Synchronization, phase locking, and metachronal wave formation in ciliary chains

Niedermayer, Thomas; Eckhardt, Bruno; Lenz, Peter

doi:10.1063/1.2956984

Cited by 212 publications

(401 citation statements)

References 43 publications

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“…Flagella have often been suggested to synchronize due to interflagellar hydrodynamic interactions. This view has been supported by several theoretical studies [3,4,12,13] and recent experiments [14,15]. Recently, another view has emerged, suggesting that the cell rocking motion causes synchronization by creating synchrony-restoring hydrodynamic drag on the flagella [16,17].…”

supporting

confidence: 48%

“…Phase transitions leading to synchronization are observed between and within a variety of biological organisms [2]. Recently, the organized dynamics of micron sized hairlike cell projections called eukaryotic flagella or cilia has attracted high levels of interest [3][4][5]. The ability of flagella to manipulate and transport fluid relies on their capacity to spontaneously beat and synchronize with one another.…”

mentioning

confidence: 99%

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Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

2015

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The influence of hydrodynamic forces on eukaryotic flagella synchronization is investigated by triggering phase locking between a controlled external flow and the flagella of C. reinhardtii. Hydrodynamic forces required for synchronization are over an order of magnitude larger than hydrodynamic forces experienced in physiological conditions. Our results suggest that synchronization is due instead to coupling through cell internal fibers connecting the flagella. This conclusion is confirmed by observations of the vfl3 mutant, with impaired mechanical connection between the flagella.

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supporting

confidence: 48%

mentioning

confidence: 99%

Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

2015

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“…In the particularly insightful model of Niedermayer, Eckhardt & Lenz (2008), a beating flagellum is represented by a microsphere of radius a and drag coefficient ζ driven around an orbit by some tangential internal force F that represents the action of molecular motors. A radial spring exerts a force −λ(R − R 0 ) that tends to return the orbit to a radius R 0 .…”

Section: Fluid Dynamics At the Scale Of The Cellmentioning

confidence: 99%

Batchelor Prize Lecture Fluid dynamics at the scale of the cell

Goldstein

2016

J. Fluid Mech.

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The world of cellular biology provides us with many fascinating fluid dynamical phenomena that lie at the heart of physiology, development, evolution and ecology. Advances in imaging, micromanipulation and microfluidics over the past decade have made possible high-precision measurements of such flows, providing tests of microhydrodynamic theories and revealing a wealth of new phenomena calling out for explanation. Here I summarize progress in four areas within the field of 'active matter': cytoplasmic streaming in plant cells, synchronization of eukaryotic flagella, interactions between swimming cells and surfaces and collective behaviour in suspensions of microswimmers. Throughout, I emphasize open problems in which fluid dynamical methods are key ingredients in an interdisciplinary approach to the mysteries of life.

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“…Thus, the beating flagellum is represented as a non-isochronous oscillator (with approximate isochrones ϕ−2τ A ω 1 lnA=const [24]). Nonisochrony of non-linear oscillators has been related to synchronization [25,26].…”

mentioning

confidence: 99%

Active Phase and Amplitude Fluctuations of Flagellar Beating

et al. 2014

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The eukaryotic flagellum beats periodically, driven by the oscillatory dynamics of molecular motors, to propel cells and pump fluids. Small, but perceivable fluctuations in the beat of individual flagella have physiological implications for synchronization in collections of flagella as well as for hydrodynamic interactions between flagellated swimmers. Here, we characterize phase and amplitude fluctuations of flagellar bending waves using shape mode analysis and limit-cycle reconstruction.We report a quality factor of flagellar oscillations, Q = 38.0 ± 16.7 (mean±s.e.). Our analysis shows that flagellar fluctuations are dominantly of active origin. Using a minimal model of collective motor oscillations, we demonstrate how the stochastic dynamics of individual motors can give rise to active small-number fluctuations in motor-cytoskeleton systems. Here, we report direct measurements of phase and amplitude fluctuations of the flagellar beat and discuss the microscopic origin of active flagellar fluctuations using a minimal model. We further illustrate the impact of flagellar fluctuations on swimming and synchronization. Our analysis contributes to a recent interest in driven, outof-equilibrium systems and their fluctuation fingerprint [15][16][17][18] by characterizing noisy limit-cycle dynamics in an ubiquitous motility system, the flagellum.Flagellar shape analysis. We characterize flagellar beat patterns as superposition of principal shape modes. This dimensionality reduction is key to our fluctuation analysis. We analyze planar beat patterns of bull sperm swimming close to a boundary surface [19], filmed at 250 frames-per-second (corresponding to about 8 frames per beat cycle). The flagellar centerline r(s, t), tracked as function of arclength position s and time t, can be expressed with respect to a material frame of the sperm head in terms of a tangent angle ψ(s, t)Here, r h (t) denotes the sperm head center, and e 1 and e 2 are ortho-normal vectors with e 1 pointing along the long head axis, see Fig. 1A. A space-timeplot of ψ(s, t) reveals the periodicity of the flagellar beat, see Fig. 1B. This high-dimensional data set can be projected on a low dimensional 'shape space' using shape mode analysis based on principal component analysis [20]. The time-averaged tangent angle ψ 0 (s)= n i=1 ψ(s, t i )/n characterizes the mean shape of the beating flagellum (n=1024 frames in each movie). We further define a two-point correlation matrix arXiv:1401.7036v2 [q-bio.CB]

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Synchronization, phase locking, and metachronal wave formation in ciliary chains

Cited by 212 publications

References 43 publications

Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

Hydrodynamics Versus Intracellular Coupling in the Synchronization of Eukaryotic Flagella

Batchelor Prize Lecture Fluid dynamics at the scale of the cell

Active Phase and Amplitude Fluctuations of Flagellar Beating

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