Xiao-Lun Wu

Swimming efficiency of bacterium Escherichia coli.

We use measurements of swimming bacteria in an optical trap to determine fundamental properties of bacterial propulsion. In particular, we directly measure the force required to hold the bacterium in the optical trap and determine the propulsion matrix, which relates the translational and angular velocity of the flagellum to the torques and forces propelling the bacterium. From the propulsion matrix, dynamical properties such as torques, swimming speed, and power can be obtained by measuring the angular velocity of the motor. We find significant heterogeneities among different individuals even though all bacteria started from a single colony. The propulsive efficiency, defined as the ratio of the propulsive power output to the rotary power input provided by the motors, is found to be ≈2%, which is consistent with the efficiency predicted theoretically for a rigid helical coil.

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 tf and backward tb swimming times are uncorrelated. Interestingly, although tf and tb are not distributed in a Poissonian fashion, their difference Δt = |tf - tb| is. Near a point source of attractant, on the other hand, tf and tb 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.

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.

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 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 of the bacterial motor exhibits a biphasic behavior, showing a fast initial response followed by a slow relaxation to the steady-state switching rate . The measured 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.

Stochastic Receptor Expression Allows Sensitive Bacteria to Evade Phage Attack. Part I: Experiments

It has long been suspected that population heterogeneity, either at a genetic level or at a protein level, can improve the fitness of an organism under a variety of environmental stresses. However, quantitative measurements to substantiate such a hypothesis turn out to be rather difficult and have rarely been performed. Herein, we examine the effect of expression heterogeneity of lambda-phage receptors on the response of an Escherichia coli population to attack by a high concentration of lambda-phage. The distribution of the phage receptors in the population was characterized by flow cytometry, and the same bacterial population was then subjected to different phage pressures. We show that a minority population of bacteria that produces the receptor slowly and at low levels determines the long-term survivability of the bacterial population and that phage-resistant mutants can be efficiently isolated only when the persistent phage pressure >10(10) viruses/cm(3) is present. Below this phage pressure, persistors instead of mutants are dominant in the population.

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. colis response are also discussed.

Universal distribution of centers and saddles in two-dimensional turbulence.

The statistical properties of the local topology of two-dimensional turbulence are investigated using an electromagnetically forced soap film. The local topology of the incompressible 2D flow is characterized by the Jacobian determinant Lambda(x,y) = 1 / 4(omega(2)-sigma(2)), where omega(x,y) is the local vorticity and sigma(x,y) is the local strain rate. For turbulent flows driven by different external force configurations, P(Lambda) is found to be a universal function when rescaled using the turbulent intensity. A simple model that agrees with the measured functional form of P(Lambda) is constructed using the assumption that the stream function, psi(x,y), is a Gaussian random field.

Hysteresis at low Reynolds number: onset of two-dimensional vortex shedding

Hysteresis has been observed in a study of the transition between laminar flow and vortex shedding in a quasi-two-dimensional system. The system is a vertical, rapidly flowing soap film which is penetrated by a rod oriented perpendicular to the film plane. Our experiments show that the transition from laminar flow to a periodic von Karman vortex street can be hysteretic, i.e., vortices can survive at velocities lower than the velocity needed to generate them.

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 cells 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 microorganisms ability to sequester nutrients in a competitive environment.