|
| |
|
|
|
|
||||
| Home Help Feedback Subscriptions Archive Search Table of Contents | ||||
Non-Sinusoidal Bending Waves of Sperm Flagella
1 Division of Biology, California Institute of Technology, Pasadena, California
1. Photomicrographs giving greater resolution than previously available have been obtained for the spermatozoa of a sea urchin, a tunicate, and an annelid.
2. The bending waves are not sine waves. They contain circular arcs, in which the amount of bending is constant, separated by shorter regions which are nearly straight.
3. The flagellum must be effectively very stiff to maintain this waveform as it moves through the medium, but this stiffness must be greatly reduced at the junctions between straight and circular regions, where the flagellum is actively bending and unbending.
4. This type of wave pattern may be generated by a simple ‘on-or-off’ activation of bending elements, but the amount of bending which occurs can be influenced by environmental conditions, such as the viscosity of the medium.
5. A mathematical analysis of the wave movement can be carried out more easily than with sinusoidal waves, and expressions have been obtained for the forward swimming speed, the distribution of bending moment along the flagellum, and the energy expenditure for movement, in terms of the parameters of the waves.
6. The expression for the forward swimming speed accurately predicts the swimming speed of headless spermatozoa, confirming the validity of the hydrodynamic assumptions used in this analysis.
Note:
This work has been supported in part by a grant from the United States Public Health Service (RG-6965).
Submitted on December 12, 1964
This article has been cited by other articles:
|
|
 |
|
  C. J. Brokaw FLAGELLAR PROPULSION J. Exp. Biol., March 15, 2006; 209(6): 985 - 986. [Full Text] [PDF]
|
|
|
|
|
|
U. K. Muller and J. L. van Leeuwen Swimming of larval zebrafish: ontogeny of body waves and implications for locomotory development J. Exp. Biol., February 15, 2004; 207(5): 853 - 868. [Abstract] [Full Text] [PDF]
|
|
|
|
 |
|
 C. B. Lindemann Structural-Functional Relationships of the Dynein, Spokes, and Central-Pair Projections Predicted from an Analysis of the Forces Acting within a Flagellum Biophys. J., June 1, 2003; 84(6): 4115 - 4126. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. M. Woolley and G. G. Vernon Functional State of the Axonemal Dyneins during Flagellar Bend Propagation Biophys. J., October 1, 2002; 83(4): 2162 - 2169. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
M. J. McHenry Mechanisms of helical swimming: asymmetries in the morphology, movement and mechanics of larvae of the ascidian Distaplia occidentalis J. Exp. Biol., January 9, 2001; 204(17): 2959 - 2973. [Abstract] [Full Text] [PDF]
|
|
|
|
|
|
D. Woolley and G. Vernon A study of helical and planar waves on sea urchin sperm flagella, with a theory of how they are generated J. Exp. Biol., January 4, 2001; 204(7): 1333 - 1345. [Abstract] [PDF]
|
|
|
|
 |
|
 C. Brokaw Direct measurements of sliding between outer doublet microtubules in swimming sperm flagella Science, March 24, 1989; 243(4898): 1593 - 1596. [Abstract] [PDF]
|
|
|
|
|
|
C. J. Brokaw Flagellar Movement: A Sliding Filament Model: An explanation is suggested for the spontaneous propagation of bending waves by flagella Science, November 3, 1972; 178(4060): 455 - 462. [Abstract] [PDF]
|
|
|
|
|
|
C. J. Brokaw Adenosine Triphosphate Usage by Flagella Science, April 7, 1967; 156(3771): 76 - 78. [Abstract] [PDF]
|
|
