Skip to main content

Brownian ratchet models of molecular motors

Cell Biochemistry and Biophysics volume 38, pages 191–213 (2003)Cite this article

Abstract

Brownian ratchet theory refers to the phenomenon that nonequilibrium fluctuations in an isothermal medium and anisotropic system can induce mechanical force and motion. This concept of noise-induced transport has motivated an abundance of theoretical and applied research. One of the exciting applications of the ratchet theory lies in the possible explanation of the operating mode of biological molecular motors. Biomolecular motors are proteins able of converting chemical energy into mechanical motion and force. Because of their dimension, the many small parts that make up molecular motors must operate at energies only a few times greater than those of the thermal baths. The description of molecular motors must be stochastic in nature. Here, we review the theoretical concepts of the Brownian ratchet theory and its possible link to the operation of biomolecular motors. We illustrate the principle of the ratchet theory with models of two molecular motors: a rotary motor (F0F1ATP synthase) and a linear motor (myosin II).

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

USD 39.95

Price includes VAT (USA)
Tax calculation will be finalised during checkout.

References

  1. Vallee, B. and Sheetz, M. P. (1996) Targeting of motor proteins. Science 271, 1539–1544.

    PubMed  Article  CAS  Google Scholar 

  2. Huxley, A. F. (1957) Muscle structure and theories of contraction. Prog. Biophys. Biophysical Chem. 7, 255–318.

    CAS  Google Scholar 

  3. Boyer, P. (1993) The binding change mechanism for ATP synthase: some probabilities and possibilities. Biochim. Biophys. Acta. 1140, 215–250.

    PubMed  Article  CAS  Google Scholar 

  4. Walker, E. J. (1998) ATP synthesis by rotary catalysis. Angew. Chem. Int. Ed. 37, 2308–2319.

    Article  CAS  Google Scholar 

  5. Skou, J. C. (1998) The identification of the sodium-potassium pump. Angew. Chem. Int. Ed. 37, 2320–2328.

    Article  CAS  Google Scholar 

  6. Bustamante, C., Keller, D., and Oster, G. (2001) The physics of molecular motors. Acc. Chem. Res. 34, 412–420.

    PubMed  Article  CAS  Google Scholar 

  7. Keller, D. and Bustamante, C. (2000) The mechanochemistry of molecular motors. Biophys. J. 78, 541–556.

    PubMed  CAS  Google Scholar 

  8. Ishijima, A., Kojima, H., Funatsu, T., Tokunaga, M., Higuchi, H., Tanaka, H., and Yanagida, T. (1998) Simultaneous observation of individual ATPase and mechanical events by a single myosin molecule during interaction with actin. Cell. 92, 161–171.

    PubMed  Article  CAS  Google Scholar 

  9. Elston, T. C., Wang, H., and Oster, G. (1998) Energy transduction in ATP synthase. Nature. 391, 510–513.

    PubMed  Article  CAS  Google Scholar 

  10. Wang, H. and Oster, G. (1998) Energy transduction in the F1 motor of ATP synthase. Nature. 396, 279–282.

    PubMed  Article  CAS  Google Scholar 

  11. Cyranoski, D. (2000) Swimming against the tide. Nature 408, 764–766.

    PubMed  Article  CAS  Google Scholar 

  12. Liu, D. S., Astumian, R. D., and Tsong, T. Y. (1990) Activation of Na+ and K+ pumping mode of (Na,K)-ATPase by an oscillating electric field. J. Biol. Chem. 265, 2760–2767.

    Google Scholar 

  13. Xie, T. D., Chen, Y., Marszalek, P., and Tsong, T. Y. (1997) Fluctuation-driven directional flow in biochemical cycles: further study of electric activation of Na,K pumps. Biophys. J. 72, 2495–2502.

    Google Scholar 

  14. Rice, S., Lin, A. W., Safer, D., Hart, C. L., Naber, N., Carragher, S., et al. (1999) A structural change in the kinesin motor protein that drive motility. Nature 402, 778–784.

    PubMed  Article  CAS  Google Scholar 

  15. Uyeda, T. Q. P., Abramson, P. D., Spudich, J. (1996) The neck region of the myosin motor domain acts as a lever arm to generate movement. Proc. Natl. Acad. Sci. USA. 93, 4459–4464.

    PubMed  Article  CAS  Google Scholar 

  16. Feynman, R. P., Leighton, R. B., and Sand, M. The Feynman Lectures on Physics. Addison-Wesley, Reading, MA, 1966.

    Google Scholar 

  17. Ajdari, A. and Prost, J. (1992) Mouvement induit par un potential periodique de basse symmetrie: dielectrophorese pulse. C. R. Acad. Sci. Paris 315, 1635–1640.

    Google Scholar 

  18. Astumian, R. D. (1997) Thermodynamics and kinetics of a Brownian motor. Science 276, 917–922.

    PubMed  Article  CAS  Google Scholar 

  19. Brown, R. (1928) A Brief account of microscopical observations made in the months on June, July, and August, 1827, on the particles contained in the pollen of plants; and on the general existence of active molecules in organic and inorganic bodies. Phil. Mag. 4, 161–173.

    Google Scholar 

  20. Einstein, A. Investigations on the Theory of Brownian Movement. Dover, NY 1956.

    Google Scholar 

  21. Perrin, J. B. Les Atomes. 3rd ed. Alean: Lib Felix, 1913, p. 188.

    Google Scholar 

  22. Maxwell, J. C. Theory of Heat. Longmans, Green and Co., London, 1871.

    Google Scholar 

  23. Szillard, L. The collected works of Leo Szilard: Scientific papers. Field, B. T. and Szilard, G. W. (eds.). MIT Press, Cambridge, 1972.

    Google Scholar 

  24. Brillouin, L. Science and Information Theory. Academic Press, London, 1956.

    Google Scholar 

  25. Bennet, C. H. (1987) Demons, engines, and the second law. Sci. Am. 257, 108–116.

    Google Scholar 

  26. Prigogine, I. (2001) La Fin des Certitudes. Odile Jacob, Paris.

    Google Scholar 

  27. Astumian, R. D. and Bier, M. (1994) Fluctuation driven ratchets: molecular motors?. Phys. Rev. Lett. 72, 917–922.

    Article  Google Scholar 

  28. Faucheaux, L. P., Bourdieu, L. S., Kaplan, P. D., and Libchaber, A. (1995) Optical thermal ratchets. Phys. Rev. Lett. 74, 1504–1507.

    Article  Google Scholar 

  29. Astumian, R. D., and Bier, M. (1996) Mechanochemical coupling of the motion of molecular motors to ATP hydrolysis. Biophys. J. 70, 689–711.

    Google Scholar 

  30. Julicher, F. Force and motion generation in molecular motors: A generic description. In: Transport and Structure in Biophysical and Chemical Phenomena. Muller, S. C., Parisi, J., and Zimmermann, W. (eds.). Lecture Notes in Physics, Springer, Berlin, 1999.

    Google Scholar 

  31. Astumian, R. D. and Der'enyi, I. (1998) Fluctuation driven transport and models of molecular motors and pumps. Eur. Biophys. J. 27, 474–489.

    PubMed  Article  CAS  Google Scholar 

  32. Parrondo, M. R. J., Espanol, P. Criticism of Feynman's analysis of the ratchet as an engine. Am. J. Phys. 64, 1125–1130.

  33. Vale, R. D. and Oosawa, F. (1990) Protein motors and Maxwell's demon: Does mechanochemical transduction involve a thermal ratchet?. Adv. Biophys. 26, 97–134.

    PubMed  Article  CAS  Google Scholar 

  34. Scott, A. C. (1985) Davydov solitons in polypeptides. Phil. Trans. R. Soc. London. 315, 423–436.

    Article  CAS  Google Scholar 

  35. Risken, H., The Fokker-Planck Equation: Methods, Solutions and Applications. Springer-Verlag, NY, 1989.

    Google Scholar 

  36. Mogilner, A. H., Wang, T., Elston, T., and Oster, G. Molecular motors: theory and experiments. In: Joel Keizer's Mathematical Biology. C. Fall, E. Marland, J. Wagner, and J. Tyson (eds.). Springer Verlag, NY, 2001.

    Google Scholar 

  37. Qian, H. (2000) The mathematical theory of molecular motor movement and chemomechanical energy transduction. J. Math. Chem. 27, 219–234.

    Article  CAS  Google Scholar 

  38. Peskin, C. S., Ermountrout, G. B., and Oster, G. F. The correlation ratchet: a novel mechanism for generating directed motion by ATP hydrolysis. In: Cell Mechanics and Cellular Engineering. Mow, V. C., Guilak, R., Tran-Son-Tay, R., and Hochmuth, R. M. (eds.). Springer-Verlag, NY, 1993, pp. 479–482.

    Google Scholar 

  39. Harmer, G. P. and Abbott, D. (1999) Losing strategies can win by Parrondo's paradox. Nature 402, 864.

    Article  CAS  Google Scholar 

  40. Parrondo, J. M. R., Harmer, G. P., Abbott, D. (2000) New paradoxical games based on Brownian ratchets. Phys. Rev. Lett. 85, 5226–5229.

    PubMed  Article  CAS  Google Scholar 

  41. Magnasco, M. O. (1993) Forced thermal ratchets. Phys. Rev. Lett. 71, 1477–1481.

    PubMed  Article  Google Scholar 

  42. Blanter, Ya. M. and Buttiker, M. (1998) Rectification of fluctuations in an underdamped ratchet. Phys. Rev. Lett. 81, 4040–4043.

    Article  CAS  Google Scholar 

  43. Kettner, C., Riemann, P., Hanggi, P., and Muller, F. (2000) Drift ratchet. Phys. Rev. E. 61, 312–323.

    Article  CAS  Google Scholar 

  44. Ajdari, A., Mukamel, D., Peliti, L., and Prost, J. (1994) Rectified motion induced by AC forces in periodic structures. J. Phys. I (France) 4, 1551–1557.

    Article  Google Scholar 

  45. Mcquarrie, D. A., Statistical Mechanics. Harper & Row, NY, 1976.

    Google Scholar 

  46. Kramers, H. A. (1940) Brownian motion in a field of force and the diffusion theory of chemical reactions. Physica 7, 284–304.

    Article  CAS  Google Scholar 

  47. Junge, W., Lill, H., and Engelbrecht, S. (1997) ATP synthase: an electrochemical transducer with rotary mechanics. Trends. Biochem. Sci. 263, 420–423.

    Article  Google Scholar 

  48. Kinoshita, K., Yasuda, R., Noji, K., Ishiwata, S., and Yoshida, M. (1998) F1ATPase: a rotary motor made of a single molecule. Cell 93, 21–24.

    Article  Google Scholar 

  49. Nakamoto, R. K. (1999) Molecular features of energy coupling in the F0F1 ATP synthase. News Physiol. Sci. 14, 40–46.

    PubMed  CAS  Google Scholar 

  50. Walker, J. E. and Cozens, A. L. (1986) Evolution of ATP synthase. Chem. Scr. 26B, 263–272.

    CAS  Google Scholar 

  51. Abrahams, J., Leslie, A., Lutter, R., and Walker, J. E. (1994) Structure at 2.8 0 A resolution of the F1-ATPase from bovine heart mitochondria. Nature 370, 621–628.

    PubMed  Article  CAS  Google Scholar 

  52. Abrahams, J. P., Buchanan, S. K., Van Raaij, I. M., Fearnley, A. G., Leslie, A. G. W., and Walker, J. E. (1996) The structure of bovine F1-ATPase complexed with the peptide antibiotic efrapeptin. Proc. Natl. Acad. Sci. USA, 92, 10964–10968.

    Google Scholar 

  53. Boyer, P. (1989) A perspective of the binding change mechanism for ATP synthesis. FASEB J. 3, 2164–2178.

    PubMed  CAS  Google Scholar 

  54. Kato-Yamada, Y., Noji, H., Yasuda, R., Kinosita, K., and Yoshida, M. (1998) Direct observation of the rotation of epsilon subunit in F1-ATPase. J. Biol. Chem. 273, 19375–19377.

    PubMed  Article  CAS  Google Scholar 

  55. Noji, H., Yasuda, R., Yoshida, M., and Kinosita, K. (1997) Direct observation of the rotation of the F1 ATPase. Nature 386, 299–302.

    PubMed  Article  CAS  Google Scholar 

  56. Oster, G. and Wang, H. (2000) Why the efficiency of the F1 ATPase is high?. J. Bioeneerg. Biomembr. 32, 459–469.

    Article  CAS  Google Scholar 

  57. Wilkens, S., Zhou, J., Nakayama, R., Dunn, S. D., and Capaldi, R. A. (2000) Localization of the α subunit in the Escherichia coli F1F0 ATP synthase by immuno electron microscopy: the α subunit binds on top of the F1. J. Mol. Biol. 295, 387–391.

    PubMed  Article  CAS  Google Scholar 

  58. Parrondo, J. M. R. (1998) Reversible ratchets as Brownian particles in an adiabatically changing periodic potential. Phys. Rev. E. 57, 7297–7300.

    Article  CAS  Google Scholar 

  59. Huxley, H. E. (1953). Electron microscope studies of the organization of the filaments in striated muscle. Biochem. Biophys. Acta. 12, 387–394.

    PubMed  Article  CAS  Google Scholar 

  60. Huxley, H. E. (1957). The double array of filaments in cross-striated muscle. J. Biophys. Biochem. Cytol. 3, 631–648.

    PubMed  CAS  Article  Google Scholar 

  61. Rayment, I., Holden, H. M., Whittaker, M., Yohn, C. B., Lorenz, M., Holmes, K. C., and Milligan, R. A. (1993) Structure of the actinmyosin complex and its implications for muscle contraction. Science 261, 58–65.

    PubMed  Article  CAS  Google Scholar 

  62. Julicher, F., and Prost, J. (1995) Cooperative molecular motors. Phys. Rev. Lett. 75, 2618–2621.

    PubMed  Article  Google Scholar 

  63. Visscher, K., Schnitzer, M. J., and Block, S. M. (1999) Single kinesin molecules studied with a molecular force clamp. Nature 400, 184–189.

    PubMed  Article  CAS  Google Scholar 

  64. Lattanzi, G., and Maritan, A. (2001) Force dependence of the Michaelis constant in a two-state ratchet model for molecular motors. Phys. Rev. Lett. 86, 1134–1137.

    PubMed  Article  CAS  Google Scholar 

  65. Yasuda, K., Shindo, Y., and Ishiwata, S. (1996) Synchronous behavior of spontaneous oscillations of sarcomeres in skeletal myofibrils under isotonic conditions. Biophys. J. 70, 1823–1829.

    PubMed  CAS  Article  Google Scholar 

  66. Astumian, R. D. (2001) Making molecules into motors. Sci. Am. 285, 57–64.

    Article  Google Scholar 

  67. Lodish, H., Baltimore, D., Berk, A., Zipursky, L., Matsidaira, P., and Darnell, J. Molecular Cell Biology. 3rd ed. Scientific American Books Inc., London, 1995.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Human Performance Laboratory, University of Calgary, T2N 1N4, Calgary, Alberta, Canada

    Rachid Ait-Haddou & Walter Herzog

Authors
  1. Rachid Ait-Haddou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Walter Herzog
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Walter Herzog.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Ait-Haddou, R., Herzog, W. Brownian ratchet models of molecular motors. Cell Biochem Biophys 38, 191–213 (2003). https://doi.org/10.1385/CBB:38:2:191

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1385/CBB:38:2:191

Index Entries

  • Brownian ratchet
  • Feynman ratchet
  • flashing ratchet
  • molecular motors
  • myosin II
  • FATP synthase