Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?

H. Gadelha, E. A. Gaffney, D. J. Smith, J. C. Kirkman-Brown

Research output: Contribution to journalArticlepeer-review

89 Scopus citations


Throughout biology, cells and organisms use flagella and cilia to propel fluid and achieve motility. The beating of these organelles, and the corresponding ability to sense, respond to and modulate this beat is central to many processes in health and disease. While the mechanics of flagellum-fluid interaction has been the subject of extensive mathematical studies, these models have been restricted to being geometrically linear or weakly nonlinear, despite the high curvatures observed physiologically. We study the effect of geometrical nonlinearity, focusing on the spermatozoon flagellum. For a wide range of physiologically relevant parameters, the nonlinear model predicts that flagellar compression by the internal forces initiates an effective buckling behaviour, leading to a symmetry-breaking bifurcation that causes profound and complicated changes in the waveform and swimming trajectory, as well as the breakdown of the linear theory. The emergent waveform also induces curved swimming in an otherwise symmetric system, with the swimming trajectory being sensitive to head shape-no signalling or asymmetric forces are required. We conclude that nonlinear models are essential in understanding the flagellar waveform in migratory human sperm; these models will also be invaluable in understanding motile flagella and cilia in other systems.
Original languageEnglish (US)
Pages (from-to)1689-1697
Number of pages9
JournalJournal of the Royal Society Interface
Issue number53
StatePublished - May 12 2010
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUK-C1-013-04
Acknowledgements: The authors thank Mr Henry Shum for many helpful discussions and Professor John R. Blake for continued insight. H.G. acknowledges the Capes Foundation (Brazilian sponsor) for financial support through grant no. BEX 4676/06-8, and also through the Hester Cordelia Parsons Fund and Timothy Bailey Trust. D.J.S. thanks the Medical Research Council through grant no. G0600178. This publication is based on work supported in part by Award no. KUK-C1-013-04, made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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