Collective bacterial dynamics revealed using a three-dimensional population-scale defocused particle tracking technique

Potassium-mediated bacterial chemotactic response

Bacteria in biofilms secrete potassium ions to attract free swimming cells. However, the basis of chemotaxis to potassium remains poorly understood. Here, using a microfluidic device, we found that Escherichia coli can rapidly accumulate in regions of high potassium concentration on the order of millimoles. Using a bead assay, we measured the dynamic response of individual flagellar motors to stepwise changes in potassium concentration, finding that the response resulted from the chemotaxis signaling pathway. To characterize the chemotactic response to potassium, we measured the dose-response curve and adaptation kinetics via an Förster resonance energy transfer (FRET) assay, finding that the chemotaxis pathway exhibited a sensitive response and fast adaptation to potassium. We further found that the two major chemoreceptors Tar and Tsr respond differently to potassium. Tar receptors exhibit a biphasic response, whereas Tsr receptors respond to potassium as an attractant. These different responses were consistent with the responses of the two receptors to intracellular pH changes. The sensitive response and fast adaptation allow bacteria to sense and localize small changes in potassium concentration. The differential responses of Tar and Tsr receptors to potassium suggest that cells at different growth stages respond differently to potassium and may have different requirements for potassium.

Metapopulation model of phage therapy of an acute Pseudomonas aeruginosa lung infection

Infections caused by multi-drug resistant (MDR) pathogenic bacteria are a global health threat. Phage therapy, which uses phage to kill bacterial pathogens, is increasingly used to treat patients infected by MDR bacteria. However, the therapeutic outcome of phage therapy may be limited by the emergence of phage resistance during treatment and/or by physical constraints that impede phage-bacteria interactions in vivo. In this work, we evaluate the role of lung spatial structure on the efficacy of phage therapy for Pseudomonas aeruginosa infection. To do so, we developed a spatially structured metapopulation network model based on the geometry of the bronchial tree, and included the emergence of phage-resistant bacterial mutants and host innate immune responses. We model the ecological interactions between bacteria, phage, and the host innate immune system at the airway (node) level. The model predicts the synergistic elimination of a P. aeruginosa infection due to the combined effects of phage and neutrophils given sufficiently active immune states and suitable phage life history traits. Moreover, the metapopulation model simulations predict that local MDR pathogens are cleared faster at distal nodes of the bronchial tree. Notably, image analysis of lung tissue time series from wild-type and lymphocyte-depleted mice (n=13) revealed a concordant, statistically significant pattern: infection intensity cleared in the bottom before the top of the lungs. Overall, the combined use of simulations and image analysis of in vivo experiments further supports the use of phage therapy for treating acute lung infections caused by P. aeruginosa while highlighting potential limits to therapy given a spatially structured environment, such as impaired innate immune responses and low phage efficacy.

Methods and Measures for Investigating Microscale Motility

Motility is an essential factor for an organism's survival and diversification. With the advent of novel single-cell technologies, analytical frameworks, and theoretical methods, we can begin to probe the complex lives of microscopic motile organisms and answer the intertwining biological and physical questions of how these diverse lifeforms navigate their surroundings. Herein, we summarize the main mechanisms of microscale motility and give an overview of different experimental, analytical, and mathematical methods used to study them across different scales encompassing the molecular-, individual-, to population-level. We identify transferable techniques, pressing challenges, and future directions in the field. This review can serve as a starting point for researchers who are interested in exploring and quantifying the movements of organisms in the microscale world.

Machine learning-based motion tracking reveals an inverse correlation between adhesivity and surface motility of the leptospirosis spirochete

Bacterial motility is often a crucial virulence factor for pathogenic species. A common approach to study bacterial motility is fluorescent labeling, which allows detection of individual bacterial cells in a population or in host tissues. However, the use of fluorescent labeling can be hampered by protein expression stability and/or interference with bacterial physiology. Here, we apply machine learning to microscopic image analysis for label-free motion tracking of the zoonotic bacterium Leptospira interrogans on cultured animal cells. We use various leptospiral strains isolated from a human patient or animals, as well as mutant strains. Strains associated with severe disease, and mutant strains lacking outer membrane proteins (OMPs), tend to display fast mobility and reduced adherence on cultured kidney cells. Our method does not require fluorescent labeling or genetic manipulation, and thus could be applied to study motility of many other bacterial species.

Learning black- and gray-box chemotactic PDEs/closures from agent based Monte Carlo simulation data

We propose a machine learning framework for the data-driven discovery of macroscopic chemotactic Partial Differential Equations (PDEs)-and the closures that lead to them- from high-fidelity, individual-based stochastic simulations of Escherichia coli bacterial motility. The fine scale, chemomechanical, hybrid (continuum-Monte Carlo) simulation model embodies the underlying biophysics, and its parameters are informed from experimental observations of individual cells. Using a parsimonious set of collective observables, we learn effective, coarse-grained "Keller-Segel class" chemotactic PDEs using machine learning regressors: (a) (shallow) feedforward neural networks and (b) Gaussian Processes. The learned laws can be black-box (when no prior knowledge about the PDE law structure is assumed) or gray-box when parts of the equation (e.g. the pure diffusion part) is known and "hardwired" in the regression process. More importantly, we discuss data-driven corrections (both additive and functional), to analytically known, approximate closures.

Bacterial mobility and motility in porous media mimicked by microspheres

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

Flagellar Motility During E. coli Biofilm Formation Provides a Competitive Disadvantage Which Recedes in the Presence of Co-Colonizers

In nature, bacteria form biofilms in very diverse environments, involving a range of specific properties and exhibiting competitive advantages for surface colonization. However, the underlying mechanisms are difficult to decipher. In particular, the contribution of cell flagellar motility to biofilm formation remains unclear. Here, we examined the ability of motile and nonmotile E. coli cells to form a biofilm in a well-controlled geometry, both in a simple situation involving a single-species biofilm and in the presence of co-colonizers. Using a millifluidic channel, we determined that motile cells have a clear disadvantage in forming a biofilm, exhibiting a long delay as compared to nonmotile cells. By monitoring biofilm development in real time, we observed that the decisive impact of flagellar motility on biofilm formation consists in the alteration of surface access time potentially highly dependent on the geometry of the environment to be colonized. We also report that the difference between motile and nonmotile cells in the ability to form a biofilm diminishes in the presence of co-colonizers, which could be due to motility inhibition through the consumption of key resources by the co-colonizers. We conclude that the impact of flagellar motility on surface colonization closely depends on the environment properties and the population features, suggesting a unifying vision of the role of cell motility in surface colonization and biofilm formation.

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.

Methods to Evaluate Bacterial Motility and Its Role in Bacterial–Host Interactions

Bacterial motility is a widespread characteristic that can provide several advantages for the cell, allowing it to move towards more favorable conditions and enabling host-associated processes such as colonization. There are different bacterial motility types, and their expression is highly regulated by the environmental conditions. Because of this, methods for studying motility under realistic experimental conditions are required. A wide variety of approaches have been developed to study bacterial motility. Here, we present the most common techniques and recent advances and discuss their strengths as well as their limitations. We classify them as macroscopic or microscopic and highlight the advantages of three-dimensional imaging in microscopic approaches. Lastly, we discuss methods suited for studying motility in bacterial–host interactions, including the use of the zebrafish model.

Tuning chemotactic and diffusiophoretic spreading via hydrodynamic flows

The transport of microorganisms by chemotaxis is described by the same "log-sensing" response as colloids undergoing diffusiophoresis, despite their different mechanistic origins. We employ a recently-developed macrotransport theory to analyze the advective-diffusive transport of a chemotactic or diffusiophoretic colloidal species (both referred to as "colloids") in a circular tube under a steady pressure-driven flow (referred to as hydrodynamic flow) and transient solute gradient. First, we derive an exact solution to the log-sensing chemotactic/diffusiophoretic macrotransport equation. We demonstrate that a strong hydrodynamic flow can reduce spreading of solute-repelled colloids, by eliminating super-diffusion which occurs in an otherwise quiescent system. In contrast, hydrodynamic flows always enhance spreading of solute-attracted colloids. Second, we generalize the exact solution to show that the above tunable spreading phenomena by hydrodynamic flows persist quantitatively for decaying colloids, as may occur with cell death, for example. Third, we examine the spreading of chemotactic colloids by employing a more general model that captures a hallmark of chemotaxis, that log-sensing occurs only over a finite range of solute concentration. Apart from demonstrating for the first time the generality of the macrotransport theory to incorporate an arbitrary chemotactic flow model, we reveal via numerical solutions new regimes of anomalous spreading, which match qualitatively with experiments and are tunable by hydrodynamic flows. The results presented here could be employed to tailor chemotactic/diffusiophoretic colloid transport using hydrodynamic flows, which are central to applications such as oil recovery and bioremediation of aquifers.

Unraveling the Kinematics of Sperm Motion by Reconstructing the Flagellar Wave Motion in 3D

Sperm swim through the female reproductive tract by propagating a 3D flagellar wave that is self-regulatory in nature and driven by dynein motors. Traditional microscopy methods fail to capture the full dynamics of sperm flagellar activity as they only image and analyze sperm motility in 2D. Here, an automated platform to analyze sperm swimming behavior in 3D by using thin-lens approximation and high-speed dark field microscopy to reconstruct the flagellar waveform in 3D is presented. It is found that head-tethered mouse sperm exhibit a rolling beating behavior in 3D with the beating frequency of 6.2 Hz using spectral analysis. The flagellar waveform bends in 3D, particularly in the distal regions, but is only weakly nonplanar and ambidextrous in nature, with the local helicity along the flagellum fluctuating between clockwise and counterclockwise handedness. These findings suggest a nonpersistent flagellar helicity. This method provides new opportunities for the accurate measurement of the full motion of eukaryotic flagella and cilia which is essential for a biophysical understanding of their activation by dynein motors.

Premelting controlled active matter in ice

Self-propelled particles can undergo complex dynamics due to a range of bulk and surface interactions. When a particle is embedded in a host solid near its bulk melting temperature, the latter may melt at the surface of the former in a process known as interfacial premelting. The thickness of the melt film depends on the temperature, impurities, material properties and geometry. A temperature gradient is accompanied by a thermomolecular pressure gradient that drives the interfacial liquid from high to low temperatures and hence the particle from low to high temperatures, in a process called thermal regelation. When the host material is ice and the embedded particle is a biological entity, one has a particularly different form of active matter, which addresses interplay between a wide range of problems, from extremophiles of both terrestrial and exobiological relevance to ecological dynamics in Earth's cryosphere. Of basic importance in all such settings is the combined influence of biological activity and thermal regelation in controlling the redistribution of bioparticles. Therefore, we recast this class of regelation phenomena in the stochastic framework of active Ornstein-Uhlenbeck dynamics and make predictions relevant to this and related problems of interest in biological and geophysical problems. We examine how thermal regelation compromises paleoclimate studies in the context of ice core dating and we find that the activity influences particle dynamics during thermal regelation by enhancing the effective diffusion coefficient. Therefore, accurate dating relies on a quantitative treatment of both effects.

Modification to axial tracking for mobile magnetic microspheres

Three-dimensional particle tracking is a routine experimental procedure for various biophysical applications including magnetic tweezers. A common method for tracking the axial position of particles involves the analysis of diffraction rings whose pattern depends sensitively on the axial position of the bead relative to the focal plane. To infer the axial position, the observed rings are compared with reference images of a bead at known axial positions. Often the precision or accuracy of these algorithms is measured on immobilized beads over a limited axial range, while many experiments are performed using freely mobile beads. This inconsistency raises the possibility of incorrect estimates of experimental uncertainty. By manipulating magnetic beads in a bidirectional magnetic tweezer setup, we evaluated the error associated with tracking mobile magnetic beads and found that the error of tracking a moving magnetic bead increases by almost an order of magnitude compared to the error of tracking a stationary bead. We found that this additional error can be ameliorated by excluding the center-most region of the diffraction ring pattern from tracking analysis. Evaluation of the limitations of a tracking algorithm is essential for understanding the error associated with a measurement. These findings promise to bring increased resolution to three-dimensional bead tracking of magnetic microspheres.

Surveying a Swarm: Experimental Techniques to Establish and Examine Bacterial Collective Motion

The survival and successful spread of many bacterial species hinges on their mode of motility. One of the most distinct of these is swarming, a collective form of motility where a dense consortium of bacteria employ flagella to propel themselves across a solid surface. Surface environments pose unique challenges, derived from higher surface friction/tension and insufficient hydration. Bacteria have adapted by deploying an array of mechanisms to overcome these challenges. Beyond allowing bacteria to colonize new terrain in the absence of bulk liquid, swarming also bestows faster speeds and enhanced antibiotic resistance to the collective. These crucial attributes contribute to the dissemination, and in some cases pathogenicity, of an array of bacteria. This mini-review highlights; 1) aspects of swarming motility that differentiates it from other methods of bacterial locomotion. 2) Facilitatory mechanisms deployed by diverse bacteria to overcome different surface challenges. 3) The (often difficult) approaches required to cultivate genuine swarmers. 4) The methods available to observe and assess the various facets of this collective motion, as well as the features exhibited by the population as a whole.

Separation and enrichment of sodium-motile bacteria using cost-effective microfluidics

Many motile bacteria are propelled by the rotation of flagellar filaments. This rotation is driven by a membrane protein known as the stator-complex, which drives the rotor of the bacterial flagellar motor. Torque generation is powered in most cases by proton transit through membrane protein complexes known as stators, with the next most common ionic power source being sodium. Sodium-powered stators can be studied through the use of synthetic chimeric stators that combine parts of sodium- and proton-powered stator proteins. The most well studied example is the use of the sodium-powered PomA-PotB chimeric stator unit in the naturally proton-powered Escherichia coli. Here we designed a fluidics system at low cost for rapid prototyping to separate motile and non-motile populations of bacteria while varying the ionic composition of the media and thus the sodium-motive force available to drive this chimeric flagellar motor. We measured separation efficiencies at varying ionic concentrations and confirmed using fluorescence that our device delivered eightfold enrichment of the motile proportion of a mixed population. Furthermore, our results showed that we could select bacteria from reservoirs where sodium was not initially present. Overall, this technique can be used to implement the selection of highly motile fractions from mixed liquid cultures, with applications in directed evolution to investigate the adaptation of motility in bacterial ecosystems.

Bacteriophage-Based Biosensing of Pseudomonas aeruginosa: An Integrated Approach for the Putative Real-Time Detection of Multi-Drug-Resistant Strains

During the last decennium, it has become widely accepted that ubiquitous bacterial viruses, or bacteriophages, exert enormous influences on our planet’s biosphere, killing between 4–50% of the daily produced bacteria and constituting the largest genetic diversity pool on our planet. Currently, bacterial infections linked to healthcare services are widespread, which, when associated with the increasing surge of antibiotic-resistant microorganisms, play a major role in patient morbidity and mortality. In this scenario, Pseudomonas aeruginosa alone is responsible for ca. 13–15% of all hospital-acquired infections. The pathogen P. aeruginosa is an opportunistic one, being endowed with metabolic versatility and high (both intrinsic and acquired) resistance to antibiotics. Bacteriophages (or phages) have been recognized as a tool with high potential for the detection of bacterial infections since these metabolically inert entities specifically attach to, and lyse, bacterial host cells, thus, allowing confirmation of the presence of viable cells. In the research effort described herein, three different phages with broad lytic spectrum capable of infecting P. aeruginosa were isolated from environmental sources. The isolated phages were elected on the basis of their ability to form clear and distinctive plaques, which is a hallmark characteristic of virulent phages. Next, their structural and functional stabilization was achieved via entrapment within the matrix of porous alginate, biopolymeric, and bio-reactive, chromogenic hydrogels aiming at their use as sensitive matrices producing both color changes and/or light emissions evolving from a reaction with (released) cytoplasmic moieties, as a bio-detection kit for P. aeruginosa cells. Full physicochemical and biological characterization of the isolated bacteriophages was the subject of a previous research paper.

Swimming Escherichia coli Cells Explore the Environment by Lévy Walk

Escherichia coli cells swim in aqueous environment in a random walk of alternating runs and tumbles. The diffusion characteristics of this random walk remains unclear. In this study, by tracking the swimming of wild-type cells in a three-dimensional (3D) homogeneous environment, we found that their trajectories are superdiffusive, consistent with Lévy walk behavior. For comparison, we tracked the swimming of mutant cells that lack the chemotaxis signaling noise (the steady-state fluctuation of the concentration of the chemotaxis response regulator CheY-P) and found that their trajectories are normal diffusive. Therefore, wild-type E. coli cells explore the environment by Lévy walk, which originates from the chemotaxis signaling noise. This Lévy walk pattern enhances their efficiency in environmental exploration.IMPORTANCE E. coli cells explore the environment in a random walk of alternating runs and tumbles. By tracking the 3D trajectories of E. coli cells in an aqueous environment, we found that their trajectories are superdiffusive, with a power-law shape for the distribution of run lengths, which is characteristics of Lévy walk. We further show that this Lévy walk behavior is due to the random fluctuation of the output level of the bacterial chemotaxis pathway, and it enhances the efficiency of the bacteria in exploring the environment.

Dynamic swimming pattern of Pseudomonas aeruginosa near a vertical wall during initial attachment stages of biofilm formation

Studying the swimming behaviour of bacteria in 3 dimensions (3D) allows us to understand critical biological processes, such as biofilm formation. It is still unclear how near wall swimming behaviour may regulate the initial attachment and biofilm formation. It is challenging to address this as visualizing the movement of bacteria with reasonable spatial and temporal resolution in a high-throughput manner is technically difficult. Here, we compared the near wall (vertical) swimming behaviour of P. aeruginosa (PAO1) and its mutants ΔdipA (reduced in swarming motility and increased in biofilm formation) and ΔfimX (deficient in twitching motility and reduced in biofilm formation) using our new imaging technique based on light sheet microscopy. We found that P. aeruginosa (PAO1) increases its speed and changes its swimming angle drastically when it gets closer to a wall. In contrast, ΔdipA mutant moves toward the wall with steady speed without changing of swimming angle. The near wall behavior of ΔdipA allows it to be more effective to interact with the wall or wall-attached cells, thus leading to more adhesion events and a larger biofilm volume during initial attachment when compared with PAO1. Furthermore, we found that ΔfimX has a similar near wall swimming behavior as PAO1. However, it has a higher dispersal frequency and smaller biofilm formation when compared with PAO1 which can be explained by its poor twitching motility. Together, we propose that near wall swimming behavior of P. aeruginosa plays an important role in the regulation of initial attachment and biofilm formation.

Tumor spheroids under perfusion within a 3D microfluidic platform reveal critical roles of cell-cell adhesion in tumor invasion

Tumor invasion within the interstitial space is critically regulated by the force balance between cell-extracellular matrix (ECM) and cell-cell interactions. Interstitial flows (IFs) are present in both healthy and diseased tissues. However, the roles of IFs in modulating cell force balance and subsequently tumor invasion are understudied. In this article, we develop a microfluidic model in which tumor spheroids are embedded within 3D collagen matrices with well-defined IFs. Using co-cultured tumor spheroids (1:1 mixture of metastatic and non-tumorigenic epithelial cells), we show that IFs downregulate the cell-cell adhesion molecule E-cadherin on non-tumorigenic cells and promote tumor invasion. Our microfluidic model advances current tumor invasion assays towards a more physiologically realistic model using tumor spheroids instead of single cells under perfusion. We identify a novel mechanism by which IFs can promote tumor invasion through an influence on cell-cell adhesion within the tumor and highlight the importance of biophysical parameters in regulating tumor invasion.

Flagellar nanorobot with kinetic behavior investigation and 3D motion

Wirelessly controlled nanorobots have the potential to perform highly precise maneuvers within complex in vitro and in vivo environments. Flagellar nanorobots will be useful in a variety of biomedical applications, however, to date there has been little effort to investigate essential kinetic behavior changes related to the geometric properties of the nanorobot and effects imparted to it by nearby boundaries. Flagellar nanorobots are composed of an avidin-coated magnetic nanoparticle head (MH) and a single biotin-tipped repolymerized flagellum that are driven by a wirelessly generated rotating magnetic field. Nanorobots with different MHs and flagellar lengths were manually guided to perform complex swimming trajectories under both bright-field and fluorescence microscopy visualizations. The experimental results show that rotational frequency, handedness of rotation direction, MH size, flagellar length, and distance to the bottom boundary significantly affect the kinematics of the nanorobot. The results reported herein summarize fundamental research that will be used for the design specifications necessary for optimizing the application of helical nanorobotic devices for use in delivery of therapeutic and imaging agents. Additionally, robotic nanoswimmers were successfully navigated and tracked in 3D using quantitative defocusing, which will significantly improve the efficiency, function, and application of the flagellar nanorobot.

E. coli "super-contaminates" narrow ducts fostered by broad run-time distribution

One notable feature of bacterial motion is their ability to swim upstream along corners and crevices, by leveraging hydrodynamic interactions. This motion through anatomic ducts or medical devices might be at the origin of serious infections. However, it remains unclear how bacteria can maintain persistent upstream motion while exhibiting run-and-tumble dynamics. Here, we demonstrate that Escherichia coli can travel upstream in microfluidic devices over distances of 15 mm in times as short as 15 min. Using a stochastic model relating the run times to the time that bacteria spend on surfaces, we quantitatively reproduce the evolution of the contamination profiles when considering a broad distribution of run times. The experimental data cannot be reproduced using the usually accepted exponential distribution of run times. Our study demonstrates that the run-and-tumble statistics determine macroscopic bacterial transport properties. This effect, which we name "super-contamination," could explain the fast onset of some life-threatening medical emergencies.

Mean-field models in swarm robotics: a survey

We present a survey on the application of fluid approximations, in the form of mean-field models, to the design of control strategies in swarm robotics. Mean-field models that consist of ordinary differential equations, partial differential equations, and difference equations have been used in the swarm robotics literature, depending on whether the state of each agent and the time variable take values from a discrete or continuous set. These macroscopic models are independent of the number of agents in the swarm, and hence can be used to synthesize robot control strategies in a scalable manner, in contrast to individual-based microscopic models of swarms that represent finite numbers of discrete agents. Moreover, mean-field models are amenable to rigorous investigation using tools from dynamical systems theory, control theory, stochastic processes, and analysis of partial differential equations, enabling new insights and provable guarantees on the dynamics of collective behaviors. In this paper, we survey the applications of these models to problems in swarm robotics that include coverage, task allocation, self-assembly, consensus, and environmental mapping.

Single Cells Exhibit Differing Behavioral Phases during Early Stages of Pseudomonas aeruginosa Swarming

Pseudomonas aeruginosa is among the many bacteria that swarm, where groups of cells coordinate to move over surfaces. It has been challenging to determine the behavior of single cells within these high-cell-density swarms. To track individual cells within P. aeruginosa swarms, we imaged a fluorescently labeled subset of the larger population. Single cells at the advancing swarm edge varied in their motility dynamics as a function of time. From these data, we delineated four phases of early swarming prior to the formation of the tendril fractals characteristic of P. aeruginosa swarming by collectively considering both micro- and macroscale data. We determined that the period of greatest single-cell motility does not coincide with the period of greatest collective swarm expansion. We also noted that flagellar, rhamnolipid, and type IV pilus motility mutants exhibit substantially less single-cell motility than the wild type.IMPORTANCE Numerous bacteria exhibit coordinated swarming motion over surfaces. It is often challenging to assess the behavior of single cells within swarming communities due to the limitations of identifying, tracking, and analyzing the traits of swarming cells over time. Here, we show that the behavior of Pseudomonas aeruginosa swarming cells can vary substantially in the earliest phases of swarming. This is important to establish that dynamic behaviors should not be assumed to be constant over long periods when predicting and simulating the actions of swarming bacteria.

Dynamics-dependent density distribution in active suspensions

Self-propelled colloids constitute an important class of intrinsically non-equilibrium matter. Typically, such a particle moves ballistically at short times, but eventually changes its orientation, and displays random-walk behaviour in the long-time limit. Theory predicts that if the velocity of non-interacting swimmers varies spatially in 1D, v(x), then their density ρ(x) satisfies ρ(x) = ρ(0)v(0)/v(x), where x = 0 is an arbitrary reference point. Such a dependence of steady-state ρ(x) on the particle dynamics, which was the qualitative basis of recent work demonstrating how to 'paint' with bacteria, is forbidden in thermal equilibrium. Here we verify this prediction quantitatively by constructing bacteria that swim with an intensity-dependent speed when illuminated and implementing spatially-resolved differential dynamic microscopy (sDDM) for quantitative analysis over millimeter length scales. Applying a spatial light pattern therefore creates a speed profile, along which we find that, indeed, ρ(x)v(x) = constant, provided that steady state is reached.

Interference Disturbance Analysis Enables Single-Cell Level Growth and Mobility Characterization for Rapid Antimicrobial Susceptibility Testing

To support the emerging battle against antimicrobial resistance (AMR), detection methods that allow fast and accurate antimicrobial susceptibility testing (AST) are urgently needed. The early identification and application of an appropriate antibiotic treatment leads to lower mortality rates and substantial cost savings and prevents the development of resistant pathogens. In this work, we present a diffraction-based method, which is capable of quantitative bacterial growth, mobility, and susceptibility measurements. The method is based on the temporal analysis of the intensity of a light diffraction peak, which arises due to interference at a periodic pattern of gold nanostructures. The presence of bacteria disturbs the constructive interference, leading to an intensity decrease and thus allows the monitoring of bacterial growth in very low volumes. We demonstrate the direct correlation of the decrease in diffraction peak intensity with bacterial cell number starting from single cells and show the capability for rapid high-throughput AST measurements by determining the minimum inhibitory concentration for three different antimicrobials in less than 2-3 h as well as the susceptibility in less than 30-40 min. Furthermore, bacterial mobility is obtained from short-term fluctuations of the diffraction peak intensity and is shown to decrease by a factor of 3 during bacterial attachment to a surface. This multiparameter detection method allows for rapid AST of planktonic and of biofilm-forming bacterial strains in low volumes and in real-time without the need of high initial cell numbers.

The 3D architecture of a bacterial swarm has implications for antibiotic tolerance

Swarming bacteria are an example of a complex, active biological system, where high cell density and super-diffusive cell mobility confer survival advantages to the group as a whole. Previous studies on the dynamics of the swarm have been limited to easily observable regions at the advancing edge of the swarm where cells are restricted to a plane. In this study, using defocused epifluorescence video imaging, we have tracked the motion of fluorescently labeled individuals within the interior of a densely packed three-dimensional (3D) region of a swarm. Our analysis reveals a novel 3D architecture, where bacteria are constrained by inter-particle interactions, sandwiched between two distinct boundary conditions. We find that secreted biosurfactants keep bacteria away from the swarm-air upper boundary, and added antibiotics at the lower swarm-surface boundary lead to their migration away from this boundary. Formation of the antibiotic-avoidance zone is dependent on a functional chemotaxis signaling system, in the absence of which the swarm loses its high tolerance to the antibiotics.

Anomalous Chained Turbulence in Actively Driven Flows on Spheres

Recent experiments demonstrate the importance of substrate curvature for actively forced fluid dynamics. Yet, the covariant formulation and analysis of continuum models for nonequilibrium flows on curved surfaces still poses theoretical challenges. Here, we introduce and study a generalized covariant Navier-Stokes model for fluid flows driven by active stresses in nonplanar geometries. The analytical tractability of the theory is demonstrated through exact stationary solutions for the case of a spherical bubble geometry. Direct numerical simulations reveal a curvature-induced transition from a burst phase to an anomalous turbulent phase that differs distinctly from externally forced classical 2D Kolmogorov turbulence. This new type of active turbulence is characterized by the self-assembly of finite-size vortices into linked chains of antiferromagnetic order, which percolate through the entire fluid domain, forming an active dynamic network. The coherent motion of the vortex chain network provides an efficient mechanism for upward energy transfer from smaller to larger scales, presenting an alternative to the conventional energy cascade in classical 2D turbulence.

Rapid, topology-based particle tracking for high-resolution measurements of large complex 3D motion fields

Spatiotemporal tracking of tracer particles or objects of interest can reveal localized behaviors in biological and physical systems. However, existing tracking algorithms are most effective for relatively low numbers of particles that undergo displacements smaller than their typical interparticle separation distance. Here, we demonstrate a single particle tracking algorithm to reconstruct large complex motion fields with large particle numbers, orders of magnitude larger than previously tractably resolvable, thus opening the door for attaining very high Nyquist spatial frequency motion recovery in the images. Our key innovations are feature vectors that encode nearest neighbor positions, a rigorous outlier removal scheme, and an iterative deformation warping scheme. We test this technique for its accuracy and computational efficacy using synthetically and experimentally generated 3D particle images, including non-affine deformation fields in soft materials, complex fluid flows, and cell-generated deformations. We augment this algorithm with additional particle information (e.g., color, size, or shape) to further enhance tracking accuracy for high gradient and large displacement fields. These applications demonstrate that this versatile technique can rapidly track unprecedented numbers of particles to resolve large and complex motion fields in 2D and 3D images, particularly when spatial correlations exist.

Painting with light-powered bacteria

Self-assembly is a promising route for micro- and nano-fabrication with potential to revolutionise many areas of technology, including personalised medicine. Here we demonstrate that external control of the swimming speed of microswimmers can be used to self assemble reconfigurable designer structures in situ. We implement such ‘smart templated active self assembly’ in a fluid environment by using spatially patterned light fields to control photon-powered strains of motile Escherichia coli bacteria. The physics and biology governing the sharpness and formation speed of patterns is investigated using a bespoke strain designed to respond quickly to changes in light intensity. Our protocol provides a distinct paradigm for self-assembly of structures on the 10 μm to mm scale.

The ability to generate microscale patterns and control microswimmers may be useful for engineering smart materials. Here Arlt et al. use genetically modified bacteria with fast response to changes in light intensity to produce light-induced patterns.

Modeling of active swimmer suspensions and their interactions with the environment

In this article, we review mathematical models used to study the behaviour of suspensions of micro-swimmers and the accompanying biophysical phenomena, with specific focus on stimulus response. The methods discussed encompass a range of interactions exhibited by the micro-swimmers; including passive hydrodynamic (gyrotaxis) and gravitational (gravitaxis) effects, and active responses to chemical cues (chemotaxis) and light intensities (phototaxis). We introduce the simplest models first, and then build towards more sophisticated recent developments, in the process, identifying the limitations of the former and the new results obtained by the latter. We comment on the accuracy/validity of the models adopted, based on the agreement between theoretical results and experimental observations. We conclude by identifying some of the open problems and associated challenges faced by researchers in the realm of active suspensions.

Multi-fractal characterization of bacterial swimming dynamics: a case study on real and simulated Serratia marcescens

To add to the current state of knowledge about bacterial swimming dynamics, in this paper, we study the fractal swimming dynamics of populations of Serratia marcescens bacteria both in vitro and in silico, while accounting for realistic conditions like volume exclusion, chemical interactions, obstacles and distribution of chemoattractant in the environment. While previous research has shown that bacterial motion is non-ergodic, we demonstrate that, besides the non-ergodicity, the bacterial swimming dynamics is multi-fractal in nature. Finally, we demonstrate that the multi-fractal characteristic of bacterial dynamics is strongly affected by bacterial density and chemoattractant concentration.

Visualizing Flagella while Tracking Bacteria

A complete description of the swimming behavior of a bacterium requires measurement of the displacement and orientation of the cell body together with a description of the movement of the flagella. We rebuilt a tracking microscope so that we could visualize flagellar filaments of tracked cells by fluorescence. We studied Escherichia coli (cells of various lengths, including swarm cells), Bacillus subtilis (wild-type and a mutant with fewer flagella), and a motile Streptococcus (now Enterococcus). The run-and-tumble statistics were nearly the same regardless of cell shape, length, and flagellation; however, swarm cells rarely tumbled, and cells of Enterococcus tended to swim in loops when moving slowly. There were events in which filaments underwent polymorphic transformations but remained in bundles, leading to small deflections in direction of travel. Tumble speeds were ∼2/3 as large as run speeds, and the rates of change of swimming direction while running or tumbling were smaller when cells swam more rapidly. If a smaller fraction of filaments were involved in tumbles, the tumble intervals were shorter and the angles between runs were smaller.

Radiative decay engineering 8: Coupled emission microscopy for lens-free high-throughput fluorescence detection

Fluorescence spectroscopy and imaging are now used throughout the biosciences. Fluorescence microscopes, spectrofluorometers, microwell plate readers and microarray imagers all use multiple optical components to collect, redirect and focus the emission onto single point or array imaging detectors. For almost all biological samples, except those with regular nanoscale features, emission occurs in all directions. With the exception of complex microscope objectives with large collection angles (NA ≤ 0.5), all these instruments collect only a small fraction of the total emission. Because of the increasing knowledge base on fluorophores within near-field (<200 nm) distances from plasmonic and photonic structures we can anticipate the development of compact devices in which the sample to be detected is located directly on solid state detectors such as CCDs or CMOS cameras. Near-field interactions of fluorophores with metallic or dielectric multi-layer structures (MLSs) can capture a large fraction of the total emission. Depending on the composition and dimensions of the MLSs, the spatial distribution of the sample emission results in distinct optical patterns on the detector surface. With either plain glass slides or MLSs the most commonly used front focal plane (FFP) images reveal the x-y spatial distribution of emission from the sample. Another approach, which is often used with two or three-dimensional nanostructures, is back focal plane (BFP) imaging. The BFP images reveal the angular distribution of the emission. The FFP and BFP images occur at certain distances from the sample which is determined by the details of the optical components. Obtaining these images requires multiple optical components and distances which are too large for the compact devices. For devices described in this paper, the images will be detected at a fixed distance between the sample and some arbitrary distance below the MLS which is determined by the geometry and thicknesses of the components. We refer to measurements at these locations as out-of-focal plane (OFP) imaging. Herein we describe a method to measure the optical fields at micron and multi-micron distances below the MLS, which will represent the images seen by an optically coupled array detector. The possibility of sub-surface optical images is illustrated using five different multi-layer structures. This is accomplished using an optical configuration which allows measurement at a front focal plane (FFP), back focal plane (BFP) or any OFP locations. Our OFP imaging method provides a link between the FFP images which reveals the surface distribution of fluorophores with the BFP images that reveal the angular distribution of emission. This linkage can be useful when examining structures which have nanoscale features due to fluorescence or leakage radiation from nanostructures.

Lagrangian 3D tracking of fluorescent microscopic objects in motion

We describe the development of a tracking device, mounted on an epi-fluorescent inverted microscope, suited to obtain time resolved 3D Lagrangian tracks of fluorescent passive or active micro-objects in microfluidic devices. The system is based on real-time image processing, determining the displacement of a x, y mechanical stage to keep the chosen object at a fixed position in the observation frame. The z displacement is based on the refocusing of the fluorescent object determining the displacement of a piezo mover keeping the moving object in focus. Track coordinates of the object with respect to the microfluidic device as well as images of the object are obtained at a frequency of several tenths of Hertz. This device is particularly well adapted to obtain trajectories of motile micro-organisms in microfluidic devices with or without flow.

Simultaneous and quantitative monitoring of co-cultured Pseudomonas aeruginosa and Staphylococcus aureus with antibiotics on a diffusometric platform

Successful treatments against bacterial infections depend on antimicrobial susceptibility testing (AST). However, conventional AST requires more than 24 h to obtain an outcome, thereby contributing to high patient mortality. An antibiotic therapy based on experiences is therefore necessary for saving lives and escalating the emergence of multidrug-resistant pathogens. Accordingly, a fast and effective drug screen is necessary for the appropriate administration of antibiotics. The mixed pathogenic nature of infectious diseases emphasizes the need to develop an assay system for polymicrobial infections. On this basis, we present a novel technique for simultaneous and quantitative monitoring of co-cultured microorganisms by coupling optical diffusometry with bead-based immunoassays. This simple integration simultaneously achieves a rapid AST analysis for two pathogens. Triple color particles were simultaneously recorded and subsequently analyzed by functionalizing different fluorescent color particles with dissimilar pathogen-specific antibodies. Results suggested that the effect of the antibiotic, gentamicin, on co-cultured Pseudomonas aeruginosa and Staphylococcus aureus was effectively distinguished by the proposed technique. This study revealed a multiplexed and time-saving (within 2 h) platform with a small sample volume (~0.5 μL) and a low initial bacterial count (50 CFU per droplet, ~10⁵ CFU/mL) for continuously monitoring the growth of co-cultured microorganisms. This technique provides insights into timely therapies against polymicrobial diseases in the near future.

Motility of Escherichia coli in a quasi-two-dimensional porous medium

Bacterial migration through confined spaces is critical for several phenomena, such as biofilm formation, bacterial transport in soils, and bacterial therapy against cancer. In the present work, E. coli (strain K12-MG1655 WT) motility was characterized by recording and analyzing individual bacterium trajectories in a simulated quasi-two-dimensional porous medium. The porous medium was simulated by enclosing, between slide and cover slip, a bacterial-culture sample mixed with uniform 2.98-μm-diameter spherical latex particles. The porosity of the medium was controlled by changing the latex particle concentration. By statistically analyzing several trajectory parameters (instantaneous velocity, turn angle, mean squared displacement, etc.), and contrasting with the results of a random-walk model developed ad hoc, we were able to quantify the effects that different obstacle concentrations have upon bacterial motility.

Quantifying the Heat Dissipation from a Molecular Motor's Transport Properties in Nonequilibrium Steady States

Theoretical analysis, which maps single-molecule time trajectories of a molecular motor onto unicyclic Markov processes, allows us to evaluate the heat dissipated from the motor and to elucidate its dependence on the mean velocity and diffusivity. Unlike passive Brownian particles in equilibrium, the velocity and diffusion constant of molecular motors are closely inter-related. In particular, our study makes it clear that the increase of diffusivity with the heat production is a natural outcome of active particles, which is reminiscent of the recent experimental premise that the diffusion of an exothermic enzyme is enhanced by the heat released from its own catalytic turnover. Compared with freely diffusing exothermic enzymes, kinesin-1, whose dynamics is confined on one-dimensional tracks, is highly efficient in transforming conformational fluctuations into a locally directed motion, thus displaying a significantly higher enhancement in diffusivity with its turnover rate. Putting molecular motors and freely diffusing enzymes on an equal footing, our study offers a thermodynamic basis to understand the heat-enhanced self-diffusion of exothermic enzymes.

Spatial dispersal of bacterial colonies induces a dynamical transition from local to global quorum sensing

Bacteria communicate using external chemical signals called autoinducers (AI) in a process known as quorum sensing (QS). QS efficiency is reduced by both limitations of AI diffusion and potential interference from neighboring strains. There is thus a need for predictive theories of how spatial community structure shapes information processing in complex microbial ecosystems. As a step in this direction, we apply a reaction-diffusion model to study autoinducer signaling dynamics in a single-species community as a function of the spatial distribution of colonies in the system. We predict a dynamical transition between a local quorum sensing (LQS) regime, with the AI signaling dynamics primarily controlled by the local population densities of individual colonies, and a global quorum sensing (GQS) regime, with the dynamics being dependent on collective intercolony diffusive interactions. The crossover between LQS to GQS is intimately connected to a trade-off between the signaling network's latency, or speed of activation, and its throughput, or the total spatial range over which all the components of the system communicate.

Live from under the lens: exploring microbial motility with dynamic imaging and microfluidics

Motility is one of the most dynamic features of the microbial world. The ability to swim or crawl frequently governs how microorganisms interact with their physical and chemical environments, and underpins a myriad of microbial processes. The ability to resolve temporal dynamics through time-lapse video microscopy and the precise control of the physicochemical microenvironment afforded by microfluidics offer powerful new opportunities to study the many motility adaptations of microorganisms and thereby further our understanding of their ecology. In this Review, we outline recent insights into the motility strategies of microorganisms brought about by these techniques, including the hydrodynamic signature of microorganisms, their locomotion mechanics, chemotaxis, their motility near and on surfaces, swimming in moving fluids and motility in dense microbial suspensions.

Rapid Bead-Based Antimicrobial Susceptibility Testing by Optical Diffusometry

This study combined optical diffusometry and bead-based immunoassays to develop a novel technique for quantifying the growth of specific microorganisms and achieving rapid AST. Diffusivity rises when live bacteria attach to particles, resulting in additional energy from motile microorganisms. However, when UV-sterilized (dead) bacteria attach to particles, diffusivity declines. The experimental data are consistent with the theoretical model predicted according to the equivalent volume diameter. Using this diffusometric platform, the susceptibility of Pseudomonas aeruginosa to the antibiotic gentamicin was tested. The result suggests that the proliferation of bacteria is effectively controlled by gentamicin. This study demonstrated a sensitive (one bacterium on single particles) and time-saving (within 2 h) platform with a small sample volume (~0.5 μL) and a low initial bacteria count (50 CFU per droplet ~ 10⁵ CFU/mL) for quantifying the growth of microorganisms depending on Brownian motion. The technique can be applied further to other bacterial strains and increase the success of treatments against infectious diseases in the near future.

Rapid, high-throughput tracking of bacterial motility in 3D via phase-contrast holographic video microscopy

Tracking fast-swimming bacteria in three dimensions can be extremely challenging with current optical techniques and a microscopic approach that can rapidly acquire volumetric information is required. Here, we introduce phase-contrast holographic video microscopy as a solution for the simultaneous tracking of multiple fast moving cells in three dimensions. This technique uses interference patterns formed between the scattered and the incident field to infer the three-dimensional (3D) position and size of bacteria. Using this optical approach, motility dynamics of multiple bacteria in three dimensions, such as speed and turn angles, can be obtained within minutes. We demonstrated the feasibility of this method by effectively tracking multiple bacteria species, including Escherichia coli, Agrobacterium tumefaciens, and Pseudomonas aeruginosa. In addition, we combined our fast 3D imaging technique with a microfluidic device to present an example of a drug/chemical assay to study effects on bacterial motility.

High-throughput 3D tracking of bacteria on a standard phase contrast microscope

Bacteria employ diverse motility patterns in traversing complex three-dimensional (3D) natural habitats. 2D microscopy misses crucial features of 3D behaviour, but the applicability of existing 3D tracking techniques is constrained by their performance or ease of use. Here we present a simple, broadly applicable, high-throughput 3D bacterial tracking method for use in standard phase contrast microscopy. Bacteria are localized at micron-scale resolution over a range of 350 × 300 × 200 μm by maximizing image cross-correlations between their observed diffraction patterns and a reference library. We demonstrate the applicability of our technique to a range of bacterial species and exploit its high throughput to expose hidden contributions of bacterial individuality to population-level variability in motile behaviour. The simplicity of this powerful new tool for bacterial motility research renders 3D tracking accessible to a wider community and paves the way for investigations of bacterial motility in complex 3D environments.

Microscopy techniques used to study the movement of swimming microbes are limited to two dimensions or require sophisticated devices. Here, Taute et al. present a simple method for high-throughput 3D tracking of bacteria using standard phase contrast microscopy.

Swarming bacteria migrate by Lévy Walk

Individual swimming bacteria are known to bias their random trajectories in search of food and to optimize survival. The motion of bacteria within a swarm, wherein they migrate as a collective group over a solid surface, is fundamentally different as typical bacterial swarms show large-scale swirling and streaming motions involving millions to billions of cells. Here by tracking trajectories of fluorescently labelled individuals within such dense swarms, we find that the bacteria are performing super-diffusion, consistent with Lévy walks. Lévy walks are characterized by trajectories that have straight stretches for extended lengths whose variance is infinite. The evidence of super-diffusion consistent with Lévy walks in bacteria suggests that this strategy may have evolved considerably earlier than previously thought.

Swimming Motility Reduces Deposition to Silica Surfaces

The transport and fate of bacteria in porous media is influenced by physicochemical and biological properties. This study investigated the effect of swimming motility on the attachment of cells to silica surfaces through comprehensive analysis of cell deposition in model porous media. Distinct motilities were quantified for different strains using global and cluster-based statistical analyses of microscopic images taken under no-flow condition. The wild-type, flagellated strain DJ showed strong swimming as a result of the actively swimming subpopulation whose average speed was 25.6 μm/s; the impaired swimming of strain DJ77 was attributed to the lower average speed of 17.4 μm/s in its actively swimming subpopulation; and both the nonflagellated JZ52 and chemically treated DJ cells were nonmotile. The approach and deposition of these bacterial cells were analyzed in porous media setups, including single-collector radial stagnation point flow cells (RSPF) and two-dimensional multiple-collector micromodels under well-defined hydrodynamic conditions. In RSPF experiments, both swimming and nonmotile cells moved with the flow when at a distance ≥20 μm above the collector surface. Closer to the surface, DJ cells showed both horizontal and vertical movement, limiting their contact with the surface, while chemically treated DJ cells moved with the flow to reach the surface. These results explain how wild-type swimming reduces attachment. In agreement, the deposition in micromodels was also lowest for DJ compared with those for DJ77 and JZ52. Wild-type swimming specifically reduced deposition on the upstream surfaces of the micromodel collectors. Conducted under environmentally relevant hydrodynamic conditions, the results suggest that swimming motility is an important characteristic for bacterial deposition and transport in the environment.

From Birds to Bacteria: Generalised Velocity Jump Processes with Resting States

There are various cases of animal movement where behaviour broadly switches between two modes of operation, corresponding to a long-distance movement state and a resting or local movement state. Here, a mathematical description of this process is formulated, adapted from Friedrich et al. (Phys Rev E, 74:041103, 2006b). The approach allows the specification any running or waiting time distribution along with any angular and speed distributions. The resulting system of integro-partial differential equations is tumultuous, and therefore, it is necessary to both simplify and derive summary statistics. An expression for the mean squared displacement is derived, which shows good agreement with experimental data from the bacterium Escherichia coli and the gull Larus fuscus. Finally, a large time diffusive approximation is considered via a Cattaneo approximation (Hillen in Discrete Continuous Dyn Syst Ser B, 5:299–318, 2003). This leads to the novel result that the effective diffusion constant is dependent on the mean and variance of the running time distribution but only on the mean of the waiting time distribution.

Fast, high-throughput measurement of collective behaviour in a bacterial population

Swimming bacteria explore their environment by performing a random walk, which is biased in response to, for example, chemical stimuli, resulting in a collective drift of bacterial populations towards 'a better life'. This phenomenon, called chemotaxis, is one of the best known forms of collective behaviour in bacteria, crucial for bacterial survival and virulence. Both single-cell and macroscopic assays have investigated bacterial behaviours. However, theories that relate the two scales have previously been difficult to test directly. We present an image analysis method, inspired by light scattering, which measures the average collective motion of thousands of bacteria simultaneously. Using this method, a time-varying collective drift as small as 50 nm s(-1) can be measured. The method, validated using simulations, was applied to chemotactic Escherichia coli bacteria in linear gradients of the attractant α-methylaspartate. This enabled us to test a coarse-grained minimal model of chemotaxis. Our results clearly map the onset of receptor methylation, and the transition from linear to logarithmic sensing in the bacterial response to an external chemoeffector. Our method is broadly applicable to problems involving the measurement of collective drift with high time resolution, such as cell migration and fluid flows measurements, and enables fast screening of tactic behaviours.

Transient freezing behavior in photophobic responses of Euglena gracilis investigated in a microfluidic device

We found that the transient freezing behavior in photophobic responses of Euglena gracilis is a good indicator of the metabolic status of the cells. The transient blue light photophobic responses of E. gracilis cells were investigated on-chip using a new measurement, 'trace momentum' (TM), to evaluate their swimming activity quantitatively in real time. When blue light of intensity >30 mW cm(-2) was repeatedly switched on and off, a large negative spike in the TM was observed at the onset of the 'blue-light-off' phase. Single-cell trace analysis at a blue light intensity of 40 mW cm(-2) showed that 48% (on average, n = 15) of tumbling Euglena cells ceased activity ('freezing') for 2-30 s at the onset of blue-light-off before commencing forward motion in a straight line (termed 'straightforward swimming'), while 45% smoothly commenced straightforward swimming without delay. The proportion of freezing Euglena cells depended on the blue light intensity (only 20% at 20 mW cm(-2)). When the cells were stimulated by four blue light pulses at the higher intensity, without pre-exposure, the transient freezing behavior was more prominent but, on repeating the stimuli after an 80 min interval in red light, the same cells did not freeze. This shows that the metabolism of the cells had changed to anti-freezing during the interval. The relationship between the interval time with/without light irradiation and the blue light adaptation was elucidated experimentally. The origin of the freezing behavior is considered to be a shortage of a metabolic substance that promotes smooth switching of flagellum movement from in situ rotation mode to a straightforward swimming mode.

Subdiffusion-reaction processes with A→B reactions versus subdiffusion-reaction processes with A+B→B reactions

We consider the subdiffusion-reaction process with reactions of a type A+B→B (in which particles A are assumed to be mobile, whereas B are assumed to be static) in comparison to the subdiffusion-reaction process with A→B reactions which was studied by Sokolov, Schmidt, and Sagués [Phys. Rev. E 73, 031102 (2006)]. In both processes a rule that reactions can only occur between particles which continue to exist is taken into account. Although in both processes a probability of the vanishing of particle A due to a reaction is independent of both time and space variables (assuming that in the system with the A+B→B reactions, particles B are distributed homogeneously), we show that subdiffusion-reaction equations describing these processes as well as their Green's functions are qualitatively different. The reason for this difference is as follows. In the case of the former reaction, particles A and B have to meet with some probability before the reaction occurs in contradiction with the case of the latter reaction. For the subdiffusion process with the A+B→B reactions we consider three models which differ in some details concerning a description of the reactions. We base the method considered in this paper on a random walk model in a system with both discrete time and discrete space variables. Then the system with discrete variables is transformed into a system with both continuous time and continuous space variables. Such a method seems to be convenient in analyzing subdiffusion-reaction processes with partially absorbing or partially reflecting walls. The reason is that within this method we can determine Green's functions without a necessity of solving a fractional differential subdiffusion-reaction equation with boundary conditions at the walls. As an example, we use the model to find the Green's functions for a subdiffusive reaction system (with the reactions mentioned above), which is bounded by a partially absorbing wall. This example shows how the model can be used to analyze the subdiffusion-reaction process in a system with partially absorbing or reflecting thin membranes. Employing a simple phenomenological model, we also derive equations related to the reaction parameters used in the considered models.

An adaptive algorithm for tracking 3D bead displacements: application in biological experiments

This paper presents a feature-vector-based relaxation method (FVRM) to track bead displacements within a three-dimensional (3D) volume. FVRM merges the feature vector method, a technique used in tracking bead displacements in biological gels, with the relaxation method, an algorithm employed successfully in tracking bead pairs in fluids. More specifically, FVRM evaluates the probability of a bead pairing event based on the quasi-rigidity condition between the feature vectors of a bead and its candidate positions within a searching domain. Computational efficiency is improved via the introduction of an adaptive searching domain size and mismatches are reduced via a two-directional matching strategy. The algorithm is validated using simulated 3D bead displacements caused by a force dipole within a linear elastic gel. Results demonstrate a consistently high recovery ratio (above 98%) and low mismatch ratio (below 0.1%) for tracking parameter (mean bead distance/maximum bead displacement) greater than 0.73.