Skip to main content
SpringerLink
Log in

Rotational effect in two-dimensional cooperative directed transport

  • Review Article
  • Published:
Frontiers of Physics Aims and scope Submit manuscript

Abstract

In this review we investigate the rotation effect in the motion of coupled dimer in a two-dimensional asymmetric periodic potential. Free rotation does not generate directed transport in translational direction, while we find it plays an critical role in the motors motility when the dimer moves under the effect of asymmetry ratchet potential. In the presence of external force, we study the relation between the average current and the force numerically and theoretically. The numerical results show that only appropriate driving force could produce nonzero current and there are current transitions when the force is large enough. An analysis of stability analysis of limit cycles is applied to explain the occurrence of these transitions. Moreover, we numerically simulate the transport of this coupled dimer driven by the random fluctuations in the rotational direction. The existence of noise smooths the current transitions induced by the driving force and the resonance-like peaks which depend on the rod length emerge in small noise strength. Thanks to the noise in the rotational direction, autonomous motion emerges without the external force and large noise could make the current reversal happen. Eventually, the new mechanism to generate directed transport by the rotation is studied.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, Myosin V walks hand-over-hand: Single fluorophore imaging with 1.5-nm localization, Science, 2003, 300(5628): 2061

    Article  ADS  Google Scholar 

  2. A. Yildiz, H. Park, D. Safer, Z. Yang, L. Q. Chen, P. R. Selvin, and H. L. Sweeney, Myosin VI steps via a handover-hand mechanism with its lever arm undergoing fluctuations when attached to actin, J. Biol. Chem., 2004, 279(36): 37223

    Article  Google Scholar 

  3. A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, Kinesin walks hand-over-hand, Science, 2004, 303(5658): 676

    Article  ADS  Google Scholar 

  4. S. L. Reck-Peterson, A. Yildiz, A. P. Carter, A. Gennerich, N. Zhang, and R. D. Vale, Single-molecule analysis of Dynein processivity and stepping behavior, Cell, 2006, 126(2): 335

    Article  Google Scholar 

  5. M. von Delius and D. A. Leigh, Walking molecules, Chem. Soc. Rev., 2011, 40(7): 3656

    Article  Google Scholar 

  6. K. Shiroguchi and K. Kinosita, Myosin V walks by lever action and brownian motion, Science, 2007, 316(5828): 1208

    Article  ADS  Google Scholar 

  7. A. R. Dunn and J. A. Spudich, Dynamics of the unbound head during myosin V processive translocation, Nat. Struct. Mol. Biol., 2007, 14(3): 246

    Article  Google Scholar 

  8. F. Jülicher, A. Ajdari, and J. Prost, Modeling molecular motors, Rev. Mod. Phys., 1997, 69(4): 1269

    Article  ADS  Google Scholar 

  9. R. D. Astumian, Thermodynamics and kinetics of a Brownian motor, Science, 1997, 276(5314): 917

    Article  Google Scholar 

  10. M. Dittrich, J. Yu, and K. Schulten, PcrA Helicase, a molecular motor studied from the electronic to the functional level, in: Atomistic Approaches in Modern Biology, edited by M. Reiher, Springer, 2007, pp. 319–347

    Chapter  Google Scholar 

  11. Z. G. Zheng, G. Hu, and B. Hu, Collective directional transport in coupled nonlinear oscillators without external bias, Phys. Rev. Lett., 2001, 86(11): 2273

    Article  ADS  Google Scholar 

  12. Z. G. Zheng, M. C. Cross, and G. Hu, Collective directed transport of symmetrically coupled lattices in symmetric periodic potentials, Phys. Rev. Lett., 2002, 89(15): 154102

    Article  ADS  Google Scholar 

  13. H. B. Chen, Q. W. Wang, and Z. G. Zheng, Deterministic directed transport of inertial particles in a flashing ratchet potential, Phys. Rev. E, 2005, 71(3 Pt 1): 031102

    Article  ADS  Google Scholar 

  14. Z. G. Zheng and H. B. Chen, Cooperative two-dimensional directed transport, Europhys. Lett., 2010, 92(3): 30004

    Google Scholar 

  15. H. B. Chen and Z. G. Zheng, Deterministic collective directional transport in one-dimensional flashing ratchet potentials, Mod. Phys. Lett. B, 2011, 25(14):1179

    Article  ADS  MATH  Google Scholar 

  16. B. Alberts, D. Bray, J. Lewis, M. Raff, K. Roberts, and J. D. Watson, Molecular Biology of the Cell, New York: Garland Publishing Comp., 1983

    Google Scholar 

  17. S. von Gehlen, M. Evstigneev, and P. Reimann, Dynamics of a dimer in a symmetric potential: Ratchet effect generated by an internal degree of freedom, Phys. Rev. E, 2008, 77(3): 031136

    Article  ADS  Google Scholar 

  18. D. Dan, A. Jayannavar, and G. I. Menon, A biologically inspired model for two-headed Brownian motors, Physica A, 2003, 318: 40

    Article  ADS  Google Scholar 

  19. B. Geislinger and R. Kawai, Brownian molecular motors driven by rotation-translation coupling, Phys. Rev. E, 2006, 74(1): 011912

    Article  ADS  Google Scholar 

  20. C. Veigel, F. Wang, M. L. Bartoo, J. R. Sellers, and J. E. Molloy, The gated gait of the processive molecular motor, myosin V, Nat. Cell Biol., 2001, 4(1): 59

    Article  Google Scholar 

  21. G. Cappello, P. Pierobon, C. Symonds, L. Busoni, J. Christof, M. Gebhardt, M. Rief, and J. Prost, Myosin V stepping mechanism, Proc. Natl. Acad. Sci. USA, 2007, 104(39): 15328

    Article  ADS  Google Scholar 

  22. S. Uemura, H. Higuchi, A. O. Olivares, E. M. De La Cruz, and S. Ishiwata, Mechanochemical coupling of two substeps in a single myosin V motor, Nat. Struct. Mol. Biol., 2004, 11(9): 877

    Article  Google Scholar 

  23. J. Prost, J. F. Chauwin, L. Peliti, and A. Ajdari, Asymmetric pumping of particles, Phys. Rev. Lett., 1994, 72(16): 2652

    Article  ADS  Google Scholar 

  24. J. Rousselet, L. Salome, A. Ajdari, and J. Prost, Directional motion of brownian particles induced by a periodic asymmetric potential, Nature, 1994, 370(6489): 446

    Article  ADS  Google Scholar 

  25. M. O. Magnasco, Forced thermal ratchets, Phys. Rev. Lett., 1993, 71(10): 1477

    Article  ADS  Google Scholar 

  26. R. D. Astumian and M. Bier, Fluctuation driven ratchets: Molecular motors, Phys. Rev. Lett., 1994, 72(11): 1766

    Article  ADS  Google Scholar 

  27. R. Adler, A study of locking phenomena in oscillators, Proceedings of the IRE, 1946, 34(6): 351

    Article  Google Scholar 

  28. F. Falo, J. Munárriz, and J. Mazo, Model for hand-overhand motion in molecular motors, Statistical Mechanics of Molecular Biophysics, 63 (2008)

  29. A. G. Hendricks, B. I. Epureanu, and E. Meyhöfer, Collective dynamics of kinesin, Phys. Rev. E, 2009, 79(3): 031929

    Article  ADS  MathSciNet  Google Scholar 

  30. C. L. Asbury, A. N. Fehr, and S. M. Block, Kinesin moves by an asymmetric hand-over-hand mechanism, Science, 2003, 302(5653): 2130

    Google Scholar 

  31. H. Risken, Fokker-Planck Equation, Springer, 1984

    Book  MATH  Google Scholar 

  32. P. Reimann, R. Bartussek, R. Häußler, and P. Hänggi, Brownian motors driven by temperature oscillations, Phys. Lett. A, 1996, 215(1–2): 26

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Studies, Beijing Normal University, Beijing, 100876, China

    Li-Yan Qiao & Zhi-Gang Zheng

  2. Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai, 200092, China

    Yun-yun Li

Authors
  1. Li-Yan Qiao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yun-yun Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhi-Gang Zheng
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zhi-Gang Zheng.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Qiao, LY., Li, Yy. & Zheng, ZG. Rotational effect in two-dimensional cooperative directed transport. Front. Phys. 10, 87–94 (2015). https://doi.org/10.1007/s11467-014-0423-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11467-014-0423-3

Keywords

Search

Navigation