Hydrodynamic interaction between two copepods: a numerical study

Numerical simulations were carried out to compute the flow fieldaround two tethered, stationary or swimming model-copepods withvaried separation distances between them and for different relativebody positions and orientations. Based on each simulated flowfield, the power expended by each copepod in generating theflow field and volumetric flux through the capture area of eachcopepod were calculated. The geometry of the flow field aroundeach copepod was visualized by tracking fluid particles to constructstream tubes. The hydrodynamic force on each copepod was calculated.Also, velocity magnitudes and deformation rates were calculatedalong a line just above the antennules of each copepod. Allthe results were compared to the counterpart results for a solitarycopepod (stationary or swimming) to evaluate the hydrodynamicinteraction between the two copepods. The calculations of thepower and volumetric flux show that no energetic benefits areavailable for two copepods in close proximity. The results ofthe stream tube and force calculations show that when two copepodsare in close proximity, the hydrodynamic interaction betweenthem distorts the geometry of the flow field around each copepodand changes the hydrodynamic force on each copepod. Two beneficialroles of the hydrodynamic interactions are suggested for copepodswarms: (1) to maintain the integrity of the swarms and (2)to separate the swarming members with large nearest neighbourdistances (usually more than five body lengths). To preventstrong hydrodynamic interactions, copepods in swarms have toavoid positions of strong interactions, such as those directlyabove or below their neighbours. The results of the velocitymagnitudes and deformation rates demonstrate that the hydrodynamicinteraction between two copepods generates the hydrodynamicsignals detectable by the setae on each copepod's antennules.Based on the threshold of Yen et al. (1992), the results showthat the detection distance between two copepods of comparablesize is about two to five body lengths. Copepods may employa simple form of pattern recognition to detect the distance,speed and direction of an approaching copepod of comparablesize.     

Hydrodynamic interaction of two unsteady model microorganisms

The study of pair-wise interactions between swimming microorganisms is fundamental to the understanding of the rheological and transport properties of semi-dilute suspensions. In this paper, the hydrodynamic interaction of two ciliated microorganisms is investigated numerically using a boundary-element method, and the microorganisms are modeled as spherical squirmers that swim by time-dependent surface deformations. The results show that the inclusion of the unsteady terms in the ciliary propulsion model has a large impact on the trajectories of the interacting cells, and causes a significant change in scattering angles with potential important consequences on the diffusion properties of semi-dilute suspensions. Furthermore, the analysis of the shear stress acting on the surface of the microorganisms revealed that the duration and the intensity of the near-field interaction are significantly modified by the presence of unsteadiness. This observation may account for the hydrodynamic nature of randomness in some biological reactions, and supersedes the distinction between intrinsic randomness and hydrodynamic interactions, adding a further element to the understanding and modeling of interacting microorganisms.     

Mechanisms and rates of bacterial colonization of sinking aggregates

Quantifying the rate at which bacteria colonize aggregates is a key to understanding microbial turnover of aggregates. We used encounter models based on random walk and advection-diffusion considerations to predict colonization rates from the bacteria's motility patterns (swimming speed, tumbling frequency, and turn angles) and the hydrodynamic environment (stationary versus sinking aggregates). We then experimentally tested the models with 10 strains of bacteria isolated from marine particles: two strains were nonmotile; the rest were swimming at 20 to 60 microm s(-1) with different tumbling frequency (0 to 2 s(-1)). The rates at which these bacteria colonized artificial aggregates (stationary and sinking) largely agreed with model predictions. We report several findings. (i) Motile bacteria rapidly colonize aggregates, whereas nonmotile bacteria do not. (ii) Flow enhances colonization rates. (iii) Tumbling strains colonize aggregates enriched with organic substrates faster than unenriched aggregates, while a nontumbling strain did not. (iv) Once on the aggregates, the bacteria may detach and typical residence time is about 3 h. Thus, there is a rapid exchange between attached and free bacteria. (v) With the motility patterns observed, freely swimming bacteria will encounter an aggregate in <1 day at typical upper-ocean aggregate concentrations. This is faster than even starving bacteria burn up their reserves, and bacteria may therefore rely solely on aggregates for food. (vi) The net result of colonization and detachment leads to a predicted equilibrium abundance of attached bacteria as a function of aggregate size, which is markedly different from field observations. This discrepancy suggests that inter- and intraspecific interactions among bacteria and between bacteria and their predators may be more important than colonization in governing the population dynamics of bacteria on natural aggregates.     

The Long-Time Dynamics of Two Hydrodynamically-Coupled Swimming Cells

Swimming microorganisms such as bacteria or spermatozoa are typically found in dense suspensions, and exhibit collective modes of locomotion qualitatively different from that displayed by isolated cells. In the dilute limit where fluid-mediated interactions can be treated rigorously, the long-time hydrodynamics of a collection of cells result from interactions with many other cells, and as such typically eludes an analytical approach. Here, we consider the only case where such problem can be treated rigorously analytically, namely when the cells have spatially confined trajectories, such as the spermatozoa of some marine invertebrates. We consider two spherical cells swimming, when isolated, with arbitrary circular trajectories, and derive the long-time kinematics of their relative locomotion. We show that in the dilute limit where the cells are much further away than their size, and the size of their circular motion, a separation of time scale occurs between a fast (intrinsic) swimming time, and a slow time where hydrodynamic interactions lead to change in the relative position and orientation of the swimmers. We perform a multiple-scale analysis and derive the effective dynamical system—of dimension two—describing the long-time behavior of the pair of cells. We show that the system displays one type of equilibrium, and two types of rotational equilibrium, all of which are found to be unstable. A detailed mathematical analysis of the dynamical systems further allows us to show that only two cell-cell behaviors are possible in the limit of t→∞, either the cells are attracted to each other (possibly monotonically), or they are repelled (possibly monotonically as well), which we confirm with numerical computations. Our analysis shows therefore that, even in the dilute limit, hydrodynamic interactions lead to new modes of cell-cell locomotion.     

Mechanisms and Rates of Bacterial Colonization of Sinking Aggregates

Quantifying the rate at which bacteria colonize aggregates is a key to understanding microbial turnover of aggregates. We used encounter models based on random walk and advection-diffusion considerations to predict colonization rates from the bacteria's motility patterns (swimming speed, tumbling frequency, and turn angles) and the hydrodynamic environment (stationary versus sinking aggregates). We then experimentally tested the models with 10 strains of bacteria isolated from marine particles: two strains were nonmotile; the rest were swimming at 20 to 60 μm s⁻¹ with different tumbling frequency (0 to 2 s⁻¹). The rates at which these bacteria colonized artificial aggregates (stationary and sinking) largely agreed with model predictions. We report several findings. (i) Motile bacteria rapidly colonize aggregates, whereas nonmotile bacteria do not. (ii) Flow enhances colonization rates. (iii) Tumbling strains colonize aggregates enriched with organic substrates faster than unenriched aggregates, while a nontumbling strain did not. (iv) Once on the aggregates, the bacteria may detach and typical residence time is about 3 h. Thus, there is a rapid exchange between attached and free bacteria. (v) With the motility patterns observed, freely swimming bacteria will encounter an aggregate in <1 day at typical upper-ocean aggregate concentrations. This is faster than even starving bacteria burn up their reserves, and bacteria may therefore rely solely on aggregates for food. (vi) The net result of colonization and detachment leads to a predicted equilibrium abundance of attached bacteria as a function of aggregate size, which is markedly different from field observations. This discrepancy suggests that inter- and intraspecific interactions among bacteria and between bacteria and their predators may be more important than colonization in governing the population dynamics of bacteria on natural aggregates.     

Reversible and irreversible adhesion of motile Escherichia coli cells analyzed by total internal reflection aqueous fluorescence microscopy

The initial events in bacterial adhesion are often explained as resulting from electrostatic and van der Waals forces between the cell and the surface, as described by DLVO theory (developed by Derjaguin, Landau, Verwey, and Overbeek). Such a theory predicts that negatively charged bacteria will experience greater attraction toward a negatively charged surface as the ionic strength of the medium is increased. In the present study we observed both smooth-swimming and nonmotile Escherichia coli bacteria close to plain, positively, and hydrophobically coated quartz surfaces in high- and low-ionic-strength media by using total internal reflection aqueous fluorescence microscopy. We found that reversibly adhering cells (cells which continue to swim along the surface for extended periods) are too distant from the surface for this behavior to be explained by DLVO-type forces. However, cells which had become immobilized on the surface did seem to be affected by electrostatic interactions. We propose that the "force" holding swimming cells near the surface is actually the result of a hydrodynamic effect, causing the cells to swim at an angle along the glass, and that DLVO-type forces are responsible only for the observed immobilization of irreversibly adhering cells. We explain our observations within the context of a conceptual model in which bacteria that are interacting with the surface may be thought of as occupying one of three compartments: bulk fluid, near-surface bulk, and near-surface constrained. A cell in these compartments feels either no effect of the surface, only the hydrodynamic effect of the surface, or both the hydrodynamic and the physicochemical effects of the surface, respectively.     

Reversible and Irreversible Adhesion of Motile Escherichia coli Cells Analyzed by Total Internal Reflection Aqueous Fluorescence Microscopy

The initial events in bacterial adhesion are often explained as resulting from electrostatic and van der Waals forces between the cell and the surface, as described by DLVO theory (developed by Derjaguin, Landau, Verwey, and Overbeek). Such a theory predicts that negatively charged bacteria will experience greater attraction toward a negatively charged surface as the ionic strength of the medium is increased. In the present study we observed both smooth-swimming and nonmotile Escherichia coli bacteria close to plain, positively, and hydrophobically coated quartz surfaces in high- and low-ionic-strength media by using total internal reflection aqueous fluorescence microscopy. We found that reversibly adhering cells (cells which continue to swim along the surface for extended periods) are too distant from the surface for this behavior to be explained by DLVO-type forces. However, cells which had become immobilized on the surface did seem to be affected by electrostatic interactions. We propose that the “force” holding swimming cells near the surface is actually the result of a hydrodynamic effect, causing the cells to swim at an angle along the glass, and that DLVO-type forces are responsible only for the observed immobilization of irreversibly adhering cells. We explain our observations within the context of a conceptual model in which bacteria that are interacting with the surface may be thought of as occupying one of three compartments: bulk fluid, near-surface bulk, and near-surface constrained. A cell in these compartments feels either no effect of the surface, only the hydrodynamic effect of the surface, or both the hydrodynamic and the physicochemical effects of the surface, respectively.     

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.     

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.     

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 free-energy-based stochastic simulation of the Tar receptor complex

We recently developed a stochastic-based program that allows individual molecules in a cell signalling pathway to be simulated. This program has now been used to model the Tar complex, a multimeric signalling complex employed by coliform bacteria. This complex acts as a solid-state computational cassette, integrating and disseminating information on the presence of attractants and repellents in the environment of the bacterium. In our model, the Tar complex exists in one of two conformations which differ in the rate at which they generate labile phosphate groups and hence signal to the flagellar motor. Individual inputs to the complex (aspartate binding, methylation at different sites, binding of CheB, CheR and CheY) are represented as binary flags, and each combination of flags confers a different free energy to the two conformations. Binding and catalysis by the complex are performed stochastically according to the complete set of known reactions allowing the swimming performance of the bacterium to be predicted.The assumption of two conformational states together with the use of free energy values allows us to bring together seemingly unrelated experimental parameters. Because of thermodynamic constraints, we find that the binding affinity for aspartate is linked to changes in phosphorylation activity. We estimate the pattern of Tar methylation and effective affinity constant of receptors over a range of aspartate levels. We also obtain evidence that both the methylating and demethylating enzymes must operate exclusively on one or other of the two conformations, and that sites of methylation of the complex are occupied in sequential order rather than independently. Detailed analysis of the response to aspartate reveals several quantitative discrepancies between simulated and experimental data which indicate areas for future research.     

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.     

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.     

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     

The determination of drag in front crawl swimming

The measurement of drag while swimming (i.e. active drag) is a controversial issue. Therefore, in a group of six elite swimmers two active drag measurement methods were compared to assess whether both measure the same retarding force during swimming. In method 1 push-off forces are measured directly using the system to measure active drag (MAD-system). In method 2 (the velocity perturbation method, VPM) drag is estimated from the difference in swimming speed when subjects swim twice at maximal effort (assuming equal power output and assuming a quadratic drag-speed relationship): once swimming free, and once swimming with a hydrodynamic body attached that created a known additional resistance. The average drag for the VPM tests (53.2 N) was statistically significant and different from the active drag for the MAD-test (66.9 N), paired Student's t-test: 2.484, 12 DF, p=0.029. A post hoc analysis was performed to assess whether the two methods measure a different phenomenon. Based on the drag speed curve obtained with the MAD-system, the VPM-data were re-examined. For diverging drag determinations the assumption of equal power output of the 'free' trial (swimming free) vs. the towing trial (swimming with hydrodynamic buoy) appeared to be violated. The regression of the relative difference in force (MAD vs. VPM) on the relative difference in power (swimming free vs. swimming with hydrodynamic body) was: %Deltadrag=1.898 x %Deltapower -4.498, r2=0.88. This suggests that the major part of the difference in active drag values is due to a non-equal power output in the 'free' relative towing trial during the VPM-test. The simulation of the violation of the equal power output assumption and the calculation of the effect of an other than quadratic drag-speed relationship corroborated the tentative conclusion that both methods measure essentially the same phenomenon and that active drag differences can be explained by a violation of test assumptions.     

Probing surface structures of Shewanella spp. by microelectrophoresis

Long-range electrostatic forces substantially influence bacterial interactions and bacterial adhesion during the preliminary steps of biofilm formation. The strength of these forces depends strongly on the structure of the bacterium surfaces investigated. The latter may be addressed from appropriate analysis of electrophoretic mobility measurements. Due to the permeable character of the bacterium wall and/or surrounding polymer layer, bacteria may be regarded as paradigms of soft bioparticles. The electrophoretic motion of such particles in a direct-current electric field differs considerably from that of their rigid counterparts in the sense that electroosmotic flow takes place around and within the soft surface layer. Recent developments of electrokinetic theories for soft particles now render possible the evaluation of the softness degree (or equivalently the hydrodynamic permeability) from the raw electrokinetic data. In this article, the electrophoretic mobilities of three Shewanella strains (MR-4, CN32, and BrY) presenting various and well-characterized phenotypes of polymer fringe are reported over a wide range of pH and ionic strength conditions. The data are quantitatively analyzed on the basis of a rigorous numerical evaluation of the governing electrostatic and hydrodynamic equations for soft particles. It is clearly shown how the peculiar surface structures of the bacteria investigated are reflected in their electrohydrodynamic properties.     

Reinforcing effects of non-pathogenic bacteria and predation risk: from physiology to life history

The important ecological role of predation risk in shaping populations, communities and ecosystems is becoming increasingly clear. In this context, synergistic effects between predation risk and other natural stressors on prey organisms are gaining attention. Although non-pathogenic bacteria can be widespread in aquatic ecosystems, their role in mediating effects of predation risk has been ignored. We here address the hypothesis that non-pathogenic bacteria may reinforce the negative effects of predation risk in larvae of the damselfly Coenagrion puella. We found synergistic effects for all three life history variables studied: mortality increased, growth reductions were magnified and bacterial load was higher when both non-lethal stressors were combined. The combined exposure to the bacterium and predation risk considerably impaired the two key antipredator mechanisms of the damselfly larvae: they no longer reduced their food intake under predation risk and showed a synergistic reduction in escape swimming speed. The reinforcing negative effects on the fitness-related traits could be explained by the observed synergistic effects on food intake, swimming muscle mass, immune function and oxidative damage. These are likely widespread consequences of energetic constraints and increased metabolic rates associated with the fight-or-flight response. We therefore hypothesize that the here documented synergistic interactions with non-pathogenic bacteria may be widespread. Our results highlight the ignored ecological role of non-pathogenic bacteria in reinforcing the negative effects of predation risk on prey organisms.     

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.     

The Hydrodynamics of a Run-and-Tumble Bacterium Propelled by Polymorphic Helical Flagella

To study the swimming of a peritrichous bacterium such as Escherichia coli, which is able to change its swimming direction actively, we simulate the “run-and-tumble” motion by using a bead-spring model to account for: 1), the hydrodynamic and the mechanical interactions among the cell body and multiple flagella; 2), the reversal of the rotation of a flagellum in a tumble; and 3), the associated polymorphic transformations of the flagellum. Because a flexible hook connects the cell body and each flagellum, the flagella can take independent orientations with respect to the cell body. This simulation reproduces the experimentally observed behaviors of E. coli, namely, a three-dimensional random-walk trajectory in run-and-tumble motion and steady clockwise swimming near a wall. We show that the polymorphic transformation of a flagellum in a tumble facilitates the reorientation of the cell, and that the time-averaged flow-field near a cell in a run has double-layered helical streamlines, with a time-dependent flow magnitude large enough to affect the transport of surrounding chemoattractants.