Propulsion of microorganisms by a helical flagellum

Rodenborn, Bruce; Chen, C. H.; Swinney, Harry L.; Liu, Bin; Zhang, Hepeng

doi:10.1073/pnas.1219831110

Cited by 211 publications

(223 citation statements)

References 35 publications

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“…where t is the local unit tangent vector, and z k and z t are the local tangential and normal drag coefficients per unit length for a slender rod, respectively, derived in (19) to account for the effects of helicity, and shown to work moderately well (18,20) for typical flagella by setting:…”

Section: Dynamic Toy Modelmentioning

confidence: 99%

Buckling Instabilities and Complex Trajectories in a Simple Model of Uniflagellar Bacteria

Nguyen

Graham

2017

Biophysical Journal

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Observations of uniflagellar bacteria show that buckling instabilities of the hook protein connecting the cell body and flagellum play a role in locomotion. To understand this phenomenon, we develop models at varying levels of description with a particular focus on the parameter dependence of the buckling instability. A key dimensionless group called the flexibility number measures the hook flexibility relative to the thrust exerted by the flagellum; this parameter and the geometric parameters of the cell determine the stability of straight swimming. Two very simple models amenable to analytical treatment are developed to examine buckling in stationary (pinned) and moving swimmers. We then consider a more detailed model incorporating a helical flagellum and the rotational degrees of freedom of the cell body and flagellum, and we use numerical simulations to map out the parameter dependence of the buckling instability. In all models, a bifurcation occurs as the flexibility number increases, separating equilibrium configurations into straight or bent, and for the full model, separating trajectories into straight or helical. More specifically for the latter, the critical flexibility marks the transition from periodicity to quasi-periodicity in the behavior of variables determining configuration. We also find that for a given body geometry, there is a specific flagellar geometry that minimizes the critical flexibility number at which buckling occurs. These results highlight the role of flexibility in the biology of real organisms and the engineering of artificial microswimmers.

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Section: Dynamic Toy Modelmentioning

confidence: 99%

Buckling Instabilities and Complex Trajectories in a Simple Model of Uniflagellar Bacteria

Nguyen

Graham

2017

Biophysical Journal

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“…4A, dotted line). To apply the theory to our experimental data, we model the flagellum using slender-body theory, from which we can calculate σ f , τ f , and « f with good accuracy (19). Using typical values for the geometry of C. crescentus [radius a f ∼ 0.01 μm, arc length per pitch Λ ∼ 1.1 μm, total length L ∼ 6 μm, pitch angle θ f ∼ 0.65 rad (14)], we calculate b = 1.1 μm −1 and c = 0.65 μm × 4πμ.…”

Section: Applied Physical Sciencesmentioning

confidence: 99%

Helical motion of the cell body enhances Caulobacter crescentus motility

Liu

Gulino

Morse

et al. 2014

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

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We resolve the 3D trajectory and the orientation of individual cells for extended times, using a digital tracking technique combined with 3D reconstructions. We have used this technique to study the motility of the uniflagellated bacterium Caulobacter crescentus and have found that each cell displays two distinct modes of motility, depending on the sense of rotation of the flagellar motor. In the forward mode, when the flagellum pushes the cell, the cell body is tilted with respect to the direction of motion, and it precesses, tracing out a helical trajectory. In the reverse mode, when the flagellum pulls the cell, the precession is smaller and the cell has a lower translation distance per rotation period and thus a lower motility. Using resistive force theory, we show how the helical motion of the cell body generates thrust and can explain the direction-dependent changes in swimming motility. The source of the cell body precession is believed to be associated with the flexibility of the hook that connects the flagellum to the cell body.microorganisms | kinematics | fluid mechanics | torque | flicking

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“…This method has been used extensively to study the hydrodynamics and mobility of cells as reviewed in (28). However, ironically, experiments show that RFT actually works much better in granular media than in viscous fluids, a seemingly simpler material (29).…”

Section: Introductionmentioning

confidence: 99%

Intrusion rheology in grains and other flowable materials

Askari

Kamrin

2016

Nature Mater

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The interaction of intruding objects with deformable materials is a common phenomenon, arising in impact and penetration problems, animal and vehicle locomotion, and various geo-space applications. The dynamics of arbitrary intruders can be simplified using Resistive Force Theory (RFT), an empirical framework originally used for fluids but works surprisingly well, better in fact, in granular materials. That such a simple model describes behavior in dry grains, a complex nonlinear material, has invigorated a search to determine the underlying mechanism of RFT. We have discovered that a straightforward friction-based continuum model generates RFT, establishing a link between RFT and local material behavior. Our theory reproduces experimental RFT data without any parameter fitting and generates RFT's key simplifying assumption: a geometry-independent local force formula. Analysis of the system explains why RFT works better in grains than in viscous fluids, and leads to an analytical criterion to predict RFT's in other materials. IntroductionThe interaction of solid objects with a surrounding, plastically-deforming media is a common aspect of many natural and man-made processes. In the animal world, when organisms undulate, pulse, crawl, burrow, walk, or run on loose terrain they implicitly deform their environment to produce propulsive reaction forces giving rise to their motion (1). The physics of such interactions have been the subject of many studies, from aquatic organisms (2,3) to small insects and lizards (4,5) to humans and other legged-mammals (6,7). Similar principals are used for robotic applications to design machines that run (8), fly (9), swim (10), or walk in fluids or sand (11,12).Such complex interactions are also key to terramechanics of vehicular locomotion on granular substrates, models of excavation in sand and soil (13,14), and the study of similar problems in extraplanetary conditions (15,16). These topics and others, including cratering dynamics and penetration in plastic solids (17,18), all depend crucially on the way local material properties produce global resistive forces on arbitrary intruders.Motivated by past observations in fluids (19), a simple yet very effective empirical tool known as Resistive Force Theory (RFT) for granular materials has been proposed to approximate the forces on intruding objects moving through granular media. Despite the fact that a fundamental derivation is missing, when coupled with the force balance equations, the theory provides a simple and predictive tool for simulating the locomotion of arbitrarily shaped moving bodies in loose terrain (5,20,21). The simplicity of the theory and its predictive effectiveness are surprising in light of the complex, nonlinear, history-dependent, and oftentimes visibly nonlocal constitutive properties of granular media (22)(23)(24)(25)(26). RFT was initially developed to approximate 2 the speed of swimming micro-organisms at low Reynolds numbers (27) by studying the thrust and drag of individually moving elements of its bod...

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Propulsion of microorganisms by a helical flagellum

Cited by 211 publications

References 35 publications

Buckling Instabilities and Complex Trajectories in a Simple Model of Uniflagellar Bacteria

Buckling Instabilities and Complex Trajectories in a Simple Model of Uniflagellar Bacteria

Helical motion of the cell body enhances Caulobacter crescentus motility

Intrusion rheology in grains and other flowable materials

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