Synchronization of rotating helices by hydrodynamic interactions

Abstract.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.

• Publication year

  2004

• Venue

  The European Physical Journal E : Soft matter

• Publication date

  2004-10-29

• Fields of study

  Biology, Medicine, Physics

• Identifiers
  DOI 10.1140/epje/i2004-10152-7arXiv cond-mat/0410771PMID 16096696
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar, PubMed

• No claims are published for this paper.

• No concepts are published for this paper.

• Life at Low Reynolds Number

  2008cited by this paper
• Particle image velocimetry experiments on a macro-scale model for bacterial flagellar bundling

  2004cited by this paper
• Circling particles and drafting in optical vortices

  2004cited by this paper
• Hydrodynamic interactions between rotating helices.

  2004cited by this paper
• E. coli in Motion

  2003influential reference
• A macroscopic scale model of bacterial flagellar bundling

  2003cited by this paper
• Metachronal waves for deterministic switching two-state oscillators with hydrodynamic interaction.

  2003cited by this paper
• The rotary motor of bacterial flagella.

  2003cited by this paper
• Rowers coupled hydrodynamically. Modeling possible mechanisms for the cooperation of cilia

  2001cited by this paper
• Baryon number transfer in hadronic interactions

  2001cited by this paper
• Real-Time Imaging of Fluorescent Flagellar Filaments

  2000cited by this paper
• Energetic considerations of ciliary beating and the advantage of metachronal coordination.

  1999cited by this paper
• An introduction to dynamics of colloids

  1996cited by this paper
• HYDROLIB: a library for the evaluation of hydrodynamic interactions in colloidal suspensions

  1995cited by this paper
• Energetics of flagellar rotation in bacteria.

  1980cited by this paper
• Flagellar hydrodynamics. A comparison between resistive-force theory and slender-body theory.

  1979cited by this paper
• Bacterial flagella rotating in bundles: a study in helical geometry.

  1977cited by this paper
• Normal-to-curly flagellar transitions and their role in bacterial tumbling. Stabilization of an alternative quaternary structure by mechanical force.

  1977cited by this paper
• Bacteria Swim by Rotating their Flagellar Filaments

  1973cited by this paper
• Mathematical Methods for Physicists

  1967cited by this paper
• The Stokes resistance of an arbitrary particle

  1964cited by this paper
• Analysis of the swimming of microscopic organisms

  1951cited by this paper
• Hydrodynamics

  1924cited by this paper

• Modeling complex particle suspensions: Perspectives on the rigid multiblob method

  2025cites this paper
• Dynamics of rotating helices in a viscous fluid

  2025cites this paper
• Synchronization and metachronal waves of elastic cilia caused by unsteady viscous flow

  2025cites this paper
• Dynamics of rotating helices in viscous fluid

  2025cites this paper
• Tracking of motile bacteria with instance segmentation aided by semi-synthetic image augmentation and quantitative analysis of run-and-tumble motion.

  2025cites this paper
• Run-and-tumble dynamics of Escherichia coli is governed by its mechanical properties

  2025cites this paper
• Propulsion contribution from individual filament in a flagellar bundle

  2024cites this paper
• Hydrodynamic synchronization of elastic cilia: How surface effects determine the characteristics of metachronal waves.

  2024cites this paper
• Synchronization of Two Bacterial Flagella as a Stochastic Process

  2024cites this paper
• Twist and turn: elastohydrodynamics of microscale active fibres

  2024cites this paper
• Twist and turn. Elastohydrodynamics of microscale active fibres

  2024cites this paper
• Hydrodynamic synchronization of elastic cilia: How flow confinement determines the characteristics of metachronal waves

  2023cites this paper
• Nonreciprocal interactions give rise to fast cilium synchronization in finite systems

  2023cites this paper
• Active Synthetic Microrotors: Design Strategies and Applications.

  2023cites this paper
• Mathematical modeling to the motion control of magnetic nano/microrobotic tools performing in bodily fluids, especially blood/plasma

  2022cites this paper
• Elastohydrodynamic Synchronization of Rotating Bacterial Flagella.

  2022cites this paper
• Hydrodynamic interactions hinder transport of flow-driven colloidal particles.

  2022cites this paper
• Bacteria-inspired robotic propulsion from bundling of soft helical filaments at low Reynolds number.

  2021cites this paper
• Hydrodynamic synchronization in strong confinement.

  2021cites this paper
• Energetics of synchronization for model flagella and cilia.

  2021cites this paper
• Stability of sedimenting flexible loops

  2021cites this paper
• Hydrodynamics and direction change of tumbling bacteria

  2021cites this paper
• Phoretic self-propulsion of helical active particles

  2021cites this paper
• Effect of ligand sensing on flagellar bundle formation in bacteria

  2021cites this paper
• Bacteria Inspired Multi-Flagella Propelled Soft Robot at Low Reynolds Number

  2021cites this paper
• The Squirmer Model

  2020cites this paper
• Hydrodynamics in Motile Active Matter

  2020cites this paper
• Biological Background

  2020cites this paper
• The Fluid Dynamics of Microscopic Locomotion

  2020cites this paper
• Index

  2020cites this paper
• Hydrodynamics of Slender Filaments

  2020cites this paper
• Waving of Eukaryotic Flagella

  2020cites this paper
• Cellular Locomotion

  2020cites this paper
• Flows and Stresses Induced by Cells

  2020cites this paper
• Flagella and the Physics of Viscous Propulsion

  2020cites this paper
• Hydrodynamic Synchronisation

  2020cites this paper
• Rotation of Bacterial Flagellar Filaments

  2020cites this paper
• Hydrodynamics of Collective Locomotion

  2020cites this paper
• Preface

  2020cites this paper
• Locomotion and Transport in Complex Fluids

  2020cites this paper
• References

  2020cites this paper
• Diffusion and Noisy Swimming

  2020cites this paper
• Self-Propulsion and Surfaces

  2020cites this paper
• Swimming Cells in Flows

  2020cites this paper
• Direct versus indirect hydrodynamic interactions during bundle formation of bacterial flagella

  2020cites this paper
• The Fluid Dynamics of Cell Motility

  2020cites this paper
• Propulsion, navigation and control of biological and artificial microswimmers

  2020cites this paper
• Geometrical Constraints on the Tangling of Bacterial Flagellar Filaments

  2020cites this paper
• The Waving Sheet Model

  2020cites this paper
• Computational models for active matter

  2019cites this paper
• Chirality-dependent forces in simple shear flow for helix aligned with streamlines

  2019cites this paper
• Interactions

  2019cites this paper
• Swimming with magnets: From biological organisms to synthetic devices

  2019cites this paper
• Mechanical shear controls bacterial penetration in mucus

  2019cites this paper
• Thermodynamic uncertainty relation of interacting oscillators in synchrony

  2018cites this paper
• Nonlinear dynamics and fluctuations in biological systems (Habilitation thesis)

  2018cites this paper
• Advances in colloidal manipulation and transport via hydrodynamic interactions.

  2018cites this paper
• Spontaneous Synchronization of Beating Cilia: An Experimental Proof Using Vision-Based Control

  2018cites this paper
• Control of synchronization in models of hydrodynamically coupled motile cilia

  2018cites this paper
• Mixing and pumping by pairs of helices in a viscous fluid.

  2018cites this paper
• Impacts of multiflagellarity on stability and speed of bacterial locomotion

  2018cites this paper
• Spontaneous oscillation and fluid–structure interaction of cilia

  2018cites this paper
• In-phase and anti-phase flagellar synchronization by waveform compliance and basal coupling

  2017cites this paper
• Three-body correlations and conditional forces in suspensions of active hard disks.

  2017cites this paper
• Synchronization and Collective Dynamics of Flagella and Cilia as Hydrodynamically Coupled Oscillators

  2017cites this paper
• Bundling of elastic filaments induced by hydrodynamic interactions

  2017cites this paper
• Autonomously responsive pumping by a bacterial flagellar forest: A mean-field approach.

  2016cites this paper
• Energetics of synchronization in coupled oscillators rotating on circular trajectories.

  2016cites this paper
• Nonlinear dynamics and fluctuations in biological systems

  2016cites this paper
• Transitional behavior in hydrodynamically coupled oscillators.

  2015cites this paper
• Metachronal waves in the flagellar beating of Volvox and their hydrodynamic origin

  2015cites this paper
• Bacterial hydrodynamics

  2015cites this paper
• Hydrodynamic synchronization of flagellar oscillators

  2015cites this paper
• Realizing the physics of motile cilia synchronization with driven colloids

  2015cites this paper
• Modelling the mechanics and hydrodynamics of swimming E. coli.

  2015cites this paper
• Decoupling translational and rotational effects on the phase synchronization of rotating helices.

  2015cites this paper
• Zipping and entanglement in flagellar bundle of E. coli: Role of motile cell body.

  2015cites this paper
• Flagella, flexibility and flow: Physical processes in microbial ecology

  2015cites this paper
• Focused Optical Beams for Driving and Sensing Helical and Biological Microobjects

  2015cites this paper
• Tuned, driven, and active soft matter

  2015cites this paper
• Physics of microorganism behaviour: motility, synchronisation, run-and-tumble, phototaxis.

  2015cites this paper
• Effects of thermal fluctuations and fluid compressibility on hydrodynamic synchronization of microrotors at finite oscillatory Reynolds number: a multiparticle collision dynamics simulation study.

  2014cites this paper
• Swimming and pumping of rigid helical bodies in viscous fluids

  2014cites this paper
• Rotation, oscillation and hydrodynamic synchronization of optically trapped oblate spheroidal microparticles.

  2014cites this paper
• Physics of microswimmers—single particle motion and collective behavior: a review

  2014cites this paper
• Fluid mechanics of swimming bacteria with multiple flagella.

  2014cites this paper
• Collective excitations of hydrodynamically coupled driven colloidal particles.

  2013cites this paper
• Synchronization and liquid crystalline order in soft active fluids.

  2013cites this paper
• Phase-dependent forcing and synchronization in the three-sphere model of Chlamydomonas

  2013cites this paper
• Stochastic hydrodynamic synchronization in rotating energy landscapes.

  2013cites this paper
• Cell-body rocking is a dominant mechanism for flagellar synchronization in a swimming alga

  2013cites this paper
• Synchronization, Slippage, and Unbundling of Driven Helical Flagella

  2013cites this paper
• Synchronization of rigid microrotors by time-dependent hydrodynamic interactions.

  2013cites this paper
• Rotation-induced polymorphic transitions in bacterial flagella.

  2013cites this paper
• Nonequilibrium dynamics and self-organization in field-driven dipolar colloidal particles

  2013cites this paper
• Structure and dynamics of self-assembling colloidal monolayers in oscillating magnetic fields.

  2013cites this paper
• The Evolution of Tumor‐Targeted Drug Delivery: From the EPR Effect to Nanoswimmers

  2013cites this paper
• Emergent run-and-tumble behavior in a simple model of Chlamydomonas with intrinsic noise.

  2012cites this paper
• The bacterial flagellum: Modeling the dynamics of the elastic filament and its transition between polymorphic helical forms

  2012cites this paper
• A geometric approach to the synchronization of a pair of two-state switching rowers interacting hydrodynamically

  2012cites this paper