ArticleBiophysical journal2014
Equations of interdoublet separation during flagella motion reveal mechanisms of wave propagation and instability.
Article in Biophysical journal, 2014. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 24 papers.
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24 citing papers in PubMed.
- Quantification of flagellar gait changes with combined shape mode analysis and swimming simulations.Philosophical transactions. Series A, Mathematical, physical, and engineering sciences · 2025Article
- Effect of fluid elasticity on the emergence of oscillations in an active elastic filament.Journal of the Royal Society, Interface · 2024Article
- The reaction-diffusion basis of animated patterns in eukaryotic flagella.Nature communications · 2023Article
- Ciliary beating patterns map onto a low-dimensional behavioural space.Nature physics · 2022Article
- Predicting the locations of force-generating dyneins in beating cilia and flagella.Frontiers in cell and developmental biology · 2022Article
- Modelling Motility: The Mathematics of Spermatozoa.Frontiers in cell and developmental biology · 2021Review
- Calcium signaling modulates the dynamics of cilia and flagella.European biophysics journal : EBJ · 2020Article
- Internal friction controls active ciliary oscillations near the instability threshold.Science advances · 2020Article
- Buckling instabilities and spatio-temporal dynamics of active elastic filaments.Journal of the Royal Society, Interface · 2020Article
- Cilia oscillations.Philosophical transactions of the Royal Society of London. Series B, Biological sciences · 2020Article
- How Does Cilium Length Affect Beating?Biophysical journal · 2019Article
- Flagellar ultrastructure suppresses buckling instabilities and enables mammalian sperm navigation in high-viscosity media.Journal of the Royal Society, Interface · 2019Article
- Instability-driven oscillations of elastic microfilaments.Journal of the Royal Society, Interface · 2018Article
- Human sperm steer with second harmonics of the flagellar beat.Nature communications · 2017Article
- The counterbend dynamics of cross-linked filament bundles and flagella.Journal of the Royal Society, Interface · 2017Article
- Nonlinear amplitude dynamics in flagellar beating.Royal Society open science · 2017Article
- Elastohydrodynamic Synchronization of Adjacent Beating Flagella.Physical review fluids · 2016Article
- Steady dynein forces induce flutter instability and propagating waves in mathematical models of flagella.Journal of the Royal Society, Interface · 2016Article
- Dynamic curvature regulation accounts for the symmetric and asymmetric beats of Chlamydomonas flagella.eLife · 2016Article
- Genetics and biology of primary ciliary dyskinesia.Paediatric respiratory reviews · 2016Review
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No grant is acknowledged in the PubMed record.
Abstract
The motion of flagella and cilia arises from the coordinated activity of dynein motor protein molecules arrayed along microtubule doublets that span the length of axoneme (the flagellar cytoskeleton). Dynein activity causes relative sliding between the doublets, which generates propulsive bending of the flagellum. The mechanism of dynein coordination remains incompletely understood, although it has been the focus of many studies, both theoretical and experimental. In one leading hypothesis, known as the geometric clutch (GC) model, local dynein activity is thought to be controlled by interdoublet separation. The GC model has been implemented as a numerical simulation in which the behavior of a discrete set of rigid links in viscous fluid, driven by active elements, was approximated using a simplified time-marching scheme. A continuum mechanical model and associated partial differential equations of the GC model have remained lacking. Such equations would provide insight into the underlying biophysics, enable mathematical analysis of the behavior, and facilitate rigorous comparison to other models. In this article, the equations of motion for the flagellum and its doublets are derived from mechanical equilibrium principles and simple constitutive models. These equations are analyzed to reveal mechanisms of wave propagation and instability in the GC model. With parameter values in the range expected for Chlamydomonas flagella, solutions to the fully nonlinear equations closely resemble observed waveforms. These results support the ability of the GC hypothesis to explain dynein coordination in flagella and provide a mathematical foundation for comparison to other leading models.
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