Zipping and entanglement in flagellar bundle of<i>E. coli</i>: Role of motile cell body

Adhyapak, Tapan Chandra; Stark, Holger

doi:10.1103/physreve.92.052701

Cited by 23 publications

(38 citation statements)

References 40 publications

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“…On small length scales it describes the motion of biological microswimmers such as swimming bacteria or motile cells, and of artificial microswimmers, such as active Janus particles or self-propelled emulsion droplets [5][6][7][8][9][10]. In a homogeneous environment, microswimmers at low Reynolds number first move ballistically and then cross over to enhanced diffusion due to random rotational motion of their swimming direction [4,11].…”

Section: Introductionmentioning

confidence: 99%

Active Brownian particles moving in a random Lorentz gas

2017

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Abstract. Biological microswimmers often inhabit a porous or crowded environment such as soil. In order to understand how such a complex environment influences their spreading, we numerically study noninteracting active Brownian particles (ABPs) in a two-dimensional random Lorentz gas. Close to the percolation transition in the Lorentz gas, they perform the same subdiffusive motion as ballistic and diffusive particles. However, due to their persistent motion they reach their long-time dynamics faster than passive particles and also show superdiffusive motion at intermediate times. While above the critical obstacle density η c the ABPs are trapped, their long-time diffusion below ηc is strongly influenced by the propulsion speed v 0. With increasing v0, ABPs are stuck at the obstacles for longer times. Thus, for large propulsion speed, the long-time diffusion constant decreases more strongly in a denser obstacle environment than for passive particles. This agrees with the behavior of an effective swimming velocity and persistence time, which we extract from the velocity autocorrelation function.

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Section: Introductionmentioning

confidence: 99%

Active Brownian particles moving in a random Lorentz gas

2017

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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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“…The main part of the flagellum is coupled to the motor tripod through the Kirchhoff elastic free energy density f K with a bending rigidity A -A h = 10 À3 pN mm 2 , and a twist rigidity C -C h = 2.0 pN mm 2 . 45,49 Thus, the flagellum is connected to the motor shaft through a 'hook' that acts like a universal joint with low bending and high twist rigidities 50 and allows the first flagellar segment along e 3 (1) to be at any angle to the motor shaft and yet efficiently transferring the driving torque to the flagellum. The cell body translates and rotates with velocities given, respectively, by…”

Section: Equations Of Motion and Numerical Methodsmentioning

confidence: 99%

“…51 As in ref. 45 the angle between e 3 (0) and the long axis of the cell body is set to 551 to tune the ratio for the bundle-to-body rotation rates during forward propulsion, to the experimentally observed range. 18 Finally, the excluded volume interaction between the cell body and the flagellum is again modeled as in ref.…”

Section: Equations Of Motion and Numerical Methodsmentioning

confidence: 99%

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Dynamics of a bacterial flagellum under reverse rotation

Adhyapak

Stark

2016

Soft Matter

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To initiate tumbling of an E. coli, one of the helical flagella reverses its sense of rotation. It then transforms from its normal form first to the transient semicoiled state and subsequently to the curly-I state. The dynamics of polymorphism is effectively modeled by describing flagellar elasticity through an extended Kirchhoff free energy. However, the complete landscape of the free energy remains undetermined because the ground state energies of the polymorphic forms are not known. We investigate how variations in these ground state energies affect the dynamics of a reversely rotated flagellum of a swimming bacterium. We find that the flagellum exhibits a number of distinct dynamical states and comprehensively summarize them in a state diagram. As a result, we conclude that tuning the landscape of the extended Kirchhoff free energy alone cannot generate the intermediate full-length semicoiled state. However, our model suggests an ad hoc method to realize the sequence of polymorphic states as observed for a real bacterium. Since the elastic properties of bacterial flagella are similar, our findings can easily be extended to other peritrichous bacteria.

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Zipping and entanglement in flagellar bundle ofE. coli: Role of motile cell body

Cited by 23 publications

References 40 publications

Active Brownian particles moving in a random Lorentz gas

Active Brownian particles moving in a random Lorentz gas

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

Dynamics of a bacterial flagellum under reverse rotation

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