Marine Bacterial Chemoresponse to a Stepwise Chemoattractant Stimulus

We found recently that polar flagellated marine bacterium Vibrio alginolyticus is capable of exhibiting taxis toward a chemical source in both forward and backward swimming directions. How the microorganism coordinates these two swimming intervals, however, is not known. The work presented herein is aimed at determining the response functions of the bacterium by applying a stepwise chemoattractant stimulus while it is swimming forward or backward. The important finding of our experiment is that the bacterium responds to an identical chemical signal similarly during the two swimming intervals. For weak stimuli, the difference is mainly in the amplitudes of the response functions while the reaction and adaptation times remain unchanged. In this linear-response regime, the amplitude in the forward swimming interval is approximately a factor of two greater than in the backward direction. Our observation suggests that the cell processes chemical signals identically in both swimming intervals, but the responses of the flagellar motor to the output of the chemotaxis network, the regulator CheY-P concentration, are different. The biological significance of this asymmetrical response in polar flagellated marine bacteria is discussed.     

Collective swimming and the dynamics of bacterial turbulence

To swim, a bacterium pushes against the fluid within which it is immersed, generating fluid flow that dies off on a length scale comparable to the size of the bacterium. However, in dense colonies of bacteria, the bacteria are close enough that flow generated by swimming is substantial. For these cases, complex flows can arise due to the interaction and feedback between the bacteria and the fluid. Recent experiments on dense populations of swimming Bacillus subtilis have revealed a volume fraction-dependent transition from random swimming to transient jet and vortex patterns in the bacteria/fluid mixture. The fluid motions that are observed are reminiscent of flows that are observed around translating objects at moderate to high Reynolds numbers. In this work, I present a two-phase model for the bacterial/fluid mixture. The model explains turbulent flows in terms of the dipole stress that the bacteria exert on the fluid, entropic elasticity due to the rod shape of each bacterium, and the torque on the bacteria due to fluid gradients. Solving the equations in two dimensions using realistic parameters, the model reproduces empirically observed velocity fields. Dimensional analysis provides scaling relations for the dependence of the characteristic scales on the model parameters.     

A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary

The singly flagellated bacterium, Vibrio alginolyticus, moves forward and backward by alternating the rotational direction of its flagellum. The bacterium has been observed retracing a previous path almost exactly and swimming in a zigzag pattern. In the presence of a boundary, however, the motion changes significantly, to something closer to a circular trajectory. Additionally, when the cell swims close to a wall, the forward and backward speeds differ noticeably. This study details a boundary element model for the motion of a bacterium swimming near a rigid boundary and the results of numerical analyses conducted using this model. The results reveal that bacterium motion is apparently influenced by pitch angle, i.e., the angle between the boundary and the swimming direction, and that forward motion is more stable than backward motion with respect to pitching of the bacterium. From these results, a set of diagrammatic representations have been created that explain the observed asymmetry in trajectory and speed between the forward and backward motions. For forward motion, a cell moving parallel to the boundary will maintain this trajectory. However, for backward motion, the resulting trajectory depends upon whether the bacterium is approaching or departing the boundary. Fluid-dynamic interactions between the flagellum and the boundary vary with cell orientation and cause peculiarities in the resulting trajectories.     

Study of the motion of magnetotactic bacteria

Motion of flagellate bacteria is considered from the point of view of rigid body mechanics. As a general case we consider a flagellate coccus magnetotactic bacterium swimming in a fluid in the presence of an external magnetic field. The proposed model generalizes previous approaches to the problem and allows one to access parameters of the motion that can be measured experimentally. The results suggest that the strong helical pattern observed in typical trajectories of magnetotactic bacteria can be a biological advantage complementary to magnetic orientation. In the particular case of zero magnetic interaction the model describes the motion of a non-magnetotactic coccus bacterium swimming in a fluid. Theoretical calculations based on experimental results are compared with the experimental track obtained by dark field optical microscopy. Correspondence to: H. G. P. Lins de Barros     

Biomechanical model of swimming rehabilitation after hip and knee surgery

As a low-to-moderate intensity rehabilitation exercise after hip and knee surgery, we propose a dynamical model of the legs motion through the water medium in freestyle and backstroke swimming. We formulate a general Kirchhoff-Lagrangian dynamics model of the legs-propulsion through the water in post-surgical rehabilitation swimming.We start by defining the two-leg-propulsion configuration manifold. This is composed of eight Euclidean groups of rigid motions in 3D space for each of the four leg segments. Next, we define Newton-Euler dynamics for each segment. This single segmental dynamics is further generalized into Lagrangian dynamics for the whole leg-propulsion system. Finally, the water effects are added in the form of Kirchhoff’s vector cross-products.In agreement with orthopaedic recommendations for post-surgical rehabilitation, numerical simulation is performed on a simplified version of the full Kirchhoff-Lagrangian dynamics model, which we call the “robotic swimming leg” – with intentionally reduced number of (microscopic, non-sagittal) degrees-of-freedom.The purpose of this development is both qualitative, for medical and physiotherapist practitioners to study, and quantitative, for biomechanics experts to analyze and further develop.     

An Element of Determinism in a Stochastic Flagellar Motor Switch

Marine bacterium Vibrio alginolyticus uses a single polar flagellum to navigate in an aqueous environment. Similar to Escherichia coli cells, the polar flagellar motor has two states; when the motor is counter-clockwise, the cell swims forward and when the motor is clockwise, the cell swims backward. V. alginolyticus also incorporates a direction randomization step at the start of the forward swimming interval by flicking its flagellum. To gain an understanding on how the polar flagellar motor switch is regulated, distributions of the forward Δ_f and backward Δ_b intervals are investigated herein. We found that the steady-state probability density functions, P(Δ_f) and P(Δ_b), of freely swimming bacteria are strongly peaked at a finite time, suggesting that the motor switch is not Poissonian. The short-time inhibition is sufficiently strong and long lasting, i.e., several hundred milliseconds for both intervals, which is readily observed and characterized. Treating motor reversal dynamics as a first-passage problem, which results from conformation fluctuations of the motor switch, we calculated P(Δ_f) and P(Δ_b) and found good agreement with the measurements.     

A Simple Technique Based on a Single Optical Trap for the Determination of Bacterial Swimming Pattern

Bacterial motility is associated to a wide range of biological processes and it plays a key role in the virulence of many pathogens. Here we describe a method to distinguish the dynamic properties of bacteria by analyzing the statistical functions derived from the trajectories of a bacterium trapped by a single optical beam. The approach is based on the model of the rotation of a solid optically trapped sphere. The technique is easily implemented in a biological laboratory, since with only a small number of optical and electronic components a simple biological microscope can be converted into the required analyzer. To illustrate the functionality of this method, we probed several serovar Typhimurium mutants that differed from the wild-type with respect to their swimming patterns. In a further application, the motility dynamics of the Typhimurium mutant were characterized.     

Switching of Swimming Modes in Magnetospirillium gryphiswaldense

The microaerophilic magnetotactic bacterium Magnetospirillum gryphiswaldense swims along magnetic field lines using a single flagellum at each cell pole. It is believed that this magnetotactic behavior enables cells to seek optimal oxygen concentration with maximal efficiency. We analyze the trajectories of swimming M. gryphiswaldense cells in external magnetic fields larger than the earth’s field, and show that each cell can switch very rapidly (in <0.2 s) between a fast and a slow swimming mode. Close to a glass surface, a variety of trajectories were observed, from straight swimming that systematically deviates from field lines to various helices. A model in which fast (slow) swimming is solely due to the rotation of the trailing (leading) flagellum can account for these observations. We determined the magnetic moment of this bacterium using a to our knowledge new method, and obtained a value of (2.0 ± 0.6) × 10^?16 A · m². This value is found to be consistent with parameters emerging from quantitative fitting of trajectories to our model.     

Variations in morphologic alterations in the hearts of white rats during adaptation to different types of physical loads

While adapting to physical loadings various in their character, most of rats develop a moderate hypertrophy in the right cardiac ventricle without any noticeable changes in the organ's mass. ECG dynamics is positive. Myocardial hypertrophy, at the expense of increasing mass of the left ventricle, is most regularly observed in animals subjected to forced endurance training (daily swimming); less regularly--if the loading is applied with intervals (swimming every other day) and is practically absent in rats performing work with force application. Pathological ECG changes occur more often on the background of myocardial hypertrophy and are brought about by dystrophic disorders in muscular fibres, their focal micronecrosis, by edema of the interstitial and perivascular tissue.     

Hydrodynamic interactions between two swimming bacteria

This article evaluates the hydrodynamic interactions between two swimming bacteria precisely. We assume that each bacterium is force free and torque free, with a Stokes flow field around it. The geometry of each bacterium is modeled as a spherical or spheroidal body with a single helical flagellum. The movements of two interacting bacteria in an infinite fluid otherwise at rest are computed using a boundary element method, and the trajectories of the two interacting bacteria and the stresslet are investigated. The results show that as the two bacteria approach each other, they change their orientations considerably in the near field. The bacteria always avoided each other; no stable pairwise swimming motion was observed in this study. The effects of the hydrodynamic interactions between two bacteria on the rheology and diffusivity of a semidilute bacterial suspension are discussed.     

Numerical streamline patterns at swimmer's surface using RANS equations

The objective of this article is to perform a numerical modeling on the flow dynamics around a competitive female swimmer during the underwater swimming phase for a velocity of 2.2 m/s corresponding to national swimming levels. Flow around the swimmer is assumed turbulent and simulated with a computational fluid dynamics method based on a volume control approach. The 3D numerical simulations have been carried out with the code ANSYS FLUENT and are presented using the standard k-ω turbulence model for a Reynolds number of 6.4 × 10(6). To validate the streamline patterns produced by the simulation, experiments were performed in the swimming pools of the National Institute of Sports and Physical Education in Paris (INSEP) by using the tufts method.     

Flow Loading Induces Oscillatory Trajectories in a Bloodstream Parasite

The dynamics of isolated microswimmers are studied in bounded flow using the African trypanosome, a unicellular parasite, as the model organism. With the help of a microfluidics platform, cells are subjected to flow and found to follow an oscillatory path that is well fit by a sine wave. The frequency and amplitudes of the oscillatory trajectories are dependent on the flow velocity and cell orientation. When traveling in such a manner, trypanosomes orient upstream while downstream-facing cells tumble within the same streamline. A comparison with immotile trypanosomes demonstrates that self-propulsion is essential to the trajectories of trypanosomes even at flow velocities up to ～40 times higher than their own swimming speed. These studies reveal important swimming dynamics that may be generally pertinent to the transport of microswimmers in flow and may be relevant to microbial pathogenesis.     

Swimming behavior of selected species of Archaea

The swimming behavior of Bacteria has been studied extensively, at least for some species like Escherichia coli. In contrast, almost no data have been published for Archaea on this topic. In a systematic study we asked how the archaeal model organisms Halobacterium salinarum, Methanococcus voltae, Methanococcus maripaludis, Methanocaldococcus jannaschii, Methanocaldococcus villosus, Pyrococcus furiosus, and Sulfolobus acidocaldarius swim and which swimming behavior they exhibit. The two Euryarchaeota M. jannaschii and M. villosus were found to be, by far, the fastest organisms reported up to now, if speed is measured in bodies per second (bps). Their swimming speeds, at close to 400 and 500 bps, are much higher than the speed of the bacterium E. coli or of a very fast animal, like the cheetah, each with a speed of ca. 20 bps. In addition, we observed that two different swimming modes are used by some Archaea. They either swim very rapidly, in a more or less straight line, or they exhibit a slower kind of zigzag swimming behavior if cells are in close proximity to the surface of the glass capillary used for observation. We argue that such a "relocate-and-seek" behavior enables the organisms to stay in their natural habitat.     

Residence time calculation for chemotactic bacteria within porous media

Local chemical gradients can have a significant impact on bacterial population distributions within subsurface environments by evoking chemotactic responses. These local gradients may be created by consumption of a slowly diffusing nutrient, generation of a local food source from cell lysis, or dissolution of nonaqueous phase liquids trapped within the interstices of a soil matrix. We used a random walk simulation algorithm to study the effect of a local microscopic gradient on the swimming behavior of bacteria in a porous medium. The model porous medium was constructed using molecular dynamics simulations applied to a fluid of equal-sized spheres. The chemoattractant gradient was approximated with spherical symmetry, and the parameters for the swimming behavior of soil bacterium Pseudomonas putida were based on literature values. Two different mechanisms for bacterial chemotaxis, one in which the bacteria responded to both positive and negative gradients, and the other in which they responded only to positive gradients, were compared. The results of the computer simulations showed that chemotaxis can increase migration through a porous medium in response to microscopic-scale gradients. The simulation results also suggested that a more significant role of chemotaxis may be to increase the residence time of the bacteria in the vicinity of an attractant source.     

Feedback control strategies for spatial navigation revealed by dynamic modelling of learning in the Morris water maze

The Morris water maze is an experimental procedure in which animals learn to escape swimming in a pool using environmental cues. Despite its success in neuroscience and psychology for studying spatial learning and memory, the exact mnemonic and navigational demands of the task are not well understood. Here, we provide a mathematical model of rat swimming dynamics on a behavioural level. The model consists of a random walk, a heading change and a feedback control component in which learning is reflected in parameter changes of the feedback mechanism. The simplicity of the model renders it accessible and useful for analysis of experiments in which swimming paths are recorded. Here, we used the model to analyse an experiment in which rats were trained to find the platform with either three or one extramaze cue. Results indicate that the 3-cues group employs stronger feedback relying only on the actual visual input, whereas the 1-cue group employs weaker feedback relying to some extent on memory. Because the model parameters are linked to neurological processes, identifying different parameter values suggests the activation of different neuronal pathways.     

A Computational Model of the Fluid Dynamics of Undulatory and Flagellar Swimming

We present a mathematical model and numerical method designedto study the fluid dynamics of swimming organisms. The fullNavier— Stokes equations are solved in a domain of fluidwithin which an organism undergoing time—dependent motionsis immersed. Of interest are both the dynamics of a single organismand the relationship of its morphology to its motility properties,as well as the collective hydrodynamic interactions of groupsof swimmers with each other and their environment. Biologicalapplications include spermatozoa motility in the reproductivetract, swimming of non-smooth filaments, and collective swimmingof algal cells.     

Swimming in circles: motion of bacteria near solid boundaries

Near a solid boundary, Escherichia coli swims in clockwise circular motion. We provide a hydrodynamic model for this behavior. We show that circular trajectories are natural consequences of force-free and torque-free swimming and the hydrodynamic interactions with the boundary, which also leads to a hydrodynamic trapping of the cells close to the surface. We compare the results of the model with experimental data and obtain reasonable agreement. In particular, the radius of curvature of the trajectory is observed to increase with the length of the bacterium body.     

Renewable fluid dynamic energy derived from aquatic animal locomotion

Aquatic animals swimming in isolation and in groups are known to extract energy from the vortices in environmental flows, significantly reducing muscle activity required for locomotion. A model for the vortex dynamics associated with this phenomenon is developed, showing that the energy extraction mechanism can be described by simple criteria governing the kinematics of the vortices relative to the body in the flow. In this way, we need not make direct appeal to the fluid dynamics, which can be more difficult to evaluate than the kinematics. Examples of these principles as exhibited in swimming fish and existing energy conversion devices are described. A benefit of the developed framework is that the potentially infinite-dimensional parameter space of the fluid-structure interaction is reduced to a maximum of eight combinations of three parameters. The model may potentially aid in the design and evaluation of unsteady aero- and hydrodynamic energy conversion systems that surpass the Betz efficiency limit of steady fluid dynamic energy conversion systems.     

Ion selectivity of the Vibrio alginolyticus flagellar motor.

The marine bacterium, Vibrio alginolyticus, normally requires sodium for motility. We found that lithium will substitute for sodium. In neutral pH buffers, the membrane potential and swimming speed of glycolyzing bacteria reached maximal values as sodium or lithium concentration was increased. While the maximal potentials obtained in the two cations were comparable, the maximal swimming speed was substantially lower in lithium. Over a wide range of sodium concentration, the bacteria maintained an invariant sodium electrochemical potential as determined by membrane potential and intracellular sodium measurements. Over this range the increase of swimming speed took Michaelis-Menten form. Artificial energization of swimming motility required imposition of a voltage difference in concert with a sodium pulse. The cation selectivity and concentration dependence exhibited by the motile apparatus depended on the viscosity of the medium. In high-viscosity media, swimming speeds were relatively independent of either ion type or concentration. These facts parallel and extend observations of the swimming behavior of bacteria propelled by proton-powered flagella. In particular, they show that ion transfers limit unloaded motor speed in this bacterium and imply that the coupling between ion transfers and force generation must be fairly tight.     

Evidence for two flagellar stators and their role in the motility of Pseudomonas aeruginosa

Pseudomonas aeruginosa is a ubiquitous bacterium capable of twitching, swimming, and swarming motility. In this study, we present evidence that P. aeruginosa has two flagellar stators, conserved in all pseudomonads as well as some other gram-negative bacteria. Either stator is sufficient for swimming, but both are necessary for swarming motility under most of the conditions tested, suggesting that these two stators may have different roles in these two types of motility.