Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential

doi:10.1007/s11467-021-1057-x

Front. Phys.

2021, Vol. 16

Issue (3) : 31500 https://doi.org/10.1007/s11467-021-1057-x

RESEARCH ARTICLE

Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential

Wei-Xia Wu¹, Chen-Pu Li², Yan-Li Song³, Ying-Rong Han⁴, Zhi-Gang Zheng⁵(

)

¹. Science Education Department, Beijing Institute of Graphic Communication, Beijing 102600, China
². College of Science, Hebei University of Architecture, Zhangjiakou 075000, China
³. School of Science, Tianjin University, Tianjin 300072, China
⁴. School of Science, Hebei University of Technology, Tianjin 300401, China
⁵. Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China

Download: PDF(1968 KB)
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

Abstract

Considering a double-headed Brownian motor moving with both translational and rotational degrees of freedom, we investigate the directed transport properties of the system in a traveling-wave potential. It is found that the traveling wave provides the essential condition of the directed transport for the system, and at an appropriate angular frequency, the positive current can be optimized. A general current reversal appears by modulating the angular frequency of the traveling wave, noise intensity, external driving force and the rod length. By transforming the dynamical equation in traveling-wave potential into that in a tilted potential, the mechanism of current reversal is analyzed. For both cases of Gaussian and Lévy noises, the currents show similar dependence on the parameters. Moreover, the current in the tilted potential shows a typical stochastic resonance effect. The external driving force has also a resonance-like effect on the current in the tilted potential. But the current in the traveling-wave potential exhibits the reverse behaviors of that in the tilted potential. Besides, the currents obviously depend on the stability index of the Lévy noise under certain conditions.

Keywords Brownian motor rotation-translation coupling traveling-wave potential current reversal

Corresponding Author(s): Zhi-Gang Zheng

Issue Date: 15 April 2021

Cite this article:

Wei-Xia Wu,Chen-Pu Li,Yan-Li Song, et al. Rotation-translation coupling of a double-headed Brownian motor in a traveling-wave potential[J]. Front. Phys. , 2021, 16(3): 31500.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-021-1057-x
https://academic.hep.com.cn/fop/EN/Y2021/V16/I3/31500

1	P. Reimann, Brownian motors: Noisy transport far from equilibrium, Phys. Rep. 361(2–4), 57 (2002) https://doi.org/10.1016/S0370-1573(01)00081-3
2	P. Hänggi and F. Marchesoni, Artificial Brownian motors: Controlling transport on the nanoscale, Rev. Mod. Phys. 81(1), 387 (2009) https://doi.org/10.1103/RevModPhys.81.387
3	C. S. Peskin, G. M. Odell, and G. F. Oster, Cellular motions and thermal fluctuations: The Brownian ratchet, Biophys. J. 65(1), 316 (1993) https://doi.org/10.1016/S0006-3495(93)81035-X
4	R. D. Astumian, Thermodynamics and kinetics of a Brownian motor, Science 276(5314), 917 (1997) https://doi.org/10.1126/science.276.5314.917
5	P. Reimann and P. Hänggi, Introduction to the physics of Brownian motors, Appli. Phys. A 75(2), 169 (2002) https://doi.org/10.1007/s003390201331
6	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) https://doi.org/10.1103/PhysRevE.79.031114
7	M. Khoury, A. M. Lacasta, J. M. Sancho, and K. Lindenberg, Weak disorder: anomalous transport and diffusion are normal yet again, Phys. Rev. Lett. 106(9), 090602 (2011) https://doi.org/10.1103/PhysRevLett.106.090602
8	D. Cubero and F. Renzoni, Brownian Ratchets: From Statistical Physics to Bio- and Nano-motors, Cambridge University Press, Cambridge, 2016 https://doi.org/10.1017/CBO9781107478206
9	C. Hyeon and W. Hwang, Physical insight into the thermodynamic uncertainty relation using Brownian motion in tilted periodic potentials, Phys. Rev. E 96(1), 012156 (2017) https://doi.org/10.1103/PhysRevE.96.012156
10	T. Siebert, F. Dittrich, F. Schmid, K. Binder, T. Speck, and P. Virnau, Critical behavior of active Brownian particles, Phys. Rev. E 98(3), 030601 (2018) https://doi.org/10.1103/PhysRevE.98.030601
11	M. J. Skaug, C. Schwemmer, S. Fringes, C. D. Rawlings, and A. W. Knoll, Nanofluidic rocking Brownian motors, Science 359(6383), 1505 (2018) https://doi.org/10.1126/science.aal3271
12	R. Salgado-García, Noise-induced rectification in out-ofequilibrium structures, Phys. Rev. E 99(1), 012128 (2019) https://doi.org/10.1103/PhysRevE.99.012128
13	S. Pattanayak, R. Das, M. Kumar, and S. Mishra, Enhanced dynamics of active Brownian particles in periodic obstacle arrays and corrugated channels, Eur. Phys. J. E 42(5), 62 (2019) https://doi.org/10.1140/epje/i2019-11826-7
14	P. Hänggi, J. Tuczka, and J. Spiechowicz, Many faces of nonequilibrium: Anomalous transport phenomena in driven periodic systems, Acta Phys. Pol. 51(5), 1131 (2020) https://doi.org/10.5506/APhysPolB.51.1131
15	A. Nakamura, K. I. Okazaki, T. Furuta, M. Sakurai, J. Ando, and R. Iino, Crystalline chitin hydrolase is a burntbridge Brownian motor, Biophys. 17, 51 (2020) https://doi.org/10.2142/biophysico.BSJ-2020004
16	H. Qian, A simple theory of motor protein Kinesin and energetics, Biophys. Chem. 67(1–3), 263 (1997) https://doi.org/10.1016/S0301-4622(97)00051-3
17	W. R. Schief and J. Howard, Conformational changes during Kinesin motility, Curr. Opin. Cell Biol. 13(1), 19 (2001) https://doi.org/10.1016/S0955-0674(00)00169-1
18	A. B. Kolomeisky and M. E. Fisher, A simple kinetic model describes the processivity of myosin-V, Biophys. J. 84(3), 1642 (2003) https://doi.org/10.1016/S0006-3495(03)74973-X
19	L. C. Kapitein, B. H. Kwok, J. S. Weinger, C. F. Schmidt, T. M. Kapoor, and E. J. G. Peterman, Microtubule crosslinking triggers the directional motility of kinesin-5, J. Cell Biol. 182(3), 421 (2008) https://doi.org/10.1083/jcb.200801145
20	M. Takanoa, T. P. Teradab, and M. Sasai, Unidirectional Brownian motion observed in an in silico single molecule experiment of an actomyosin motor, Proc. Natl. Acad. Sci. USA 107(17), 7769 (2010) https://doi.org/10.1073/pnas.0911830107
21	F. J. Kull and S. A. Endow, Force generation by kinesin and myosin cytoskeletal motor proteins, J. Cell Sci. 126(Pt 1), 9 (2013) https://doi.org/10.1242/jcs.103911
22	J. E. Komianos and G. A. Papoian, Stochastic ratcheting on a funneled energy landscape is necessary for highly efficient contractility of actomyosin force dipoles, Phys. Rev. X 8(2), 021006 (2018) https://doi.org/10.1103/PhysRevX.8.021006
23	G. Knoops and C. Vanderzande, Motion of kinesin in a viscoelastic medium, Phys. Rev. E 97(5), 052408 (2018) https://doi.org/10.1103/PhysRevE.97.052408
24	R. D. Astumian and M. Bier, Fluctuation driven ratchets: Molecular motors, Phys. Rev. Lett. 72(11), 1766 (1994) https://doi.org/10.1103/PhysRevLett.72.1766
25	A. Sarmiento and H. Larralde, Deterministic transport in ratchets, Phys. Rev. E 59(5), 4878 (1999) https://doi.org/10.1103/PhysRevE.59.4878
26	A. Yildiz, J. N. Forkey, S. A. McKinney, T. Ha, Y. E. Goldman, and P. R. Selvin, Myosin V walks hand-overhand: Single fluorophore imaging with 1.5-nm localization, Science 300(5628), 2061 (2003) https://doi.org/10.1126/science.1084398
27	C. L. Asbury, A. N. Fehr, and S. M. Block, Kinesin moves by an asymmetric hand-over-hand mechanism, Science 302(5653), 2130 (2003) https://doi.org/10.1126/science.1092985
28	A. Yildiz, M. Tomishige, R. D. Vale, and P. R. Selvin, Kinesin walks hand-over-hand, Science 303(5658), 676 (2004) https://doi.org/10.1126/science.1093753
29	A. Mehta, Myosin learns to walk, J. Cell Sci. 114(11), 1981 (2001)
30	Z. Ökten, L. S. Churchman, R. S. Rock, and J. A. Spudich, Myosin VI walks hand-over-hand along actin, Nat. Struct. Mol. Biol. 11(9), 884 (2004) https://doi.org/10.1038/nsmb815
31	Y. X. Li, X. Z. Wu, and Y. Z. Zhuo, Directed motion of two-headed Brownian motors, Mod. Phys. Lett. B 14(13), 479 (2000) https://doi.org/10.1142/S0217984900000604
32	A. K. Zhao, H. W. Zhang, and Y. X. Li, Feedback control of two-headed Brownian motors in flashing ratchet potential, Chin. Phys. B 19(11), 110506 (2010) https://doi.org/10.1088/1674-1056/19/11/110506
33	C. P. Li, H. B. Chen, and Z. G. Zheng, Double-temperature ratchet model and current reversal of coupled Brownian motors, Front. Phys. 12(6), 120507 (2017) https://doi.org/10.1007/s11467-017-0659-9
34	L. F. Lin, H. Q. Wang, and H. Ma, Directed transport properties of double-headed molecular motors with balanced cargo, Physica A 517, 270 (2019) https://doi.org/10.1016/j.physa.2018.11.001
35	J. Howard, The movement of kinesin along microtubules, Annu. Rev. Physiol. 58(1), 703 (1996) https://doi.org/10.1146/annurev.ph.58.030196.003415
36	E. Toprak, J. Enderlein, S. Syed, S. A. McKinney, R. G. Petschek, T. Ha, Y. E. Goldman, and P. R. Selvin, Defocused orientation and position imaging (DOPI) of myosin V, Proc. Natl. Acad. Sci. USA 103(17), 6495 (2006) https://doi.org/10.1073/pnas.0507134103
37	A. R. Dunn and J. A. Spudich, Dynamics of the unbound head during myosin V processive translocation, Nat. Struct. Mol. Biol. 14(3), 246 (2007) https://doi.org/10.1038/nsmb1206
38	B. Geislinger and R. Kawai, Brownian molecular motors driven by rotation-translation coupling, Phys. Rev. E 74(1), 011912 (2006) https://doi.org/10.1103/PhysRevE.74.011912
39	L. Y. Qiao, Y. Y. Li, and Z. G. Zheng, Rotational effect in two-dimensional cooperative directed transport, Front. Phys. 10(1), 108701 (2015) https://doi.org/10.1007/s11467-014-0423-3
40	R. N. Mantegna and B. Spagnolo, Stochastic resonance in a tunnel diode in the presence of white or coloured noise, Nuovo Cimento D 17(7–8), 873 (1995) https://doi.org/10.1007/BF02451845
41	R. N. Mantegna and B. Spagnolo, Noise enhanced stability in an unstable system, Phys. Rev. Lett. 76(4), 563 (1996) https://doi.org/10.1103/PhysRevLett.76.563
42	L. Gammaitoni, P. Hänggi, P. Jung, and F. Marchesoni, Stochastic resonance, Rev. Mod. Phys. 70(1), 223 (1998) https://doi.org/10.1103/RevModPhys.70.223
43	R. N. Mantegna, B. Spagnolo, and M. Trapanese, Linear and nonlinear experimental regimes of stochastic resonance, Phys. Rev. E 63(1), 011101 (2001) https://doi.org/10.1103/PhysRevE.63.011101
44	B. Spagnolo, D. Valenti, C. Guarcello, A. Carollo, D. Persano Adorno, S. Spezia, N. Pizzolato, and B. Di Paola, Noise-induced effects in nonlinear relaxation of condensed matter systems, Chaos Solitons Fractals 81(8), 412 (2015) https://doi.org/10.1016/j.chaos.2015.07.023
45	C. Guarcello, D. Valenti, A. Carollo, and B. Spagnolo, Effects of Lévy noise on the dynamics of sine-Gordon solitons in long Josephson junctions, J. Stat. Mech.: Theory Exp. 2016(5), 054012 (2016) https://doi.org/10.1088/1742-5468/2016/05/054012
46	B. Spagnolo, C. Guarcello, L. Magazzù, A. Carollo, D. P. Adorno, and D. Valenti, Nonlinear relaxation phenomena in metastable condensed matter systems, Entropy (Basel) 19(1), 20 (2017) https://doi.org/10.3390/e19010020
47	M. S. Simon, J. M. Sancho, and K. Lindenberg, Transport and diffusion of overdamped Brownian particles in random potentials, Phys. Rev. E 88(6), 062105 (2013) https://doi.org/10.1103/PhysRevE.88.062105
48	C. P. Li, H. B. Chen, and Z. G. Zheng, Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials, Front. Phys. 12(4), 120502 (2017) https://doi.org/10.1007/s11467-016-0622-1
49	S. N. Ethier and J. Lee, The tilted flashing Brownian ratchet, Fluct. Noise Lett. 18(1), 1950005 (2019) https://doi.org/10.1142/S0219477519500056
50	X. Zhang, J. H. Cao, B. Q. Ai, T. F. Gao, and Z. G. Zheng, Investigation on the directional transportation of coupled Brownian motors with asymmetric friction, Acta Physica Sinica 69(10), 100503 (2020) (in Chinese) https://doi.org/10.7498/aps.69.20191961
51	D. del-Castillo-Negrete, V. Yu. Gonchar, and A. V. Chechkin, Fluctuation-driven directed transport in the presence of Lévy flights, Physica A 387(27), 6693 (2008) https://doi.org/10.1016/j.physa.2008.08.034
52	Y. G. Li, Y. Xu, J. Kurths, and X. L. Yue, Lévy-noiseinduced transport in a rough triple-well potential, Phys. Rev. E 94(4), 042222 (2016) https://doi.org/10.1103/PhysRevE.94.042222
53	D. Dan, M. C. Mahato, and A. M. Jayannavar, Stochastic resonance in washboard potentials, Phys. Lett. A 258(4–6), 217 (1999) https://doi.org/10.1016/S0375-9601(99)00380-1
54	C. P. Li, H. B. Chen, H. Fan, G. Y. Xie, and Z. G. Zheng, Cooperation and competition between two symmetry breakings in a coupled ratchet, Physica A 494(6), 175 (2018) https://doi.org/10.1016/j.physa.2017.11.161
55	B. Lisowski, D. Valenti, B. Spagnolo, M. Bier, and E. Gudowska-Nowak, Stepping molecular motor amid Lévy white noise, Phys. Rev. E 91(4), 042713 (2015) https://doi.org/10.1103/PhysRevE.91.042713
56	Y. Xie and R. N. Liu, Stochastic resonance in overdamped washboard potential system, Acta Physica Sinica 66(12), 120501 (2017) (in Chinese) https://doi.org/10.7498/aps.66.120501
57	R. N. Liu and R. M. Kang, Stochastic resonance in underdamped periodic potential systems with alpha stable Lévy noise, Phys. Lett. A 382(25), 1656 (2018) https://doi.org/10.1016/j.physleta.2018.03.054
58	M. Borromeo and F. Marchesoni, Brownian surfers, Phys. Lett. A 249(3), 199 (1998) https://doi.org/10.1016/S0375-9601(98)00733-6
59	A. Fiasconaro and B. Spagnolo, Resonant activation in piecewise linear asymmetric potentials, Phys. Rev. E 83(4), 041122 (2011) https://doi.org/10.1103/PhysRevE.83.041122
60	J. M. Chambers, C. L. Mallows, and B. W. Stuck, A method for simulating stable random variables, J. Am. Stat. Assoc. 71(354), 340 (1976) https://doi.org/10.1080/01621459.1976.10480344
61	D. Fulger, E. Scalas, and G. Germano, Monte Carlo simulation of uncoupled continuous-time random walks yielding a stochastic solution of the space-time fractional diffusion equation, Phys. Rev. E 77(2), 021122 (2008) https://doi.org/10.1103/PhysRevE.77.021122

[1]	Chen-Pu Li,Hong-Bin Chen,Zhi-Gang Zheng. Double-temperature ratchet model and current reversal of coupled Brownian motors[J]. Front. Phys. , 2017, 12(6): 120507-.
[2]	Chen-Pu Li,Hong-Bin Chen,Zhi-Gang Zheng. Ratchet motion and current reversal of coupled Brownian motors in pulsating symmetric potentials[J]. Front. Phys. , 2017, 12(4): 120502-.
[3]	Li-Yan Qiao, Yun-yun Li, Zhi-Gang Zheng. Rotational effect in two-dimensional cooperative directed transport[J]. Front. Phys. , 2015, 10(1): 108701-.

Viewed

Full text

Abstract

Cited

Shared

Discussed