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本文将细胞内环境假定为分数阶牛顿黏弹性体并建立了单位质量的一维线动分子马达的时间非对称分数阶类郎之万棘齿模型，其中的周期势函数是空间对称的，而用于刻画ATP水解反应引起的环境波动的则是无偏的时间非对称类郎之万噪声. 然后本文将模型转化为离散映射以便进行计算机模拟. 最后本文以Logistic映射所生成的类郎之万噪声为例简单模拟了模型的定向输运行为. 各参数情形下的模拟结果均显示：无需势函数的空间对称破缺，时间非对称的类郎之万噪声已足以引起模型的定向输运. 负向的输运行为应归因于Logistic映射的两个不稳定不动点的非对称分布. 因此，尽管模拟结果同整数阶模型相比并无本质区别，但分数阶模型对于分子马达的噪声整流机理的刻画却无疑更接近实际情况.In this paper, a temporal-asymmetric fractional Langevin-like ratchet is constructed for the operation of a 1D linear molecular motor subjected to both spatial-symmetric periodic potential and temporal-asymmetric unbiased Langevin-like noise. In this ratchet, the Langevin-like noise is used to simulate the intracellular fluctuation induced by ATP hydrolysis. Then, for numerical study of this ratchet, the corresponding discrete mapping is derivated. Finally, as an example, the unidirectional transport of the ratchet driven by unbiased Langevin-like noise, generated by the Logistic mapping, is numerically studied. Negative transport of the ratchet indicates that without the spatial asymmetry of potential, the temporal asymmetry is enough for the presence of unidirectional transport. Since temporal asymmetry has to be regarded as a generic property of nonequilibrium system, this ratchet is expected to be resonably used for the operation of molecular motor.
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Keywords:
- Langevin-like noise /
- fractional Langevin-like ratchet /
- temporal asymmetry /
- unidirected-transport
[1] Reimann P 2002 Physics Reports 361 57
[2] Chialvo D R, Dykman M I, Millonas M M 1997 Phys. Rev. Lett. 78 1605
[3] Hänggi P, Bartussek R, Talkner P 1996 Europhys. Lett. 35 315
[4] Zheng Z G, Li X W 2001 Commun. Theor. Phys. 36 151
[5] Schreier M, Reimann P, Hänggi P 1998 Europhys. Lett. 44 146
[6] Hänggi P, Marchesoni F 2009 Reviews of Modern Physics 81 387
[7] Hondou T 1994 J. Phys. Soc. Japan 63 2014
[8] Hondou T, Sawada Y 1995 Phys. Rev. Lett. 75 3269
[9] Hondou T, Sawada Y 1996 Phys. Rev. E 54 3149
[10] Beck C, Reopstorff G 1987 Physica A 45 1
[11] Beck C 1991 Nonlinear 4 1131
[12] Chew L Y, Ting C 2002 Physica A 307 275
[13] Chew L Y, Ting C 2004 Phys. Rev. E 69 031103
[14] Chew L Y, Ting C, Lai C H 2005 Phys. Rev. E 72 036222
[15] Chew L Y 2012 Phys. Rev. E 85 016212
[16] Luby-Phelps K 2000 Review of Cytology 192 189
[17] [美国科学院研究理事会编, 王菊芳译 2013 二十一世纪新生物学(北京: 科学出版社)]
[18] Ellis R J 2001 Trends in Biochemical Sciences 26 597
[19] Ellis R J 2001 Current Opinion in Structural Biology 11 114
[20] Tarasov V E 2010 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles Fields and Media (Beijing: Higher Education Press)p442
[21] 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] (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[22] Lin L F, Zhou X W, Ma H 2013 Acta Phys. Sin. 62 240501 (in Chinese) [林丽烽, 周兴旺, 马洪 2013 62 240501]
[23] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese)[王飞, 邓翠, 屠浙 2013 62 040501]
[24] [包景东 2012 反常统计动力学导论(北京: 科学出版社)第183页]
[25] Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (London: Imperial College Press) p57
[26] Lasota A, Mackey M 1994 Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (New York: Springer-Verlag) p8
[27] [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13页]
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[1] Reimann P 2002 Physics Reports 361 57
[2] Chialvo D R, Dykman M I, Millonas M M 1997 Phys. Rev. Lett. 78 1605
[3] Hänggi P, Bartussek R, Talkner P 1996 Europhys. Lett. 35 315
[4] Zheng Z G, Li X W 2001 Commun. Theor. Phys. 36 151
[5] Schreier M, Reimann P, Hänggi P 1998 Europhys. Lett. 44 146
[6] Hänggi P, Marchesoni F 2009 Reviews of Modern Physics 81 387
[7] Hondou T 1994 J. Phys. Soc. Japan 63 2014
[8] Hondou T, Sawada Y 1995 Phys. Rev. Lett. 75 3269
[9] Hondou T, Sawada Y 1996 Phys. Rev. E 54 3149
[10] Beck C, Reopstorff G 1987 Physica A 45 1
[11] Beck C 1991 Nonlinear 4 1131
[12] Chew L Y, Ting C 2002 Physica A 307 275
[13] Chew L Y, Ting C 2004 Phys. Rev. E 69 031103
[14] Chew L Y, Ting C, Lai C H 2005 Phys. Rev. E 72 036222
[15] Chew L Y 2012 Phys. Rev. E 85 016212
[16] Luby-Phelps K 2000 Review of Cytology 192 189
[17] [美国科学院研究理事会编, 王菊芳译 2013 二十一世纪新生物学(北京: 科学出版社)]
[18] Ellis R J 2001 Trends in Biochemical Sciences 26 597
[19] Ellis R J 2001 Current Opinion in Structural Biology 11 114
[20] Tarasov V E 2010 Fractional Dynamics: Applications of Fractional Calculus to Dynamics of Particles Fields and Media (Beijing: Higher Education Press)p442
[21] 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] (in Chinese) [白文斯密, 彭皓, 屠浙, 马洪 2012 61 210501]
[22] Lin L F, Zhou X W, Ma H 2013 Acta Phys. Sin. 62 240501 (in Chinese) [林丽烽, 周兴旺, 马洪 2013 62 240501]
[23] Wang F, Deng C, Tu Z, Ma H 2013 Acta Phys. Sin. 62 040501 (in Chinese)[王飞, 邓翠, 屠浙 2013 62 040501]
[24] [包景东 2012 反常统计动力学导论(北京: 科学出版社)第183页]
[25] Mainardi F 2010 Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical Models (London: Imperial College Press) p57
[26] Lasota A, Mackey M 1994 Chaos, Fractals, and Noise: Stochastic Aspects of Dynamics (New York: Springer-Verlag) p8
[27] [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13页]
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