Analyses on Deformation of Helical Flagella of Salmonella

Takano, Yasunari; Kudo, Satoshi; Nishitoba, M.; Magariyama, Yukio

doi:10.1299/jsmec.48.513

Cited by 5 publications

(3 citation statements)

References 17 publications

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“…Studies of the deformation according to the Kirchhoff rod model combined with the Calladine model of the detailed structure of the filament provided analytical expressions for the bending moment, curvature and torsion of deformed flagellar filaments of swimming bacteria Vibrio alginolyticus and Salmonella. The deformation was obtained numerically and a comparison with experimental data provided an estimate of the elastic bending coefficient of the flagellar filament on the order of EI 10 pN(µm) 2 [47,48].…”

Section: Introductionmentioning

confidence: 99%

Propulsion by stiff elastic filaments in viscous fluids

Katsamba

Lauga

2019

Phys. Rev. E

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Flexible filaments moving in viscous fluids are ubiquitous in the natural microscopic world. For example, the swimming of bacteria and spermatozoa as well as important physiological functions at organ-level, such as the cilia-induced motion of mucus in the lungs, or individual cell-level, such as actin filaments or microtubules, all employ flexible filaments moving in viscous fluids. As a result of fluid-structure interactions, a variety of nonlinear phenomena may arise in the dynamics of such moving flexible filaments. In this paper we derive the mathematical tools required to study filament-driven propulsion in the asymptotic limit of stiff filaments. Motion in the rigid limit leads to hydrodynamic loads which deform the filament and impact the filament propulsion. We first derive the general mathematical formulation and then apply it to the case of a helical filament, a situation relevant for the swimming of flagellated bacteria and for the transport of artificial, magnetically actuated motors. We find that, as a result of flexibility, the helical filament is either stretched or compressed (conforming previous studies) and its axis also bends, a new result which we interpret physically. We then explore and interpret the dependence of the perturbed propulsion speed due to the deformation on the relevant dimensionless dynamic and geometric parameters.

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Section: Introductionmentioning

confidence: 99%

Propulsion by stiff elastic filaments in viscous fluids

Katsamba

Lauga

2019

Phys. Rev. E

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“…The analysis of the flagellar pitch is important, especially when resistive force theory is being employed, because it governs the resistive force coefficients (see equations (2.7) -(2.9)). According to our observation, the studies of Takano et al [45][46][47] are some of the few theoretical works that specifically pay very close attention to the morphology of the bacterial helical flagella. However, a major limitation of these studies is that the results are subjected to an initial swimming velocity obtained from the undeformed flagellum, and the authors did not re-compute the swimming velocity with the deformed flagellum to see how far the assumed initial velocity deviates from the velocity of the deformed flagellum.…”

Section: Shape Of the Flagellamentioning

confidence: 69%

“…Theoretical studies of the shape of helical flagella were also reported in studies of Takano et al [45][46][47], in which the flagella of Vibrio alginolyticus and Salmonella were investigated using Kirchhoff rod model combined with resistive force theory. They studied how the helical shape of the flagellum changes with its rotation rate and flexural rigidity, paying strong attention to the changes in the pitch length.…”

Section: Shape Of the Flagellamentioning

confidence: 90%

Characteristics of swimming bacteria in flow

Tran¹

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Many microorganisms utilize their flagella, which are hair-like appendages, to swim in fluid environments. The research of locomotion of flagellated microorganisms involves the study of flagella's behaviors. Since flagellated microorganisms swim by propelling their flagella through liquid environment, the propulsion of flagella plays a key role in hydrodynamics of the swimmers. In reality, the microorganisms are constantly subjected to flows and other external forces during swimming. Therefore, it is very important to understand how behaviors of the flagella contribute to the swimming in the presence of flow and external forces. In this thesis, I investigate the behavior of helically flagellated bacteria in external force field as well as the shape of a flagellum in shear flow.First, I present a model to analyze the effect of dielectrophoretic (DEP) force on a swimming helically flagellated bacterium, particularly on its swimming direction and velocity. I consider simple DEP force that is acting along X-direction, and the force's strength varies with Y-positions. Both DEP force and rotational diffusion are considered when analyzing the swimming of the bacterium. In most cases, DEP force is main factor that determines the steady swimming orientation of the bacterium; however, the impact of rotational diffusion is more significant when the DEP force's strength varies strongly in the Y-direction. Interestingly, the variation in DEP force's strength in the Y-direction causes the bacterium to translate perpendicular to its primary axis. This phenomenon is the consequence of the interaction between helical shape of the flagellum and the external force, and it could be applied to focus the bacteria. The model developed here would contribute to our knowledge on how external force affects the swimming behavior of flagellated bacteria, emphasizing on the interaction between the helical geometry of the flagellum and the external force. Polar, azimuthal angles (2 typical Euler angles) DR Rotational diffusivity c Probability of an orientation of the bacterium C0, C1, C2 Coefficients that determine components of DEP force  Angle resulted from competition between DEP and diffusion 4 W, H Width, height of a microchannel  Shear rate VT, VN Velocities in the tangential and normal direction t, n Unit vectors parallel and perpendicular to the flagellar segment EI Flexural rigidity of the flagellum Vrel, Vswim, Vwiggling Relative, swimming, and wiggling velocities Sp Sperm number Z Dimensionless shear rate y(s) Shape of the beating flagellum xvii Contents Abstract ....

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Fluid–Structure Interactions and Flagellar Actuation

2012

Microbiorobotics

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Analyses on Deformation of Helical Flagella of Salmonella

Cited by 5 publications

References 17 publications

Propulsion by stiff elastic filaments in viscous fluids

Propulsion by stiff elastic filaments in viscous fluids

Characteristics of swimming bacteria in flow

Fluid–Structure Interactions and Flagellar Actuation

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