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

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

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

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
Pages (from-to)1689-1697
Number of pages9
JournalInterface
Volume7
Issue number53
DOIs
Publication statusPublished - 6 Dec 2010

Keywords

  • Asymmetric waveforms
  • Buckling instability
  • Internally driven filaments
  • Nonlinear flagellar dynamics
  • Sperm motility
  • Symmetry breaking

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