The Effect of Long-Range Hydrodynamic Interaction on the Swimming of a Single Bacterium

Chattopadhyay, Suddhashil; Wu, Xiao-Lun

doi:10.1016/j.bpj.2008.11.046

Cited by 58 publications

(53 citation statements)

References 12 publications

(15 reference statements)

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“…The friction coefficients per unit length were calculated by Lighthill from slender-body theory taking into account the helical geometry of the rod [32]. The coefficients are summarized in appendix C. In experiments, one finds reasonable agreement with this approach [33,34]. The thermal force f th and torque m th are Gaussian stochastic variables with zero mean, f th = 0 and m th = 0.…”

Section: Dynamics Of a Helical Rodmentioning

confidence: 99%

Force-extension curves of bacterial flagella

Vogel

Stark

2010

Eur. Phys. J. E

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Abstract.Bacterial flagella assume different helical shapes during the tumbling phase of a bacterium but also in response to varying environmental conditions. Force-extension measurements by Darnton and Berg explicitly demonstrate a transformation from the coiled to the normal helical state (N.C. Darnton, H.C. Berg, Biophys. J. 92, 2230 (2007)). We here develop an elastic model for the flagellum based on Kirchhoff's theory of an elastic rod that describes such a polymorphic transformation and use resistive force theory to couple the flagellum to the aqueous environment. We present Brownian-dynamics simulations that quantitatively reproduce the force-extension curves and study how the ratio Γ of torsional to bending rigidity and the extensional rate influence the response of the flagellum. An upper bound for Γ is given. Using clamped flagella, we show in an adiabatic approximation that the mean extension, where a local coiled-to-normal transition occurs first, depends on the logarithm of the extensional rate.

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Section: Dynamics Of a Helical Rodmentioning

confidence: 99%

Force-extension curves of bacterial flagella

Vogel

Stark

2010

Eur. Phys. J. E

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“…For fluorescence microscopy, cells were labeled with Nano Orange dye (Invitrogen) and observed using a 100× oil-immersion objective (27). The fluorescence images were taken close to the surface for a better image quality.…”

Section: Methodsmentioning

confidence: 99%

Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis

Xie

Altindal²,

Chattopadhyay³

et al. 2011

Proc. Natl. Acad. Sci. U.S.A.

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274

292

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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 ¼ jt f − t b j 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.bacterial chemotaxis | bacterial swimming pattern E nteric bacteria, such as Escherichia coli, swim by rotating a set of flagella that forms a bundle when the flagellar motors turn in the counterclockwise (CCW) direction (1-3). The bundle falls apart when one or more motors turns in the clockwise (CW) direction, and the bacterium tumbles (4). A new swimming direction is selected upon resuming the CCW rotation of the flagellar motors. By modulating the CCW and CW intervals according to external chemical cues, the cells are able to migrate toward attractants or away from repellents (5, 6).Certain bacterial species possess a single polar flagellum with a bidirectional motor similar to E. coli. Being single polarly flagellated, low Reynolds number (Re) hydrodynamics dictates that, aside from random thermal motions, the bacterium can only backtrack its trajectory when the motor reverses. This raises an interesting question concerning how this type of cells performs chemotaxis. Studies of motility patterns of single polarly flagellated bacteria Pseudomonas citronellolis showed that the bacteria change the swimming direction by a brief reversal between two long runs. From the published trajectories (7), each reversal typically results in a small change in cell orientation, and thus several reversals appear to be necessary for a significant change in the swimming direction. Backtracking was also observed in a number of single flagellated marine bacteria such as Shewanella putrefaciens, Pseudoalteromonas haloplanktis, and Vibrio alginolyticus, which execute the so-called run-reverse steps when following attractants released from porous beads and from algae (8-10). A pioneering experiment in V. alginolyticus revealed that the timereversal s...

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“…15 At smaller scales, the kinematics of single bacterium have been investigated 16 and the shapes of an oscillating passive actin filament have been probed. 17 Force measurements using optical tweezers have been recently obtained on individual bacteria in an effort to test the validity of resistive force theory 18 and to determine E. coli swimming efficiency.…”

Section: Introductionmentioning

confidence: 99%

Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number

et al. 2010

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The swimming behavior of the nematode Caenorhabditis elegans is investigated in aqueous solutions of increasing viscosity. Detailed flow dynamics associated with the nematode's swimming motion as well as propulsive force and power are obtained using particle tracking and velocimetry methods. We find that C. elegans delivers propulsive thrusts on the order of a few nanonewtons. Such findings are supported by values obtained using resistive force theory; the ratio of normal to tangential drag coefficients is estimated to be approximately 1.4. Over the range of solutions investigated here, the flow properties remain largely independent of viscosity. Velocity magnitudes of the flow away from the nematode body decay rapidly within less than a body length and collapse onto a single master curve. Overall, our findings support that C. elegans is an attractive living model to study the coupling between small-scale propulsion and low Reynolds number hydrodynamics. The swimming behavior of the nematode Caenorhabditis elegans is investigated in aqueous solutions of increasing viscosity. Detailed flow dynamics associated with the nematode's swimming motion as well as propulsive force and power are obtained using particle tracking and velocimetry methods. We find that C. elegans delivers propulsive thrusts on the order of a few nanonewtons. Such findings are supported by values obtained using resistive force theory; the ratio of normal to tangential drag coefficients is estimated to be approximately 1.4. Over the range of solutions investigated here, the flow properties remain largely independent of viscosity. Velocity magnitudes of the flow away from the nematode body decay rapidly within less than a body length and collapse onto a single master curve. Overall, our findings support that C. elegans is an attractive living model to study the coupling between small-scale propulsion and low Reynolds number hydrodynamics. Disciplines Engineering | Mechanical Engineering

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The Effect of Long-Range Hydrodynamic Interaction on the Swimming of a Single Bacterium

Cited by 58 publications

References 12 publications

Force-extension curves of bacterial flagella

Force-extension curves of bacterial flagella

Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis

Propulsive force measurements and flow behavior of undulatory swimmers at low Reynolds number

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