Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration
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 i...
| Main Authors: | , , , |
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| Format: | Journal article |
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Royal Society Publishing
2010
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| _version_ | 1826257062907084800 |
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| author | Gadelha, H Gaffney, E Smith, D Kirkman-Brown, J |
| author_facet | Gadelha, H Gaffney, E Smith, D Kirkman-Brown, J |
| author_sort | Gadelha, H |
| collection | OXFORD |
| description | 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. |
| first_indexed | 2024-03-06T18:12:10Z |
| format | Journal article |
| id | oxford-uuid:0365a547-436d-4695-a90d-5ec0fe9fa0f2 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:12:10Z |
| publishDate | 2010 |
| publisher | Royal Society Publishing |
| record_format | dspace |
| spelling | oxford-uuid:0365a547-436d-4695-a90d-5ec0fe9fa0f22022-03-26T08:45:53ZNonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migrationJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:0365a547-436d-4695-a90d-5ec0fe9fa0f2Mathematical Institute - ePrintsRoyal Society Publishing2010Gadelha, HGaffney, ESmith, DKirkman-Brown, JThroughout 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. |
| spellingShingle | Gadelha, H Gaffney, E Smith, D Kirkman-Brown, J Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title | Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title_full | Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title_fullStr | Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title_full_unstemmed | Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title_short | Nonlinear instability in flagellar dynamics: a notel modulation mechanism in sperm migration |
| title_sort | nonlinear instability in flagellar dynamics a notel modulation mechanism in sperm migration |
| work_keys_str_mv | AT gadelhah nonlinearinstabilityinflagellardynamicsanotelmodulationmechanisminspermmigration AT gaffneye nonlinearinstabilityinflagellardynamicsanotelmodulationmechanisminspermmigration AT smithd nonlinearinstabilityinflagellardynamicsanotelmodulationmechanisminspermmigration AT kirkmanbrownj nonlinearinstabilityinflagellardynamicsanotelmodulationmechanisminspermmigration |