A Fluid-Dynamic Interpretation of the Asymmetric Motion of Singly Flagellated Bacteria Swimming Close to a Boundary

Goto, Tomonobu; Nakata, Kousou; Baba, Kensaku; Nishimura, Masaharu; Magariyama, Yukio

doi:10.1529/biophysj.105.067553

Cited by 66 publications

(62 citation statements)

References 23 publications

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“…While a vast majority of the theoretical works use the simplifying assumption of unbounded fluid domain, in realistic scenarios microswimmers often move in confined environments and interact with the boundaries. The presence of solid boundaries has profound effects on the dynamics and motion trajectories of low-Re swimmers, as confirmed by numerical simulations [23,28,61,72] and observed in several laboratory experiments with swimming microorganisms [14,25,45]. …”

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confidence: 52%

Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Or¹,

Zhang²,

Murray³

2011

SIAM J. Appl. Dyn. Syst.

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Abstract. The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a boundary has a significant influence on the swimmer's trajectories and poses problems of dynamic stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying geometric structure of the dynamics, and establish a relation between the reversing symmetry of the system and existence and stability of periodic and steady solutions of motion near the wall. The results are demonstrated by numerical simulations and validated by motion experiments with macroscale robotic swimmer prototypes.Key words. dynamics of locomotion, low-Reynolds swimming, dynamic stability AMS subject classifications. 37J15, 37J25, 76M60DOI. 10.1137/1008087451. Introduction. The locomotion of microorganisms, as well as of futuristic miniature robotic swimmers for biomedical applications, is governed by low-Reynolds-number hydrodynamics [30,40,60]. Reynolds number, which encompasses the ratio of inertial forces to viscous forces, is defined as Re = V L/ν, where V is a characteristic velocity, L is a characteristic length scale, and ν is the kinematic viscosity of the fluid. For example, a typical Reynolds number for a human swimmer who is governed by inertial effects is on the order of 10 4 , whereas microorganisms typically have Re ≈ 10 −4 and swim by harnessing viscous effects. The theory of low-Re locomotion of microorganisms and motile cells in nature has been widely studied in the physics, fluid mechanics, and biology literature, e.g., [12,46,58]. In the context of nanotechnology and engineering, some efforts to develop miniaturized swimmers, primarily for biomedical applications, were reported in [4,21,26,42,70]. While a vast majority of the theoretical works use the simplifying assumption of unbounded fluid domain, in realistic scenarios microswimmers often move in confined environments and interact with the boundaries. The presence of solid boundaries has profound effects on the dynamics and motion trajectories of low-Re swimmers, as confirmed by numerical simulations [23,28,61,72] and observed in several laboratory experiments with swimming microorganisms [14,25,45].

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mentioning

confidence: 52%

Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Or¹,

Zhang²,

Murray³

2011

SIAM J. Appl. Dyn. Syst.

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“…As structures under compression can lose stability, the occurrence of flicks exclusively during forward swimming led us to reason that their origin lies in a buckling instability of the flagellum, and thus depends on the flagellum's material properties. Recent simulations 23 have focused on the stability of the flagellar filament, and an instability resulting Table S1), which has a sheath that covers it and prevents polymorphic transformations 33 . f,g, Schematics (not to scale) of the flagellar filament, hook and rotary motor during backward swimming (f), when the hook is in tension, and during forward swimming (g), when the hook is in compression.…”

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confidence: 99%

Bacteria can exploit a flagellar buckling instability to change direction

2013

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Bacteria swim by rotating rigid helical flagella and periodically reorienting to follow environmental cues 1,2 . Despite the crucial role of reorientations, their underlying mechanism has remained unknown for most uni-flagellated bacteria 3,4 . Here, we report that uni-flagellated bacteria turn by exploiting a finely tuned buckling instability of their hook, the 100-nm-long structure at the base of their flagellar filament 5 . Combining high-speed video microscopy and mechanical stability theory, we demonstrate that reorientations occur 10 ms after the onset of forward swimming, when the hook undergoes compression, and that the associated hydrodynamic load triggers the buckling of the hook. Reducing the load on the hook below the buckling threshold by decreasing the swimming speed results in the suppression of reorientations, consistent with the critical nature of buckling. The mechanism of turning by buckling represents one of the smallest examples in nature of a biological function stemming from controlled mechanical failure 6 and reveals a new role for flexibility in biological materials, which may inspire new microrobotic solutions in medicine and engineering 7 .Flexibility is woven into every facet of living materials. At the cellular level, flexibility allows red blood cells to squeeze through capillaries 8 and DNA to stretch and twist to compensate for variability in binding site length 9 . At the organismal level, flexibility enhances structural performance, for example by enabling animal bones and plant branches to absorb mechanical energy 10 . Flexibility also underpins a host of dynamic life functions, including locomotion, reproduction and predation, by enabling the storage and swift release of elastic energy, a mechanism used by jumping froghoppers to escape predators 11 , by plants to catapult seeds for dispersal 12 , and by aquatic invertebrates to suck in prey 13 . An extreme consequence of flexibility is the occurrence of mechanical instabilities, such as buckling and fluttering, which in engineered systems are synonymous with failure 14 , but in natural systems can serve functional purpose. The biomechanical repertoire of organisms includes mechanical instabilities over a wide range of timescales, from the millisecond snap-buckling instabilities that allow Venus flytraps 15 and humming birds 16 to capture insects to the gradual buckling responsible for the wavy edges of leaves and flowers 17 .Flexible appendages are widely used by organisms for locomotion in fluids, from the flapping of bird and bat wings 18 , to the actuation of fish fins 19 , to the bending of sperm flagella 20 . Flexibility also plays a subtle role in the locomotion of bacteria with multiple flagella (peritrichous), such as Escherichia coli, which bundles its flagella together for propulsion (a run 1 ) by exploiting the compliance of the flagellum's base 21,22 . When one or more flagella leave the bundle following a change in the direction of rotation of their motor, the torque resulting from the unbundling, or from the asso...

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“…The motion of a model moving near a rigid surface has been calculated in the previous study [7]. The motion near a free surface is quite different from that of the model moving near a rigid surface.…”

Section: Discussionmentioning

confidence: 99%

Boundary Element Analysis on the Fluid-Dynamic Interaction between a Singly Flagellated Bacterium and a Free Surface

2010

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Abstract-Bacterial motion near a free surface was numerically investigated by use of the boundary element method. The fluid flow around a bacterial cell is approximated as a creeping flow. Boundary conditions on the free surface were satisfied by the basic solution for a half space that provides free shear stresses. The swimming speed and the rotational rate were calculated for a bacterial model with a single flagellum. The motion near a free surface was found to be quite different from the motion near a rigid surface which had been previously analyzed.

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A Fluid-Dynamic Interpretation of the Asymmetric Motion of Singly Flagellated Bacteria Swimming Close to a Boundary

Cited by 66 publications

References 23 publications

Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Dynamics and Stability of Low-Reynolds-Number Swimming Near a Wall

Bacteria can exploit a flagellar buckling instability to change direction

Boundary Element Analysis on the Fluid-Dynamic Interaction between a Singly Flagellated Bacterium and a Free Surface

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