Energetic Considerations of Ciliary Beating

  • Shay Gueron
  • Konstantin Levit-Gurevich
Conference paper
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 124)

Abstract

The internal mechanism of cilia which is responsible for their beating is among the most ancient biological motors on an evolutionary scale. Ciliary beat cycles consist of two phases: the effective stroke, where the cilium moves approximately as a straight rod, and the recovery stroke, where it bends and rolls close to the surface in a mostly tangential motion.

It is commonly agreed that for efficient functioning, the effective stroke is designed to encounter strong viscous resistance and to generate thrust, whereas the recovery stroke is designed to return to starting position while avoiding viscous resistance as much as possible. Metachronal coordination between cilia, which occurs when many of them beat close to each other, is believed to be an autonomous result of the hydrodynamical interactions in the multiciliary system. Qualitatively, metachronism is understood as a way for minimizing the energy expenditure required for beating.

This paper presents a quantitative investigation of the energetic advantages of metachronism. Using a new method for computing the work by a model cilium beating in a viscous fluid we demonstrate that the energy expenditure during the effective stroke for a single cilium is approximately five times the amount of work done during the recovery stroke. Investigation of multicilia configurations shows that having neighboring cilia beat metachronally is energetically advantageous and perhaps crucial for multiciliary functioning. Finally, the model is used to approximate the number of dynein arm attachments that are likely to occur during the effective and recovery strokes of a beat cycle.

Keywords

Hydrolysis Resis 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Baum, G., Priel, Z., Roth, Y., Liron, N., and Ostfed, E.G. (editors) (1997). Cilia, Mucus, and Mucociliary Interactions. (Marcel Dekker, New-York).Google Scholar
  2. [2]
    Brokaw, C.J. (1985). Computer simulation of flagellar movement. VI. simple curvature-controlled models are incompletely specified. Biophys. J. 48:633–642.CrossRefGoogle Scholar
  3. [3]
    Brokaw, C.J. and Johnson, K.A. (1989). Dynein-induced microtubule sliding and force generation. Cell Movement 1:191–198.Google Scholar
  4. [4]
    Gueron, S. and Levit-Gurevich, K. (1998). Computation of the internal forces in cilia: Application to ciliary motion, the effects of viscosity, and cilia interactions. Biophys. J. 74:1658–1676.CrossRefGoogle Scholar
  5. [5]
    Gueron, S., Levit-Gurevich, K., Liron, N., and Blum, J.J. (1997). Cilia internal mechanism and metachronal coordination as the result of hydrodynamical coupling. Proc. Natl. Acad. Sci. USA. 94:6001–6006.CrossRefMATHGoogle Scholar
  6. [6]
    Gueron, S. and Liron, N. (1992). Ciliary motion modeling, and dynamic multicilia interactions. Biophys. J. 63:1045–1058.CrossRefGoogle Scholar
  7. [7]
    Hamasaki, T., Holwill, M.E.J., Barkalow, K. and Satir., P. (1995). Mechanochemical aspects of axonemal dynein activity studies by in vitro microtubule translocation. Biophys. J. 69:2569–2579.CrossRefGoogle Scholar
  8. [8]
    Holwill, M.E.J., Foster, G.F., Hamasaki, T., and Satir, P. (1995). Biophysical aspects and modelling of ciliary motility. Cell Motil. Cytoskel. 32:114–120.CrossRefGoogle Scholar
  9. [9]
    Machemer, H. (1972). Ciliary activity and the origin of metachronism in Paramecium: effects of increased viscosity. J. Exp. Biology. 57:239–259.Google Scholar
  10. [10]
    Rikmenspoel, R. (1964). Measurement of motility and energy metabolism of bull spermatozoa. Trans. NY Acad. Sci. 26:1072–1086.CrossRefGoogle Scholar
  11. [11]
    Satir, P. (1994). Biochemical events in the production of ciliary movement. in Biomechanics of active movement and division of cells, ed. Akkas, N. (Springer, Heidelberg), pp. 465–470.CrossRefGoogle Scholar
  12. [12]
    Satir, P., Hamasaki, T. and Holwill, M.E.J. (1997). Modeling outer dynein arm activity and its relation to the ciliary beat cycle, in Cilia, Mucus, and Mucociliary Interaction, eds. Baum, G., Priel, Z., Roth, Y., Liron, N., and Ostfed, E.G. (Marcel Dekker, New-York), pp. 13–19.Google Scholar
  13. [13]
    Sleigh, M.A. (1962). The Biology of Cilia and Flagella. (Pergamon Press, Oxford).Google Scholar
  14. [14]
    Sleigh, M.A. (1968). Patterns of ciliary beating. Aspects of Cell Motility (22nd Symposium of the Society for Experimental Biology), ed. Miller, P.L., pp. 131–150.Google Scholar
  15. [15]
    Sleigh, M.A. and Barlow, D.I. (1982). How are different ciliary beat patterns produced? Symposia of the Society for Experimental Biology. 35:139–157.Google Scholar
  16. [16]
    Taylor, G.I. (1951). Analysis of the swimming of microscopic organisms. Proc. R. Soc. Lond. A. 209:447–461.CrossRefMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • Shay Gueron
    • 1
  • Konstantin Levit-Gurevich
    • 2
  1. 1.Department of MathematicsUniversity of HaifaHaifaIsrael
  2. 2.Department of MathematicsIsrael Institute of TechnologyHaifaIsrael

Personalised recommendations