The Mathematical Institute, University of Oxford, Eprints Archive

Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration

Gadelha, H and Gaffney, E. A. and Smith, D J and Kirkman-Brown, J C (2010) Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration. Journal of the Royal Society Interface, 7 (6). pp. 1689-1697.



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.

Item Type:Article
Subjects:A - C > Biology and other natural sciences
Research Groups:Centre for Mathematical Biology
ID Code:1362
Deposited By: Eamonn Gaffney
Deposited On:05 Aug 2011 07:54
Last Modified:29 May 2015 19:03

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