Frontiers of Physics

, 12:120507 | Cite as

Double-temperature ratchet model and current reversal of coupled Brownian motors

Research article

Abstract

On the basis of the transport features and experimental phenomena observed in studies of molecular motors, we propose a double-temperature ratchet model of coupled motors to reveal the dynamical mechanism of cooperative transport of motors with two heads, where the interactions and asynchrony between two motor heads are taken into account. We investigate the collective unidirectional transport of coupled system and find that the direction of motion can be reversed under certain conditions. Reverse motion can be achieved by modulating the coupling strength, coupling free length, and asymmetric coefficient of the periodic potential, which is understood in terms of the effective potential theory. The dependence of the directed current on various parameters is studied systematically. Directed transport of coupled Brownian motors can be manipulated and optimized by adjusting the pulsation period or the phase shift of the pulsation temperature.

Keywords

coupled Brownian motors ratchet model effective potential noise 

References

  1. 1.
    P. Reimann and M. Evstigneev, Pulsating potential ratchet, Europhys. Lett. 78(5), 50004 (2007)ADSCrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    F. Marchesoni, Transport properties in disordered ratchet potentials, Phys. Rev. E 56(3), 2492 (1997)ADSCrossRefGoogle Scholar
  3. 3.
    J. D. Bao and Y. Z. Zhuo, Biasing fluctuation model for directional stepping motion of molecular motor, Chin. Sci. Bull. 43(22), 1879 (1998)CrossRefGoogle Scholar
  4. 4.
    P. Reimann, Brownian motors: Noisy transport far from equilibrium, Phys. Rep. 361(2–4), 57 (2002)ADSCrossRefMATHMathSciNetGoogle Scholar
  5. 5.
    O. M. Braun, R. Ferrando, and G. E. Tommei, Stimulated diffusion of an adsorbed dimer, Phys. Rev. E 68(5), 051101 (2003)ADSCrossRefGoogle Scholar
  6. 6.
    S. Gonçalves, C. Fusco, A. R. Bishop, and V. M. Kenkre, Bistability and hysteresis in the sliding friction of a dimer, Phys. Rev. B 72(19), 195418 (2005)ADSCrossRefGoogle Scholar
  7. 7.
    E. Heinsalu, M. Patriarca, and F. Marchesoni, Dimer diffusion in a washboard potential, Phys. Rev. E 77(2), 021129 (2008)ADSCrossRefGoogle Scholar
  8. 8.
    A. E. Filippov, J. Klafter, and M. Urbakh, Friction through dynamical formation and rupture of molecular bonds, Phys. Rev. Lett. 92(13), 135503 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    S. Maier, Y. Sang, T. Filleter, M. Grant, R. Bennewitz, E. Gnecco, and E. Meyer, Fluctuations and jump dynamics in atomic friction experiments, Phys. Rev. B 72(24), 245418 (2005)ADSCrossRefGoogle Scholar
  10. 10.
    H. Y. Wang and J. D. Bao, Transport coherence in coupled Brownian ratchet, Physica A 374(1), 33 (2007)ADSCrossRefGoogle Scholar
  11. 11.
    J. L. Mateos, A random walker on a ratchet, Physica A 351(1), 79 (2005)ADSCrossRefGoogle Scholar
  12. 12.
    S. E. Mangioni and H. S. Wio, A random walker on a ratchet potential: Effect of a non Gaussian noise, Eur. Phys. J. B 61(1), 67 (2008)ADSCrossRefGoogle Scholar
  13. 13.
    E. M. Craig, M. J. Zuckermann, and H. Linke, Mechanical coupling in flashing ratchets, Phys. Rev. E 73(5), 051106 (2006)ADSCrossRefGoogle Scholar
  14. 14.
    J. Menche and L. Schimansky-Geier, Two particles with bistable coupling on a ratchet, Phys. Lett. A 359(2), 90 (2006)ADSCrossRefGoogle Scholar
  15. 15.
    M. Evstigneev, S. von Gehlen, and P. Reimann, Interaction-controlled Brownian motion in a tilted periodic potential, Phys. Rev. E 79(1), 011116 (2009)ADSCrossRefGoogle Scholar
  16. 16.
    C. Lutz, M. Reichert, H. Stark, and C. Bechinger, Surmounting barriers: The benefit of hydrodynamic interactions, Europhys. Lett. 74(4), 719 (2006)ADSCrossRefGoogle Scholar
  17. 17.
    T. F. Gao, B. Q. Ai, Z. G. Zheng, and J. C. Chen, The enhancement of current and efficiency in feedback coupled Brownian ratchets, J. Stat. Mech. 2016(9), 093204 (2016)CrossRefMathSciNetGoogle Scholar
  18. 18.
    H. Y. Wang and J. D. Bao, Kramers-type elastic ratchet model for ATP gating during kinesin’s mechanochemical cycle, Physica A 389(3), 433 (2010)ADSCrossRefMathSciNetGoogle Scholar
  19. 19.
    Z. G. Zheng and Z. Hong-Qing, New soliton-like solutions for (2+1)-dimensional breaking soliton equation, Commum. Theor. Phys. 43(3), 401 (2005)ADSCrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    B. O. Yan, R. M. Miura, and Y. D. Chen, Direction reversal of fluctuation-induced biased Brownian motion on distorted ratchets, J. Theor. Biol. 210(2), 141 (2001)CrossRefGoogle Scholar
  21. 21.
    A. Pototsky, N. B. Janson, F. Marchesoni, and S. Savelev, Dipole rectification in an oscillating electric field, Europhys. Lett. 88(3), 30003 (2009)ADSCrossRefGoogle Scholar
  22. 22.
    Z. G. Zheng, G. Hu, and B. Hu, Collective directional transport in coupled nonlinear oscillators without external bias, Phys. Rev. Lett. 86(11), 2273 (2001)ADSCrossRefGoogle Scholar
  23. 23.
    S. von Gehlen, M. Evstigneev, and P. Reimann, Ratchet effect of a dimer with broken friction symmetry in a symmetric potential, Phys. Rev. E 79(3), 031114 (2009)ADSCrossRefGoogle Scholar
  24. 24.
    H. Y. Wang and J. D. Bao, The roles of ratchet in transport of two coupled particles, Physica A 337(1–2), 13 (2004)ADSCrossRefGoogle Scholar
  25. 25.
    Z. G. Zheng, M. C. Cross, and G. Hu, Collective directed transport of symmetrically coupled lattices in symmetric periodic potentials, Phys. Rev. Lett. 89, 154102 (2002)ADSCrossRefGoogle Scholar
  26. 26.
    Z. G. Zheng and H. B. Chen, Cooperative twodimensional directed transport, Europhys. Lett. 92(3), 30004 (2010)ADSCrossRefGoogle Scholar
  27. 27.
    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 77(3), 031136 (2008)ADSCrossRefGoogle Scholar
  28. 28.
    A. D. Rogat and K. G. Miler, A role for myosin VI in actin dynamics at sites of membrane remodeling during Drosophila spermatogenesis, J. Cell Sci. 115(24), 4855 (2002)CrossRefGoogle Scholar
  29. 29.
    H. Park, A. Li, L. Q. Chen, A. Houdusse, P. R. Selvin, and H. L. Sweeney, The unique insert at the end of the myosin VI motor is the sole determinant of directionality, Proc. Natl. Acad. Sci. USA 104(3), 778 (2007)ADSCrossRefGoogle Scholar
  30. 30.
    E. M. De La Cruz, E. M. Ostap, and H. L. Sweeney, Kinetic mechanism and regulation of myosin VI, J. Biochem. 276(34), 32373 (2001)Google Scholar
  31. 31.
    S. Nishikawa, K. Homma, Y. Komori, M. Iwaki, T. Wazawa, A. Hikikoshi Iwone, J. Saito, R. Ikebe, E. Katayama, T. Yanagida, and M. Ikebe, Class VI myosin moves processively along actin filaments backward with large steps, Biochem. Biophys. Res. Commun. 290(1), 311 (2002)CrossRefGoogle Scholar
  32. 32.
    A. Wunderlin and H. Haken, Generalized Ginzburg-Landau equations, slaving principle and center manifold theorem, Z. Phys. B Condens. Matter 44(1–2), 135 (1981)ADSCrossRefMathSciNetGoogle Scholar
  33. 33.
    J. C. Chen and G. Z. Su, Thermodynamics and Statistical Physics (Vol. 1), Beijing: Science Press, 2010 (in Chinese)Google Scholar
  34. 34.
    J. D. Bao, Stochastic Simulation Method of Classical and Quantum Dissipative Systems, Beijing: Science Press, 2009 (in Chinese)Google Scholar
  35. 35.
    Z. G. Zheng, Collective Behaviors and Spatiotemporal Dynamics in Coupled Nonlinear System, Beijing: Higher Education Press, 2004 (in Chinese)Google Scholar
  36. 36.
    H. B. Chen, Q. W. Wang, and Z. G. Zheng, Deterministic directed transport of inertial particles in a flashing ratchet potential, Phys. Rev. E 71(3), 031102 (2005)ADSCrossRefGoogle Scholar

Copyright information

© Higher Education Press and Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  1. 1.Department of PhysicsBeijing Normal UniversityBeijingChina
  2. 2.College of ScienceHebei University of ArchitectureZhangjiakouChina
  3. 3.Institute of Systems Science (ISS)Huaqiao UniversityXiamenChina
  4. 4.College of Information Science and EngineeringHuaqiao UniversityXiamenChina

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