Coexistence of tight and loose bundled states in a model of bacterial flagellar dynamics

Janssen, Pieter; Graham, Michael D.

doi:10.1103/physreve.84.011910

Cited by 35 publications

(43 citation statements)

References 32 publications

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“…The bundle is a composite of many flagellar helices so its shape may not be precisely helical, especially at the base where flagella from different locations enter the bundle. Nonetheless, since studies of bundle dynamics (Flores et al 2005;Janssen 2011) and geometries do not currently provide detailed guidance for bundle geometry and dynamics, we use a minimal model capable of producing wiggling trajectories that treats the flagellar bundle as a rigid helix with a fixed position and orientation (apart from rotation about the helical axis) relative to the cell body. Away from the hook, flagella are stiffer, and modelling them as rigid helices can be justified by the experiments by Magariyama et al (2005).…”

Section: Bacterial Geometry and Discretizationmentioning

confidence: 99%

The wiggling trajectories of bacteria

et al. 2012

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Many motile bacteria display wiggling trajectories, which correspond to helical swimming paths. Wiggling trajectories result from flagella pushing off-axis relative to the cell body and making the cell wobble. The spatial extent of wiggling trajectories is controlled by the swimming velocity and flagellar torque, which leads to rotation of the cell body. We employ the method of regularized stokeslets to investigate the wiggling trajectories produced by flagellar bundles, which can form at many locations and orientations relative to the cell body for peritrichously flagellated bacteria. Modelling the bundle as a rigid helix with fixed position and orientation relative to the cell body, we show that the wiggling trajectory depends on the position and orientation of the flagellar bundle relative to the cell body. We observe and quantify the helical wiggling trajectories of Bacillus subtilis, which show a wide range of trajectory pitches and radii, many with pitch larger than 4 µm. For this bacterium, we show that flagellar bundles with fixed orientation relative to the cell body are unlikely to produce wiggling trajectories with pitch larger than 4 µm. An estimate based on torque balance shows that this constraint on pitch is a result of the large torque exerted by the flagellar bundle. On the other hand, multiple rigid bundles with fixed orientation, similar to those recently observed experimentally, are able to produce wiggling trajectories with large pitches.

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Section: Bacterial Geometry and Discretizationmentioning

confidence: 99%

The wiggling trajectories of bacteria

et al. 2012

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“…For instance, in a model of B. subtilus, Hyon et al (11) use regularized Stokeslets to examine helical trajectories arising from a number of fixed flagellar arrangements on the cell body. Because assigning configurations to swimmers necessarily precludes the exploration of any hook dynamics or mechanics, other studies instead use various models incorporating elasticity to examine the stability of the hook and of the overall flagellar filament (12)(13)(14)(15). Indeed, models of a standalone elastic flagellum show instability in the equilibrium helical shape above a critical applied torque load/angular velocity (6,14).…”

Section: Introductionmentioning

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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“…It is interrupted by short periods of 'tumble' events, where the reversal of the motor-rotation direction of some flagella causes the associated flagella to leave the bundle, thereby inducing erratic rotation of the cell body. [15][16][17][18][19][20] Moreover, bacterial propulsion properties have been investigated, 16,[20][21][22][23] their run-and-tumble dynamics, 16,24 as well as the influence of hydrodynamic interactions on their motion adjacent to surface. The alternating runs and tumbles allow the bacterium to efficiently execute a biased random walk toward favorable environments such as food-concentrated regions by adjusting run and tumble durations to the environmental conditions.…”

Section: Introductionmentioning

confidence: 99%

Modelling the mechanics and hydrodynamics of swimming E. coli

et al. 2015

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The swimming properties of an E. coli-type model bacterium are investigated by mesoscale hydrodynamic simulations, combining molecular dynamics simulations of the bacterium with the multiparticle particle collision dynamics method for the embedding fluid. The bacterium is composed of a spherocylindrical body with attached helical flagella, built up from discrete particles for an efficient coupling with the fluid. We measure the hydrodynamic friction coefficients of the bacterium and find quantitative agreement with experimental results of swimming E. coli. The flow field of the bacterium shows a force-dipole-like pattern in the swimming plane and two vortices perpendicular to its swimming direction arising from counterrotation of the cell body and the flagella. By comparison with the flow field of a force dipole and rotlet dipole, we extract the force-dipole and rotlet-dipole strengths for the bacterium and find that counterrotation of the cell body and the flagella is essential for describing the near-field hydrodynamics of the bacterium.

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Coexistence of tight and loose bundled states in a model of bacterial flagellar dynamics

Cited by 35 publications

References 32 publications

The wiggling trajectories of bacteria

The wiggling trajectories of bacteria

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

Modelling the mechanics and hydrodynamics of swimming E. coli

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