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. 1989 Nov;56(5):1029–1035. doi: 10.1016/S0006-3495(89)82748-1

Kinematics of helical motion of microorganisms capable of motion with four degrees of freedom.

H C Crenshaw 1
PMCID: PMC1280601  PMID: 2636879

Abstract

The kinematics of helical motion are described for an organism with four degrees of freedom, relative to the organism's frame of reference. It can rotate about any of three orthogonal axes, but can translate only in the direction of one axis. In particular, equations are developed for calculating the pitch, radius, and angular frequency of the helical path from the translational and rotational velocities of the microorganism, correcting, and expanding the analysis of Gray J. (1955. J. Exp. Biol. 32:775-801).

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Selected References

These references are in PubMed. This may not be the complete list of references from this article.

  1. Brokaw C. J. Calcium-induced asymmetrical beating of triton-demembranated sea urchin sperm flagella. J Cell Biol. 1979 Aug;82(2):401–411. doi: 10.1083/jcb.82.2.401. [DOI] [PMC free article] [PubMed] [Google Scholar]
  2. Brokaw C. J., Josslin R., Bobrow L. Calcium ion regulation of flagellar beat symmetry in reactivated sea urchin spermatozoa. Biochem Biophys Res Commun. 1974 Jun 4;58(3):795–800. doi: 10.1016/s0006-291x(74)80487-0. [DOI] [PubMed] [Google Scholar]
  3. Goldstein S. F. Asymmetric waveforms in echinoderm sperm flagella. J Exp Biol. 1977 Dec;71:157–170. doi: 10.1242/jeb.71.1.157. [DOI] [PubMed] [Google Scholar]
  4. Kamiya R., Witman G. B. Submicromolar levels of calcium control the balance of beating between the two flagella in demembranated models of Chlamydomonas. J Cell Biol. 1984 Jan;98(1):97–107. doi: 10.1083/jcb.98.1.97. [DOI] [PMC free article] [PubMed] [Google Scholar]
  5. Keller J. B., Rubinow S. I. Swimming of flagellated microorganisms. Biophys J. 1976 Feb;16(2 Pt 1):151–170. doi: 10.1016/s0006-3495(76)85672-x. [DOI] [PMC free article] [PubMed] [Google Scholar]
  6. Omoto C. K., Brokaw C. J. Bending patterns of Chlamydomonas flagella: II. Calcium effects on reactivated Chlamydomonas flagella. Cell Motil. 1985;5(1):53–60. doi: 10.1002/cm.970050105. [DOI] [PubMed] [Google Scholar]
  7. RIKMENSPOEL R., van HERPEN, EIJKHOUT P. Cinematographic observations of the movements of bull sperm cells. Phys Med Biol. 1960 Oct;5:167–181. doi: 10.1088/0031-9155/5/2/306. [DOI] [PubMed] [Google Scholar]

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