ArticleJournal of the Royal Society, Interface2015
Analysis of unstable modes distinguishes mathematical models of flagellar motion.
Article in Journal of the Royal Society, Interface, 2015. The graph could read no effect estimate from its abstract, so it casts no vote on the map. An erratum has been issued. Cited by 17 papers.
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Who cites it
17 citing papers in PubMed.
- Effect of fluid elasticity on the emergence of oscillations in an active elastic filament.Journal of the Royal Society, Interface · 2024Article
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- Generation of ciliary beating by steady dynein activity: the effects of inter-filament coupling in multi-filament models.Journal of the Royal Society, Interface · 2022Article
- Modelling Motility: The Mathematics of Spermatozoa.Frontiers in cell and developmental biology · 2021Review
- Internal friction controls active ciliary oscillations near the instability threshold.Science advances · 2020Article
- RETRACTED: Human sperm uses asymmetric and anisotropic flagellar controls to regulate swimming symmetry and cell steering.Science advances · 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
- Article
- Instability-driven oscillations of elastic microfilaments.Journal of the Royal Society, Interface · 2018Article
- Time Irreversibility and Criticality in the Motility of a Flagellate Microorganism.Physical review letters · 2018Article
- 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
Corrections and comments
- Erratum issued
Authors and funding
2 authors.
Funding
No grant is acknowledged in the PubMed record.
Abstract
The mechanisms underlying the coordinated beating of cilia and flagella remain incompletely understood despite the fundamental importance of these organelles. The axoneme (the cytoskeletal structure of cilia and flagella) consists of microtubule doublets connected by passive and active elements. The motor protein dynein is known to drive active bending, but dynein activity must be regulated to generate oscillatory, propulsive waveforms. Mathematical models of flagellar motion generate quantitative predictions that can be analysed to test hypotheses concerning dynein regulation. One approach has been to seek periodic solutions to the linearized equations of motion. However, models may simultaneously exhibit both periodic and unstable modes. Here, we investigate the emergence and coexistence of unstable and periodic modes in three mathematical models of flagellar motion, each based on a different dynein regulation hypothesis: (i) sliding control; (ii) curvature control and (iii) control by interdoublet separation (the 'geometric clutch' (GC)). The unstable modes predicted by each model are used to critically evaluate the underlying hypothesis. In particular, models of flagella with 'sliding-controlled' dynein activity admit unstable modes with non-propulsive, retrograde (tip-to-base) propagation, sometimes at the same parameter values that lead to periodic, propulsive modes. In the presence of these retrograde unstable modes, stable or periodic modes have little influence. In contrast, unstable modes of the GC model exhibit switching at the base and propulsive base-to-tip propagation.
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