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Focusing on the directed transport phenomena of the two-headed molecular motor, we adopt power function as the damping kernel function of general Langevin equation due to the power-law memory characteristics of cytosol in biological cells and present the model of fractional coupling Brownian motor in overdamped condition in this paper. We also discuss the influences of fractional order and coupling factor on the transport speed. From the simulation results there are found the directed transport phenomena and the inverse transport which is not seen in the conventional Brownian motor, in the overdamped fractional coupling Brownian motor. When the noise density is fixed, the generalized stochastic resonance appears when transport speed varies with the fractional order and coupling factor. In particular, the results reveal that the magnitude and direction of the directional flow are controlled by coupling the noise with the interaction force between the two heads, which is the movement characteristic of the two-headed molecular motor in the memory ratchet, rather than of the single-headed motor.
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Keywords:
- fractional two-headed molecular motor /
- sub-diffusion /
- directed transport /
- stochastic resonance in a broad sense
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[2] Nishyama M, Muto E, Inoue Y 2002 Nature Cell Biology 3 425
[3] Howard J 1997 Nature 389 561
[4] Hancock W O, Howard J, Gelles J 1998 Cell Biol. 140 1395
[5] Young E C, Mahtani H K, Gelles J 1998 Biochemistry 37 3467
[6] Kelly T R, Silva H, Silva R A 1999 Nature 401 150
[7] Endow S A, Higuchi H 2000 Nature 406 913
[8] 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
[9] Ren Q, Zhao Y P, Yue J C, Cui Y B 2006 Biomed. Microdev. 8 201
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[11] Deng Z T, Zhang Y, Yue J C, Tang F Q, Wei Q 2007 J. Phys. Chem. B 41 12024
[12] Qi W, Duan L, Wang K W, Yan X H, Citi Y, He Q, Li J B 2008 Adv. Mater. 20 601
[13] Song W X, He Q, Cui Y, Möhwald H, Diez S, Li J B 2009 Biochem. Biophys. Res. Commun. 379 175
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[16] Zhao T J, Zhan Y, Yu H, Song Y L, An H L 2003 Commun. Theor. Phys. 39 653
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[19] Wang H Y, He H S, Bao J D 2005 Commun. Theor. Phys. 43 229
[20] Hänggi P, Marchesoni F, Nori F 2005 Ann. Phys. 14 51
[21] Chen H B, Wang Q W, Zheng Z G 2005 Phys. Rev. E 71 031102
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[24] von Gehlen S, Evstigneev M, Reimann P 2008 Phys. Rev. E 77 031136
[25] Zheng Z G, Chen H B 2010 EPL 92 30004
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[29] 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]
[30] Lai L, Zhou X X, Ma H, Luo M K 2013 Acta Phys. Sin. 62 150502 (in Chinese) [赖莉, 周薛雪, 马洪, 罗懋康 2013 62 150502]
[31] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[32] Zhang J Q, Xin H W 2001 Prog. Chem. 13 241 (in Chinese) [张季谦, 辛厚文 2001 化学进展 13 241]
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[34] Gemant A 1936 Physics 7 311
[35] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 61 100502]
[36] Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[37] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[38] Xu R G, Hu X L, Wu C X 2007 J. Donghua Univ. (Natural Science) 33 549 (in Chinese) [徐荣归, 胡锡龙, 吴承训 2007 东华大学学报(自然科学版) 33 549]
[39] Asbury C L, Fehr A N, Block S M 2003 Science 302 2130
[40] Yildiz A, Tomishge M, Vale R D, Selvin P R 2004 Science 303 676
[41] Hua W, Chung J, Gelles J 2002 Science 295 844
[42] Bai W 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]
[43] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[44] Shao Q, Gao Y Q 2006 PNAS 21 103
[45] Csahó k Z, Family F, Vicsek T 1997 Phys. Rev. E 55 5179
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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] Howard J 1997 Nature 389 561
[4] Hancock W O, Howard J, Gelles J 1998 Cell Biol. 140 1395
[5] Young E C, Mahtani H K, Gelles J 1998 Biochemistry 37 3467
[6] Kelly T R, Silva H, Silva R A 1999 Nature 401 150
[7] Endow S A, Higuchi H 2000 Nature 406 913
[8] 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
[9] Ren Q, Zhao Y P, Yue J C, Cui Y B 2006 Biomed. Microdev. 8 201
[10] Su T, Cui Y B, Zhang X A, Liu X, Yue J C, Liu N, Jiang P 2006 Biochem. Biophys. Res. Commun. 350 1013
[11] Deng Z T, Zhang Y, Yue J C, Tang F Q, Wei Q 2007 J. Phys. Chem. B 41 12024
[12] Qi W, Duan L, Wang K W, Yan X H, Citi Y, He Q, Li J B 2008 Adv. Mater. 20 601
[13] Song W X, He Q, Cui Y, Möhwald H, Diez S, Li J B 2009 Biochem. Biophys. Res. Commun. 379 175
[14] Song W X, Möhwald H, Li J B, 2010 Biomaterials 31 1287
[15] Zhao T J, Zhan Y, Yu H, Ji Q 2003 Commun. Theor. Phys. 39 121
[16] Zhao T J, Zhan Y, Yu H, Song Y L, An H L 2003 Commun. Theor. Phys. 39 653
[17] Han Y R, Zhao T J, Zhan Y, Yan W L 2005 Commun. Theor. Phys. 43 377
[18] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[19] Wang H Y, He H S, Bao J D 2005 Commun. Theor. Phys. 43 229
[20] Hänggi P, Marchesoni F, Nori F 2005 Ann. Phys. 14 51
[21] Chen H B, Wang Q W, Zheng Z G 2005 Phys. Rev. E 71 031102
[22] Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102
[23] Wang H Y 2007 Commun. Theor. Phys. 48 859
[24] von Gehlen S, Evstigneev M, Reimann P 2008 Phys. Rev. E 77 031136
[25] Zheng Z G, Chen H B 2010 EPL 92 30004
[26] Kharchenko V, Goychuk I 2012 New J. Phys. 14 043042
[27] Gao T F, Zhang Y, Chen J C 2009 Chin. Phys. B 18 3279
[28] Zhao A K, Zhang H W, Li Y X 2010 Chin. Phys. B 19 110506
[29] 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]
[30] Lai L, Zhou X X, Ma H, Luo M K 2013 Acta Phys. Sin. 62 150502 (in Chinese) [赖莉, 周薛雪, 马洪, 罗懋康 2013 62 150502]
[31] Gitterman M 2005 Phys. Stat. Mech. Appl. 352 309
[32] Zhang J Q, Xin H W 2001 Prog. Chem. 13 241 (in Chinese) [张季谦, 辛厚文 2001 化学进展 13 241]
[33] Bao J D 2009 Stochastic Simulation Method of Classic and Quantum Dissipative Sysmtem (Beijing: Science Press) p160 (in Chinese) [包景东 2009 经典和量子耗散系统的随机模拟方法 (北京: 科学出版社) 第160页]
[34] Gemant A 1936 Physics 7 311
[35] Gao S L, Zhong S C, Wei K, Ma H 2012 Acta Phys. Sin. 61 100502 (in Chinese) [高仕龙, 钟苏川, 韦鹍, 马洪 2012 61 100502]
[36] Liu F, Anh V, Turner I, Zhuang P 2003 J. Appl. Math. Comput. 13 233
[37] Qian M, Wang Y, Zhang X J 2003 Chin. Phys. Lett. 20 810
[38] Xu R G, Hu X L, Wu C X 2007 J. Donghua Univ. (Natural Science) 33 549 (in Chinese) [徐荣归, 胡锡龙, 吴承训 2007 东华大学学报(自然科学版) 33 549]
[39] Asbury C L, Fehr A N, Block S M 2003 Science 302 2130
[40] Yildiz A, Tomishge M, Vale R D, Selvin P R 2004 Science 303 676
[41] Hua W, Chung J, Gelles J 2002 Science 295 844
[42] Bai W 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]
[43] Podlubny I 1998 Fractional Differential Equation (San Diego: Academic Press)
[44] Shao Q, Gao Y Q 2006 PNAS 21 103
[45] Csahó k Z, Family F, Vicsek T 1997 Phys. Rev. E 55 5179
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