Bacterial cell-body rotation driven by a single flagellar motor and by a bundle.

Using self-trapped Escherichia coli bacteria that have intact flagellar bundles on glass surfaces, we study statistical fluctuations of cell-body rotation in a steady (unstimulated) state. These fluctuations underline direction randomization of bacterial swimming trajectories and plays a fundamental role in bacterial chemotaxis. A parallel study is also conducted using a classical rotation assay in which cell-body rotation is driven by a single flagellar motor. These investigations allow us to draw the important conclusion that during periods of counterclockwise motor rotation, which contributes to a run, all flagellar motors are strongly correlated, but during the clockwise period, which contributes to a tumble, individual motors are uncorrelated in long times. Our observation is consistent with the physical picture that formation and maintenance of a coherent flagellar bundle is provided by a single dominant flagellum in the bundle.

Rotating Bacteria on Solid Surfaces without Tethering.

Bacterial motion is strongly affected by the presence of a surface. One of the hallmarks of swimming near a surface is a defined curvature of bacterial trajectories, underlining the importance of counter rotations of the cell body and flagellum for locomotion of the microorganism. We find that there is another mode of bacterial motion on solid surfaces, i.e., self trapping due to fluid flows created by a rotating flagellum perpendicular to the surface. For a rod-like bacterium, such as Escherichia coli, this creates a peculiar situation in that the bacterium appears to swim along a minor axis of the cell body and is pressed against the surface. Although a full hydrodynamic theory is still lacking to explain the self-trapping phenomenon, the effect is intriguing and can be exploited to study a variety of biophysical phenomena of swimming bacteria. In particular, we showed that self-trapped E. coli cells display a chemotaxis response that is identical to the classical rotation assay in which antibodies are used to physically "glue" a flagellum to the surface.

Biophysical basis for convergent evolution of two veil-forming microbes.

Microbes living in stagnant water typically rely on chemical diffusion to draw nutrients from their environment. The sulfur-oxidizing bacterium Thiovulum majus and the ciliate Uronemella have independently evolved the ability to form a 'veil', a centimetre-scale mucous sheet on which cells organize to produce a macroscopic flow. This flow pulls nutrients through the community an order of magnitude faster than diffusion. To understand how natural selection led these microbes to evolve this collective behaviour, we connect the physical limitations acting on individual cells to the cell traits. We show how diffusion limitation and viscous dissipation have led individual T. majus and Uronemella cells to display two similar characteristics. Both of these cells exert a force of approximately 40 pN on the water and attach to boundaries by means of a mucous stalk. We show how the diffusion coefficient of oxygen in water and the viscosity of water define the force the cells must exert. We then show how the hydrodynamics of filter-feeding orient a microbe normal to the surface to which it attaches. Finally, we combine these results with new observations of veil formation and a review of veil dynamics to compare the collective dynamics of these microbes. We conclude that this convergent evolution is a reflection of similar physical limitations imposed by diffusion and viscosity acting on individual cells.

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 Δf and backward Δb intervals are investigated herein. We found that the steady-state probability density functions, P(Δf) and P(Δb), 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(Δf) and P(Δb) and found good agreement with the measurements.

A Non-Poissonian Flagellar Motor Switch Increases Bacterial Chemotactic Potential.

We investigate bacterial chemotactic strategies using run-tumble and run-reverse-flick motility patterns. The former is typically observed in enteric bacteria such as Escherichia coli and Salmonella and the latter was recently observed in the marine bacteria Vibrio alginolyticus and is possibly exhibited by other polar flagellated species. It is shown that although the three-step motility pattern helps the bacterium to localize near hot spots, an exploitative behavior, its exploratory potential in short times can be significantly enhanced by employing a non-Poissonian regulation scheme for its flagellar motor switches.

Fast-moving bacteria self-organize into active two-dimensional crystals of rotating cells.

We investigate a new form of collective dynamics displayed by Thiovulum majus, one of the fastest-swimming bacteria known. Cells spontaneously organize on a surface into a visually striking two-dimensional hexagonal lattice of rotating cells. As each constituent cell rotates its flagella, it creates a tornadolike flow that pulls neighboring cells towards and around it. As cells rotate against their neighbors, they exert forces on one another, causing the crystal to rotate and cells to reorganize. We show how these dynamics arise from hydrodynamic and steric interactions between cells. We derive the equations of motion for a crystal, show that this model explains several aspects of the observed dynamics, and discuss the stability of these active crystals.

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.

Bacterial motility patterns reveal importance of exploitation over exploration in marine microhabitats. Part I: theory.

Bacteria use different motility patterns to navigate and explore natural habitats. However, how these motility patterns are selected, and what their benefits may be, are not understood. In this article, we analyze the effect of motility patterns on a cell's ability to migrate in a chemical gradient and to localize at the top of the gradient, the two most important characteristics of bacterial chemotaxis. We will focus on two motility patterns, run-tumble and run-reverse-flick, that are observed and characterized in enteric bacterium Escherichia coli and marine bacterium Vibrio alginolyticus, respectively. To make an objective comparison, master equations are developed on the basis of microscopic motions of the bacteria. An unexpected yet significant result is that by adopting the run-reverse-flick motility pattern, a bacterium can reduce its diffusivity without compromising its drift in the chemical gradient. This finding is biologically important as it suggests that the motility pattern can improve a microorganism's ability to sequester nutrients in a competitive environment.

Bacterial chemotaxis in an optical trap.

An optical trapping technique is implemented to investigate the chemotactic behavior of a marine bacterial strain Vibrio alginolyticus. The technique takes the advantage that the bacterium has only a single polar flagellum, which can rotate either in the counter-clock-wise or clock-wise direction. The two rotation states of the motor can be readily and instantaneously resolved in the optical trap, allowing the flagellar motor switching rate S(t) to be measured under different chemical stimulations. In this paper the focus will be on the bacterial response to an impulsive change of chemoattractant serine. Despite different propulsion apparati and motility patterns, cells of V. alginolyticus apparently use a similar response as Escherichia coli to regulate their chemotactic behavior. Specifically, we found that the switching rate S(t) of the bacterial motor exhibits a biphasic behavior, showing a fast initial response followed by a slow relaxation to the steady-state switching rate S0. The measured S(t) can be mimicked by a model that has been recently proposed for chemotaxis in E. coli. The similarity in the response to the brief chemical stimulation in these two different bacteria is striking, suggesting that the biphasic response may be evolutionarily conserved. This study also demonstrated that optical tweezers can be a useful tool for chemotaxis studies and should be applicable to other polarly flagellated bacteria.

From the Cover: Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis.

We investigate swimming and chemotactic behaviors of the polarly flagellated marine bacteria Vibrio alginolyticus in an aqueous medium. Our observations show that V. alginolyticus execute a cyclic, three-step (forward, reverse, and flick) swimming pattern that is distinctively different from the run-tumble pattern adopted by Escherichia coli. Specifically, the bacterium backtracks its forward swimming path when the motor reverses. However, upon resuming forward swimming, the flagellum flicks and a new swimming direction is selected at random. In a chemically homogeneous medium (no attractant or repellent), the consecutive forward t(f) and backward t(b) swimming times are uncorrelated. Interestingly, although t(f) and t(b) are not distributed in a Poissonian fashion, their difference Δt = |t(f) - t(b)| is. Near a point source of attractant, on the other hand, t(f) and t(b) are found to be strongly correlated, and Δt obeys a bimodal distribution. These observations indicate that V. alginolyticus exploit the time-reversal symmetry of forward and backward swimming by using the time difference to regulate their chemotactic behavior. By adopting the three-step cycle, cells of V. alginolyticus are able to quickly respond to a chemical gradient as well as to localize near a point source of attractant.

Implications of three-step swimming patterns in bacterial chemotaxis.

We recently found that marine bacteria Vibrio alginolyticus execute a cyclic three-step (run-reverse-flick) motility pattern that is distinctively different from the two-step (run-tumble) pattern of Escherichia coli. How this novel, to our knowledge, swimming pattern is regulated by cells of V. alginolyticus is not currently known, but its significance for bacterial chemotaxis is self-evident and will be delineated herein. Using a statistical approach, we calculated the migration speed of a cell executing the three-step pattern in a linear chemical gradient, and found that a biphasic chemotactic response arises naturally. The implication of such a response for the cells to adapt to ocean environments and its possible connection to E. coli's response are also discussed.

The effect of long-range hydrodynamic interaction on the swimming of a single bacterium.

It has been theoretically suggested that when a bacterium swims in a fluid, the disturbance it creates is long-ranged and can influence its locomotion. The contribution of these long-range hydrodynamic interactions to swimming cells is examined herein for a number of bacterial strains with well-defined flagellar geometries. We show experimentally for the first time that long-range hydrodynamic interactions are important for an accurate description of the swimming of a single cell, and the effect is more pronounced for bacteria with a large cell body. The commonly used local resistive force theory assumes a stationary background fluid while ignoring flows induced due to other moving parts of the cell. Although pedagogically attractive, resistive force theory is not generally applicable to experiment.

Stick-and-diffuse and caged diffusion: a comparison of two models of synaptic vesicle dynamics.

Two models were recently proposed to enable us to understand the dynamics of synaptic vesicles in hippocampal neurons. In the caged diffusion model, the vesicles diffuse in small circular cages located randomly in the bouton, while in the stick-and-diffuse model the vesicles bind and release from a cellular cytomatrix. In this article, we obtain analytic expressions for the fluorescence correlation spectroscopy (FCS) autocorrelation function for the two models and test their predictions against our earlier FCS measurements of the vesicle dynamics. We find that the stick-and-diffuse model agrees much better with the experiment. We find also that, due to the slow dynamics of the vesicles, the finite experimental integration time has an important effect on the FCS autocorrelation function and demonstrate its effect for the different models. The two models of the dynamics are also relevant to other cellular environments where mobile species undergo slow diffusionlike motion in restricted spaces or bind and release from a stationary substrate.

Polymer effects on small- and large-scale two-dimensional turbulence.

We investigate the effect of dilute polymers on driven two-dimensional turbulence in a soap film. Transitions from strong to weak turbulence are identified by independently varying the polymer concentration phi and the energy injection rate epsilon(inj) . Studies of velocity structures in small scales reveal that strong saddles are suppressed, whereas weak ones become more populated. Interestingly, this redistribution of saddle points in turbulent flows strongly correlates with the quenching of velocity fluctuations on large scales, suggesting that this hydrodynamic structure may play a role in transferring energy from scale to scale.

Probing vesicle dynamics in single hippocampal synapses.

We use fluorescence correlation spectroscopy and fluorescence recovery after photobleaching to study vesicle dynamics inside the synapses of cultured hippocampal neurons labeled with the fluorescent vesicle marker FM 1-43. These studies show that when the cell is electrically at rest, only a small population of vesicles is mobile, taking seconds to traverse the synapse. Applying the phosphatase inhibitor okadaic acid causes vesicles to diffuse freely, moving 30 times faster than vesicles in control synapses. These results suggest that vesicles move sluggishly due to binding to elements of the synaptic cytomatrix and that this binding is altered by phosphorylation. Motivated by these results, a model is constructed consisting of diffusing vesicles that bind reversibly to the cytomatrix. This stick-and-diffuse model accounts for the fluorescence correlation spectroscopy and fluorescence recovery after photobleaching data, and also predicts the well-known exponential refilling of the readily releasable pool. Our measurements suggest that the movement of vesicles to the active zone is the rate-limiting step in this process.