect of Weak Confinement on the Orientation of Nanorods under Shear Flows

We performed a numerical analysis to study the orientation distribution of a dilute suspension of thin, rigid, rod-like nanoparticles under shearing flow near a solid boundary of weak confinement. Brownian dynamics simulation of a rod was performed under various ratios of shear rate and rod diffusivity (Peclet number), as well as the center-of-mass position (wall confinement). We discuss the effects of Peclet number and wall confinement on the angle distributions, Jeffery orbit distribution and average orientation moments. The average orientation moments, obtained as a function of Peclet number and wall confinement, can be used to improve a previous shear-induced migration model. We demonstrate that the improved model can give excellent prediction of the orientation moment distributions in a microchannel flow.

Stochastic Individual-Based Modeling of Bacterial Growth and Division Using Flow Cytometry

A realistic description of the variability in bacterial growth and division is critical to produce reliable predictions of safety risks along the food chain. Individual-based modeling of bacteria provides the theoretical framework to deal with this variability, but it requires information about the individual behavior of bacteria inside populations. In this work, we overcome this problem by estimating the individual behavior of bacteria from population statistics obtained with flow cytometry. For this objective, a stochastic individual-based modeling framework is defined based on standard assumptions during division and exponential growth. The unknown single-cell parameters required for running the individual-based modeling simulations, such as cell size growth rate, are estimated from the flow cytometry data. Instead of using directly the individual-based model, we make use of a modified Fokker-Plank equation. This only equation simulates the population statistics in function of the unknown single-cell parameters. We test the validity of the approach by modeling the growth and division of Pediococcus acidilactici within the exponential phase. Estimations reveal the statistics of cell growth and division using only data from flow cytometry at a given time. From the relationship between the mother and daughter volumes, we also predict that P. acidilactici divide into two successive parallel planes.

Population splitting of rodlike swimmers in Couette flow

We present a quantitative analysis on the response of a dilute active suspension of self-propelled rods (swimmers) in a planar channel subjected to an imposed shear flow. To best capture the salient features of the shear-induced effects, we consider the case of an imposed Couette flow, providing a constant shear rate across the channel. We argue that the steady-state behavior of swimmers can be understood in the light of a population splitting phenomenon, occurring as the shear rate exceeds a certain threshold, initiating the reversal of the swimming direction for a finite fraction of swimmers from down- to upstream or vice versa, depending on the swimmer position within the channel. Swimmers thus split into two distinct, statistically significant and oppositely swimming majority and minority populations. The onset of population splitting translates into a transition from a self-propulsion-dominated regime to a shear-dominated regime, corresponding to a unimodal-to-bimodal change in the probability distribution function of the swimmer orientation. We present a phase diagram in terms of the swim and flow Péclet numbers showing the separation of these two regimes by a discontinuous transition line. Our results shed further light on the behavior of swimmers in a shear flow and provide an explanation for the previously reported non-monotonic behavior of the mean, near-wall, parallel-to-flow orientation of swimmers with increasing shear strength.

Cell morphology governs directional control in swimming bacteria

The ability to rapidly detect and track nutrient gradients is key to the ecological success of motile bacteria in aquatic systems. Consequently, bacteria have evolved a number of chemotactic strategies that consist of sequences of straight runs and reorientations. Theoretically, both phases are affected by fluid drag and Brownian motion, which are themselves governed by cell geometry. Here, we experimentally explore the effect of cell length on control of swimming direction. We subjected Escherichia coli to an antibiotic to obtain motile cells of different lengths, and characterized their swimming patterns in a homogeneous medium. As cells elongated, angles between runs became smaller, forcing a change from a run-and-tumble to a run-and-stop/reverse pattern. Our results show that changes in the motility pattern of microorganisms can be induced by simple morphological variation, and raise the possibility that changes in swimming pattern may be triggered by both morphological plasticity and selection on morphology.

Threshold effect of growth rate on population variability of Escherichia coli cell lengths

A long-standing question in biology is the effect of growth on cell size. Here, we estimate the effect of Escherichia coli growth rate (r) on population cell size distributions by estimating the coefficient of variation of cell lengths (CV_L) from image analysis of fixed cells in DIC microscopy. We find that the CV_L is constant at growth rates less than one division per hour, whereas above this threshold, CV_L increases with an increase in the growth rate. We hypothesize that stochastic inhibition of cell division owing to replication stalling by a RecA-dependent mechanism, combined with the growth rate threshold of multi-fork replication (according to Cooper and Helmstetter), could form the basis of such a threshold effect. We proceed to test our hypothesis by increasing the frequency of stochastic stalling of replication forks with hydroxyurea (HU) treatment and find that cell length variability increases only when the growth rate exceeds this threshold. The population effect is also reproduced in single-cell studies using agar-pad cultures and 'mother machine'-based experiments to achieve synchrony. To test the role of RecA, critical for the repair of stalled replication forks, we examine the CV_L of E. coli ΔrecA cells. We find cell length variability in the mutant to be greater than wild-type, a phenotype that is rescued by plasmid-based RecA expression. Additionally, we find that RecA-GFP protein recruitment to nucleoids is more frequent at growth rates exceeding the growth rate threshold and is further enhanced on HU treatment. Thus, we find growth rates greater than a threshold result in increased E. coli cell lengths in the population, and this effect is, at least in part, mediated by RecA recruitment to the nucleoid and stochastic inhibition of division.

Threshold effect of growth rate on population variability of Escherichia coli cell lengths

A long-standing question in biology is the effect of growth on cell size. Here, we estimate the effect of Escherichia coli growth rate (r) on population cell size distributions by estimating the coefficient of variation of cell lengths (CV_L) from image analysis of fixed cells in DIC microscopy. We find that the CV_L is constant at growth rates less than one division per hour, whereas above this threshold, CV_L increases with an increase in the growth rate. We hypothesize that stochastic inhibition of cell division owing to replication stalling by a RecA-dependent mechanism, combined with the growth rate threshold of multi-fork replication (according to Cooper and Helmstetter), could form the basis of such a threshold effect. We proceed to test our hypothesis by increasing the frequency of stochastic stalling of replication forks with hydroxyurea (HU) treatment and find that cell length variability increases only when the growth rate exceeds this threshold. The population effect is also reproduced in single-cell studies using agar-pad cultures and 'mother machine'-based experiments to achieve synchrony. To test the role of RecA, critical for the repair of stalled replication forks, we examine the CV_L of E. coli ΔrecA cells. We find cell length variability in the mutant to be greater than wild-type, a phenotype that is rescued by plasmid-based RecA expression. Additionally, we find that RecA-GFP protein recruitment to nucleoids is more frequent at growth rates exceeding the growth rate threshold and is further enhanced on HU treatment. Thus, we find growth rates greater than a threshold result in increased E. coli cell lengths in the population, and this effect is, at least in part, mediated by RecA recruitment to the nucleoid and stochastic inhibition of division.

Magnetic separation of microparticles by shape

Accurate separation of microparticles by shape has diverse applications in biology and biotechnology, but is a significant challenge in separation science and engineering. We demonstrate a simple and effective mechanism that can achieve shape-based separation of magnetic particles in microscale flows. In this method, a uniform magnetic field is applied perpendicularly to the flow direction, and causes shape-dependent lateral migration of the particles. Using high-speed imaging, we studied the rotational dynamics of the ellipsoidal particles. It is found that the lateral migration is correlated with the asymmetric rotation of the particles. Different from existing techniques that use magnetic forces, our method uses shape-dependent magnetic torque but zero magnetic force.

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.

Tumbling of a Brownian particle in an extensional flow

The phenomenon of tumbling of microscopic objects is commonly associated with shear flows. We address the question of whether tumbling can also occur in stretching-dominated flows. To answer this, we study the dynamics of a semi-flexible trumbbell in a planar extensional velocity field. We show that the trumbbell undergoes a random tumbling-through-folding motion. The probability distribution of long tumbling times is exponential with a time scale exponentially increasing with the Weissenberg number.

Rheotaxis of spherical active particles near a planar wall

For active particles the interplay between the self-generated hydrodynamic flow and an external shear flow, especially near bounding surfaces, can result in a rich behavior of the particles not easily foreseen from the consideration of the active and external driving mechanisms in isolation. For instance, under certain conditions, the particles exhibit "rheotaxis", i.e., they align their direction of motion with the plane of shear spanned by the direction of the flow and the normal of the bounding surface and move with or against the flow. To date, studies of rheotaxis have focused on elongated particles (e.g., spermatozoa), for which rheotaxis can be understood intuitively in terms of a "weather vane" mechanism. Here we investigate the possibility that spherical active particles, for which the "weather vane" mechanism is excluded due to the symmetry of the shape, may nevertheless exhibit rheotaxis. Combining analytical and numerical calculations, we show that, for a broad class of spherical active particles, rheotactic behavior may emerge via a mechanism which involves "self-trapping" near a hard wall owing to the active propulsion of the particles, combined with their rotation, alignment, and "locking" of the direction of motion into the shear plane. In this state, the particles move solely up- or downstream at a steady height and orientation.

Anisotropic particle in viscous shear flow: Navier slip, reciprocal symmetry, and Jeffery orbit

The hydrodynamic reciprocal theorem for Stokes flows is generalized to incorporate the Navier slip boundary condition, which can be derived from Onsager's variational principle of least energy dissipation. The hydrodynamic reciprocal relations and the Jeffery orbit, both of which arise from the motion of a slippery anisotropic particle in a simple viscous shear flow, are investigated theoretically and numerically using the fluid particle dynamics method [Phys. Rev. Lett. 85, 1338 (2000)]. For a slippery elliptical particle in a linear shear flow, the hydrodynamic reciprocal relations between the rotational torque and the shear stress are studied and related to the Jeffery orbit, showing that the boundary slip can effectively enhance the anisotropy of the particle. Physically, by replacing the no-slip boundary condition with the Navier slip condition at the particle surface, the cross coupling between the rotational torque and the shear stress is enhanced, as manifested through a dimensionless parameter in both of the hydrodynamic reciprocal relations and the Jeffery orbit. In addition, simulations for a circular particle patterned with portions of no-slip and Navier slip are carried out, showing that the particle possesses an effective anisotropy and follows the Jeffery orbit as well. This effective anisotropy can be tuned by changing the ratio of no-slip portion to slip potion. The connection of the present work to nematic liquid crystals' constitutive relations is discussed.

Physics of bacterial near-surface motility using flagella and type IV pili: implications for biofilm formation

We review physically-motivated studies of bacterial near-surface motility driven by flagella and type IV pili (TfP) in the context of biofilm formation. We describe the motility mechanisms that individual bacteria deploying flagella and TfP use to move on and near surfaces, and discuss how the interactions of motility appendages with fluid and surfaces promote motility, attachment and dispersal of bacteria on surfaces prior to biofilm formation.

Continuous-flow Ferrohydrodynamic Sorting of Particles and Cells in Microfluidic Devices

A new sorting scheme based on ferrofluid hydrodynamics (ferrohydrodynamics) was used to separate mixtures of particles and live cells simultaneously. Two species of cells, including Escherichia coli and Saccharomyces cerevisiae, as well as fluorescent polystyrene microparticles were studied for their sorting throughput and efficiency. Ferrofluids are stable magnetic nanoparticles suspensions. Under external magnetic fields, magnetic buoyancy forces exerted on particles and cells lead to size-dependent deflections from their laminar flow paths and result in spatial separation. We report the design, modeling, fabrication and characterization of the sorting device. This scheme is simple, low-cost and label-free compared to other existing techniques.

Direct upstream motility in Escherichia coli

We provide an experimental demonstration of positive rheotaxis (rapid and continuous upstream motility) in wild-type Escherichia coli freely swimming over a surface. This hydrodynamic phenomenon is dominant below a critical shear rate and robust against Brownian motion and cell tumbling. We deduce that individual bacteria entering a flow system can rapidly migrate upstream (>20 μm/s) much faster than a gradually advancing biofilm. Given a bacterial population with a distribution of sizes and swim speeds, local shear rate near the surface determines the dominant hydrodynamic mode for motility, i.e., circular or random trajectories for low shear rates, positive rheotaxis for moderate flow, and sideways swimming at higher shear rates. Faster swimmers can move upstream more rapidly and at higher shear rates, as expected. Interestingly, we also find on average that both swim speed and upstream motility are independent of cell aspect ratio.

Transport of self-propelling bacteria in micro-channel flow

Understanding the collective motion of self-propelling organisms in confined geometries, such as that of narrow channels, is of great theoretical and practical importance. By means of numerical simulations we study the motion of model bacteria in 2D channels under different flow conditions: fluid at rest, steady and unsteady flow. We find aggregation of bacteria near channel walls and, in the presence of external flow, also upstream swimming, which turns out to be a very robust result. Detailed analysis of bacterial velocity and orientation fields allows us to quantify the phenomenon by varying cell density, channel width and fluid velocity. The tumbling mechanism turns out to have strong influence on velocity profiles and particle flow, resulting in a net upstream flow in the case of non-tumbling organisms. Finally we demonstrate that upstream flow can be enhanced by a suitable choice of an unsteady flow pattern.

Interplay between energetics and dynamics in bacterial motility

We study how self-propelled organisms administer their energetic resources in order to optimize space exploration. Noting the existence of two very different time scales, we use a quasistatic approximation to analyze the relation between bacterial dynamics and changes in the energy stored by a bacterium. We then find both steady-state and time-dependent solutions for the bacterial speed and stored energy. The model also predicts the volume of the region that a bacterium may visit in a resource-depleted medium.

Two-dimensional point singularity model of a low-Reynolds-number swimmer near a wall

This paper studies a simple two-dimensional model of a swimmer at low-Reynolds-number near a no-slip wall by utilizing methods of complex analysis. The swimmer is propelled by purely tangential surface deformations and is modeled by moving point singularities. The nonlinear dynamics of the swimmer is formulated explicitly, and its motion near the wall is fully characterized. The results show qualitative agreement with predictions of three-dimensional models and with motion experiments on a robotic swimmer. The success and simplicity of the model suggest that it will provide a simple way to study the dynamics of low-Reynolds-number swimmers in more complicated geometries.