Nonlinear instability in flagellar dynamics: a novel modulation mechanism in sperm migration?
- 12 May 2010
- journal article
- research article
- Published by The Royal Society in Journal of The Royal Society Interface
- Vol. 7 (53), 1689-1697
- https://doi.org/10.1098/rsif.2010.0136
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.Keywords
This publication has 43 references indexed in Scilit:
- Bend propagation in the flagella of migrating human sperm, and its modulation by viscosityCell Motility, 2009
- The chirality of ciliary beatsPhysical Biology, 2008
- How molecular motors shape the flagellar beatHFSP Journal, 2007
- Experimental investigations of elastic tail propulsion at low Reynolds numberPhysics of Fluids, 2006
- Generic aspects of axonemal beatingNew Journal of Physics, 2000
- Viscous Nonlinear Dynamics of Twist and WrithePhysical Review Letters, 1998
- Nonlinear Dynamics of Stiff PolymersPhysical Review Letters, 1995
- “Geometric clutch” hypothesis of axonemal function: Key issues and testable predictionsCell Motility, 1995
- Observations of the structural components of flagellar axonemes and central pair microtubules from rat spermJournal of Ultrastructure Research, 1977
- STUDIES ON CILIAThe Journal of cell biology, 1965