October 29, 2004
Some types of bacteria use rotating helical flagella to swim. The motion of such organisms takes place in the regime of low Reynolds numbers where viscous effects dominate and where the dynamics is governed by hydrodynamic interactions. Typically, rotating flagella form bundles, which means that their rotation is synchronized. The aim of this study is to investigate whether hydrodynamic interactions can be at the origin of such a bundling and synchronization. We consider two stiff helices that are modelled by rigidly connected beads, neglecting any elastic deformations. They are driven by constant and equal torques, and they are fixed in space by anchoring their terminal beads in harmonic traps. We observe that, for finite trap strength, hydrodynamic interactions do indeed synchronize the helix rotations. The speed of phase synchronization decreases with increasing trap stiffness. In the limit of infinite trap stiffness, the speed is zero and the helices do not synchronize.
Similar papers 1
September 20, 2012
Synchronization induced by long-range hydrodynamic interactions is attracting attention as a candidate mechanism behind coordinated beating of cilia and flagella. Here we consider a minimal model of hydrodynamic synchronization in the low Reynolds number limit. The model consists of rotors, each of which assumed to be a rigid bead making a fixed trajectory under periodically varying driving force. By a linear analysis, we derive the necessary and sufficient conditions for a p...
March 29, 2022
To rotate continuously without jamming, the flagellar filaments of bacteria need to be locked in phase. While several models have been proposed for eukaryotic flagella, the synchronization of bacterial flagella is less well understood. Starting from a reduced model of flexible and hydrodynamically-coupled bacterial flagella, we rigorously coarse-grain the equations of motion using the method of multiple scales, and hence show that bacterial flagella generically synchronize to...
May 21, 2020
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...
December 21, 2003
Escherichia coli and other bacteria use rotating helical filaments to swim. Each cell typically has about four filaments, which bundle or disperse depending on the sense of motor rotation. To study the bundling process, we built a macroscopic scale model consisting of stepper-motor-driven polymer helices in a tank filled with a high-viscosity silicone oil. The Reynolds number, the ratio of viscous to elastic stresses, and the helix geometry of our experimental model approxima...
September 25, 2015
We survey the theory synchronization in collections of noisy oscillators. This framework is applied to flagellar synchronization by hydrodynamic interactions. The time-reversibility of hydrodynamics at low Reynolds numbers prompts swimming strokes that break symmetry to facilitate hydrodynamic synchronization. We discuss different physical mechanisms for flagellar synchronization, which break this symmetry in different ways.
April 20, 2023
Most bacteria are driven by the cilia or flagella, consisting of a long filament and a rotary molecular motor through a short flexible hook. The beating pattern of these filaments shows synchronization properties from hydrodynamic interactions, especially in low Reynolds number fluids. Here, we introduce a model based on simple spherical oscillators which execute oscillatory movements in one dimension by an active force, as a simplified imitation of the movements of cilia or ...
November 15, 2017
Peritrichous bacteria swim in viscous fluids by rotating multiple helical flagellar filaments. As the bacterium swims forward, all its flagella rotate in synchrony behind the cell in a helical bundle. When the bacterium changes its direction, the flagellar filaments unbundle and reorient the cell for a short period of time before returning to their bundled state and resuming swimming. This rapid bundling and unbundling is, at its heart, a mechanical process whereby hydrodynam...
October 11, 2016
It is now well established that nearby beating pairs of eukaryotic flagella or cilia typically synchronize in phase. A substantial body of evidence supports the hypothesis that hydrodynamic coupling between the active filaments, combined with waveform compliance, provides a robust mechanism for synchrony. This elastohydrodynamic mechanism has been incorporated into `bead-spring' models in which flagella are represented by microspheres tethered by radial springs as internal fo...
June 16, 2021
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 in Stokes flow 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 ...
April 9, 2015
The course of a peritrichous bacterium such as E. coli crucially depends on the level of synchronization and self-organization of several rotating flagella. However, the rotation of each flagellum generates counter body movements which in turn affect the flagellar dynamics. Using a detailed numerical model of an E. coli, we demonstrate that flagellar entanglement, besides fluid flow relative to the moving body, dramatically changes the dynamics of flagella from that compared ...