Impacts of multiflagellarity on stability and speed of bacterial locomotion

Nguyen, Frank; Graham, Michael D.

doi:10.1103/physreve.98.042419

Cited by 30 publications

(20 citation statements)

References 42 publications

(91 reference statements)

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“…The number of flagella is a fundamental control parameter for multi-flagellated bacteria, and its connection to bacterial spreading and speed of locomotion has been previously investigated 23,45 . In the current study, our kinematic model for tangling allows us to examine whether the number of flagella could be linked to the robustness of bundling.…”

Section: Discussionmentioning

confidence: 99%

Geometrical Constraints on the Tangling of Bacterial Flagellar Filaments

Tătulea-Codrean

Lauga

2020

Sci Rep

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Many species of bacteria swim through viscous environments by rotating multiple helical flagella. The filaments gather behind the cell body and form a close helical bundle, which propels the cell forward during a "run". The filaments inside the bundle cannot be continuously actuated, nor can they easily unbundle, if they are tangled around one another. The fact that bacteria can passively form coherent bundles, i.e. bundles which do not contain tangled pairs of filaments, may appear surprising given that flagella are actuated by uncoordinated motors. In this article, we establish the theoretical conditions under which a pair of rigid helical filaments can form a tangled bundle, and we compare these constraints with experimental data collected from the literature. Our results suggest that bacterial flagella are too straight and too far apart to form tangled bundles based on their intrinsic, undeformed geometry alone. This makes the formation of coherent bundles more robust against the passive nature of the bundling process, where the position of individual filaments cannot be controlled.There is arguably no complex geometrical structure more central to biology than the helix. Two helical strands of nucleic acid spiral around each other to form the blueprint of life 1 , the arteries and vein that make up the human umbilical cord are twisted in a helical pattern 2 , and our human hearts beat with a spiralling contraction of the myocardium 3 . Many large eukaryotic cells, particularly in plants, set up helical flows to enhance chemical transport within the cell 4 and some viruses also take this shape 5 . Prokaryotes too have learnt how to assemble blocks of proteins into a helical structure and put it to good use 6-9 . Indeed, many species of bacteria are able to propel themselves through the viscous medium they inhabit by exploiting an apparatus known as flagellum, whereby a relatively rigid helical filament is actuated by a specialised constant-torque rotary motor 10-12 . In the case of multi-flagellated bacteria, the filaments are swept behind the cell body and rotate together in a coherent bundle, which leads to an interval of straight swimming called a "run" 13 . To change swimming direction, at least one motor must switch its sense of rotation, upon which the associated flagellum will leave the bundle and generate an imbalance of forces. The subsequent reorientation of the cell is called a "tumble" 14 .This run-and-tumble behaviour lies at the heart of bacterial motility. It is known that the initial stage of bundling is enabled by an elastohydrodynamic instability of the hook 15 , and from there onwards both the counter-rotation of the cell-body and hydrodynamic interactions between the filaments contribute to the synchronization and formation of the bundle [16][17][18][19][20][21][22] . Computational studies have investigated the effect of the number of flagella on the motility of the cell 23 , and the role played by polymorphic transformations 24 and mismatched motor torques 25 in the bundling and unbundling...

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Section: Discussionmentioning

confidence: 99%

Geometrical Constraints on the Tangling of Bacterial Flagellar Filaments

Tătulea-Codrean

Lauga

2020

Sci Rep

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“…At the heart of the tumble are two complex fluid-structure interaction processes: (i) 'unbundling', when the filament leaves the bundle, and (ii) 'bundling', when the bundle reassembles at the end of a tumble. Several studies have focused on the key role played by the instability of the hook, which has a bending rigidity several orders of magnitude smaller than that of the filament [47], in the bundling process [48] and thus in controlling the change in the swimming direction [49,50]. The synchronisation between flagellar filaments during the bundling process is also an important factor.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics and direction change of tumbling bacteria

Dvoriashyna

Lauga

2021

PLoS ONE

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The bacterium Escherichia coli (E. coli) swims in viscous fluids by rotating several helical flagellar filaments, which are gathered in a bundle behind the cell during ‘runs’ wherein the cell moves steadily forward. In between runs, the cell undergoes quick ‘tumble’ events, during which at least one flagellum reverses its rotation direction and separates from the bundle, resulting in erratic motion in place and a random reorientation of the cell. Alternating between runs and tumbles allows cells to sample space by stochastically changing their propulsion direction after each tumble. The change of direction during a tumble is not uniformly distributed but is skewed towards smaller angles with an average of about 62°–68°, as first measured by Berg and Brown (1972). Here we develop a theoretical approach to model the angular distribution of swimming E. coli cells during tumbles. We first use past experimental imaging results to construct a kinematic description of the dynamics of the flagellar filaments during a tumble. We then employ low-Reynolds number hydrodynamics to compute the consequences of the kinematic model on the force and torque balance of the cell and to deduce the overall change in orientation. The results of our model are in good agreement with experimental observations. We find that the main change of direction occurs during the ‘bundling’ part of the process wherein, at the end of a tumble, the dispersed flagellar filaments are brought back together in the helical bundle, which we confirm using a simplified forced-sphere model.

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“…Vogel & Stark have presented a very detailed picture of flagellum buckling and dynamics, and a supercritical Hopf bifurcation in the thrust force due to hook and flagellum compliance which persists when the flagellum is affixed to a spherical cell body during locomotion [40]. Full numerical simulations and modeling by Shum & Gaffney [33] and Nguyen & Graham [41,42] confirmed the existence of a critical motor torque triggering a bifurcation from straight swimming to apparently helical swimming trajectories when flagellum flexibility is included (see also Refs. [10,33,37]).…”

Section: Introductionmentioning

confidence: 99%

Helical trajectories of swimming cells with a flexible flagellar hook

Zou,

Lough,

Spagnolie

2021

Preprint

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The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.

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Impacts of multiflagellarity on stability and speed of bacterial locomotion

Cited by 30 publications

References 42 publications

Geometrical Constraints on the Tangling of Bacterial Flagellar Filaments

Geometrical Constraints on the Tangling of Bacterial Flagellar Filaments

Hydrodynamics and direction change of tumbling bacteria

Helical trajectories of swimming cells with a flexible flagellar hook

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