Journal of Biological Physics

, Volume 26, Issue 4, pp 255–260 | Cite as

Viscous Damping of Vibrations in Microtubules

  • Kenneth R. Foster
  • James W. Baish


Pokorný et al. have recently suggested that metabolic processes drivemicrotubules in a cell to vibrate at Megahertz frequencies, but the theorydoes not explicitly consider dissipative effects which will tend to damp outthe vibrations. To examine the effects of viscous damping on the structure,we determine viscous forces and rate of energy loss in a cylinderundergoing longitudinal oscillations in water. A nondimensional expressionis obtained for the viscous drag on the cylinder. When applied to amicrotubule, the results indicate that viscous damping is several orders ofmagnitude too large to allow resonant vibrations.

microtubules radiofrequency signal relaxation time vibrations viscous damping 


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  1. 1.
    Pokorný , J., Jelínek, F., Trkal, V., Lamprecht, I. and Hölzel, R.: Vibrations in Microtubules, J. Biol. Phys. 23 (1997), 171-179.Google Scholar
  2. 2.
    Jelínek, F., Pokorný , J., Šaroch, J., Trkal, V., Hasšek, J. and Palán, B.: Microelectronic Sensors for Measurement of Electromagnetic Fields of Living Cells and Experimental Results, Bioelect. Bioenerg. 48 (1999), 261-266.Google Scholar
  3. 3.
    Currie, I.G.: Fundamental Mechanics of Fluids, McGraw-Hill, New York, 1974.Google Scholar
  4. 4.
    Carslaw, H.S. and Jaeger, J.C.: Conduction of Heat in Solids, Second Ed., Oxford University Press, London, 1959.Google Scholar
  5. 5.
    Mitchison, T. and Kirschner, M.: Dynamic Instability of Microtubule Growth, Nature 312 (1984), 237-242.PubMedGoogle Scholar
  6. 6.
    Pokorný , J., Jelínek, F. and Trkal, V.: Electric Field Around Microtubules, Bioelectrochem. Bioenerg. 45 (1998), 239-245.Google Scholar
  7. 7.
    Russel, W.B., Saville, D.A. and Schowalter, W.R.: Colloidal Dispersions (Cambridge Monographs on Mechanics and Applied Mathematics), Cambridge University Press, Cambridge, 1992.Google Scholar
  8. 8.
    Stoylov, S.P.: Colloid Electro-Optics: Theory, Techniques, Applicatiosn (Colloid Science Series), Academic Press, London, 1991.Google Scholar
  9. 9.
    Wiggins, C.H., Riveline, D., Ott, A. and Goldstein, R.E.: Trapping and Wiggling: Elastohydrodynamics of Driven Microfilaments, Biophys. J. 74 (1998), 1043-1060.Google Scholar
  10. 10.
    Edwards, G.S., Davis, C.C., Saffer, J.D. and Swicord, M.L.: Resonant Microwave Absorption of Selected DNA Molecules, Phys. Rev. Lett. 53 (1984), 1284-1287.Google Scholar
  11. 11.
    Grundler, W., Keilman, F., Putterlik, V. and Strube, D.: Resonant-Like Dependence of Yeast Growth Rate on Microwave Frequencies, Br. J. Cancer (Suppl.) 45 (1982), 206-208.Google Scholar

Copyright information

© Kluwer Academic Publishers 2000

Authors and Affiliations

  • Kenneth R. Foster
    • 1
  • James W. Baish
    • 2
  1. 1.Department of BioengineeringUniversity of PennsylvaniaPhiladelphiaU.S.A
  2. 2.Department of Mechanical EngineeringBucknell UniversityLewisburgU.S.A

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