Rotational effect in two-dimensional cooperative directed transport
Li-Yan Qiao1,Yun-yun Li2,Zhi-Gang Zheng1,*()
1. Department of Physics and the Beijing-Hong Kong-Singapore Joint Center for Nonlinear and Complex Studies, Beijing Normal University, Beijing 100876, China
2. Center for Phononics and Thermal Energy Science, School of Physics Science and Engineering, Tongji University, Shanghai 200092, China
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.
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
https://doi.org/10.1126/science.1084398
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
https://doi.org/10.1074/jbc.C400252200
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
https://doi.org/10.1016/j.cell.2006.05.046
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
https://doi.org/10.1038/nsmb1206
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
https://doi.org/10.1007/128_2006_086
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
https://doi.org/10.1103/PhysRevLett.86.2273
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
https://doi.org/10.1103/PhysRevLett.89.154102
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
https://doi.org/10.1103/PhysRevE.71.031102
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
https://doi.org/10.1142/S0217984911026206
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
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
https://doi.org/10.1103/PhysRevE.77.031136
B. Geislinger and R. Kawai, Brownian molecular motors driven by rotation-translation coupling, Phys. Rev. E, 2006, 74(1): 011912
https://doi.org/10.1103/PhysRevE.74.011912
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
https://doi.org/10.1038/ncb732
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
https://doi.org/10.1073/pnas.0706653104
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
https://doi.org/10.1038/nsmb806
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
https://doi.org/10.1038/370446a0
C. L. Asbury, A. N. Fehr, and S. M. Block, Kinesin moves by an asymmetric hand-over-hand mechanism, Science, 2003, 302(5653): 2130
https://doi.org/10.1126/science.1092985
P. Reimann, R. Bartussek, R. H?u?ler, and P. H?nggi, Brownian motors driven by temperature oscillations, Phys. Lett. A, 1996, 215(1-2): 26
https://doi.org/10.1016/0375-9601(96)00222-8