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The fractional over-damped ratchet model with thermal fluctuation and periodic drive is introduced by using the damping kernel function of general Langevin equation in the form of power law based on the assumption that cytosol in biological cells has characteristics of power-law memory. On basis of the Grunwald-Letnikov definition of fractional derivative, the numerical solution of this ratchet model is obtained. And furthermore, according to the numerical solution, the transport behaviors of stochastic ratchet and corresponding deterministic ratchet (especially when the deterministic ratchet has chaotic trajectory) are investigated, based on which we try to analyze how chaotic properties of the deterministic ratchet and the actions of noise influence the transport properties of molecular motors and moreover find the possible mechanism of current reversal of fractional molecular motor. Numerical results show that, as barrier height, barrier asymmetry and memorability of model change, the current reversal in deterministic ratchet is not necessarily required to appear when happening indeed in corresponding stochastic ratchet; moreover, with the decrease of order p, there exists a chaotic regime in deterministic ratchet model before current reversal, but with the disturbance of noise, current reversal will happen more earlier, namely, chaotic current direction in deterministic ratchet model can be reversed when disturbance of noise exists. This also demonstrates that noise can essentially change the transport behavior of a ratchet; current can change from chaotic state in a ratchet with no noise to directed transport with noise. This is a possible mechanism of current reversal of a fractional stochastic ratchet, and also a reflection that noise plays an active role in directed transport.
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Keywords:
- fractional molecular motors /
- chaos /
- fractional Gaussian noise /
- current reversal
[1] Vale R D, Milligan R A 2000 Science 288 88
[2] Nishyama M, Muto E, Inoue Y 2002 Nature Cell Biology 3 425
[3] Zhan Y 2011 Biophysics (Beijing: Science Press) pp53-58 (in Chinese) [展永 2011 生物物理学 (北京: 科学出版社) 第5358页]
[4] Liu H, Schmidt J J, Bachand G D, Rizk S S, Looger L L, Hellinga H W, Montemagno C D 2002 Nature Mater. 1 173
[5] Ren Q, Zhao Y P, Yue J C, Cui Y B 2006 Biomed. Microdev. 8 201
[6] Su T, Cui Y B, Zhang X A, Liu X, Yue J C, Liu N, Jiang P 2006 Biochem. Biophys. Res. Commun. 350 1013
[7] Deng Z T, Zhang Y, Yue J C, Tang F Q, Wei Q 2007 J. Phys. Chem. B 111 12024
[8] Zhao T J, Zhan Y, Yu H, Song Y L, An H L 2003 Commun. Theor. Phys. 39 653
[9] Han Y R, Zhao T J, Zhan Y, Yan W L 2005 Commun. Theor. Phys. 43 377
[10] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[11] Wang H Y, He H S, Bao J D 2005 Commun. Theor. Phys. 43 229
[12] Hnggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[13] Xie P 2010 Int. J. Biol. Sci. 6 665
[14] Xie P, Dou S X, Wang P Y 2006 Chin. Phys. 15 536
[15] Souza S, Van V J, Morelle M 2006 Nature 440 651
[16] Igarashi A, Tsukamoto S, Goko H 2001 Phys. Rev. E 64 051908
[17] Wang H Y, Bao J D 2004 Physica A 337 13
[18] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 1179
[19] Hondou T, Sawada Y 1996 Phys. Rev. E 54 3149
[20] Zhou X W, Lin L F, Ma H, Luo M K 2014 Acta Phys. Sin. 63 110501 (in Chinese) [周兴旺, 林丽烽, 马洪, 罗懋康 2014 63 110501]
[21] Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502
[22] Mateos J L 2000 Phys. Rev. Lett. 84 258
[23] Tarasov V E 2010 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles Fields and Media (Beijing: Higher Education Press) p442
[24] Bao J D 2012 An Introduction to Anomalous Statisticl Dynamics (Beijing: Science Press) pp127-184 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第127184页]
[25] Baiwen S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[26] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 62 040501]
[27] Fereydoon F, Larrondo H A 2005 J. Phys.: Condens. Matter 17 47
[28] Jung P, Kissner J G 1996 Phys. Rev. Lett. 76 343
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[1] Vale R D, Milligan R A 2000 Science 288 88
[2] Nishyama M, Muto E, Inoue Y 2002 Nature Cell Biology 3 425
[3] Zhan Y 2011 Biophysics (Beijing: Science Press) pp53-58 (in Chinese) [展永 2011 生物物理学 (北京: 科学出版社) 第5358页]
[4] Liu H, Schmidt J J, Bachand G D, Rizk S S, Looger L L, Hellinga H W, Montemagno C D 2002 Nature Mater. 1 173
[5] Ren Q, Zhao Y P, Yue J C, Cui Y B 2006 Biomed. Microdev. 8 201
[6] Su T, Cui Y B, Zhang X A, Liu X, Yue J C, Liu N, Jiang P 2006 Biochem. Biophys. Res. Commun. 350 1013
[7] Deng Z T, Zhang Y, Yue J C, Tang F Q, Wei Q 2007 J. Phys. Chem. B 111 12024
[8] Zhao T J, Zhan Y, Yu H, Song Y L, An H L 2003 Commun. Theor. Phys. 39 653
[9] Han Y R, Zhao T J, Zhan Y, Yan W L 2005 Commun. Theor. Phys. 43 377
[10] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[11] Wang H Y, He H S, Bao J D 2005 Commun. Theor. Phys. 43 229
[12] Hnggi P, Marchesoni F 2009 Rev. Mod. Phys. 81 387
[13] Xie P 2010 Int. J. Biol. Sci. 6 665
[14] Xie P, Dou S X, Wang P Y 2006 Chin. Phys. 15 536
[15] Souza S, Van V J, Morelle M 2006 Nature 440 651
[16] Igarashi A, Tsukamoto S, Goko H 2001 Phys. Rev. E 64 051908
[17] Wang H Y, Bao J D 2004 Physica A 337 13
[18] Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 1179
[19] Hondou T, Sawada Y 1996 Phys. Rev. E 54 3149
[20] Zhou X W, Lin L F, Ma H, Luo M K 2014 Acta Phys. Sin. 63 110501 (in Chinese) [周兴旺, 林丽烽, 马洪, 罗懋康 2014 63 110501]
[21] Gao T F, Zheng Z G, Chen J C 2013 Chin. Phys. B 22 080502
[22] Mateos J L 2000 Phys. Rev. Lett. 84 258
[23] Tarasov V E 2010 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles Fields and Media (Beijing: Higher Education Press) p442
[24] Bao J D 2012 An Introduction to Anomalous Statisticl Dynamics (Beijing: Science Press) pp127-184 (in Chinese) [包景东 2012 反常统计动力学导论 (北京: 科学出版社) 第127184页]
[25] Baiwen S M, Peng H, Tu Z, Ma H 2012 Acta Phys. Sin. 61 210501 (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[26] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese) [王飞, 邓翠, 屠浙, 马洪 2013 62 040501]
[27] Fereydoon F, Larrondo H A 2005 J. Phys.: Condens. Matter 17 47
[28] Jung P, Kissner J G 1996 Phys. Rev. Lett. 76 343
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