Optimal control of temperature feedback control ratchets

Liu Tian-Yu; Cao Jia-Hui; Liu Yan-Yan; Gao Tian-Fu; Zheng Zhi-Gang

doi:10.7498/aps.70.20210517

Abstract

Biomolecular motors are macromolecules of enzyme proteins that convert chemical energy into mechanical energy. Experimental studies have shown that the directed movement of the biomolecular motor fully participates in the material transport process in the cell. Theoretically, the directed movement of biomolecular motors can be studied by the ratchet model. However, in most of feedback control ratchet models, none of the influences of external factors on experimental manipulation is considered, especially the inevitable random error, systematic error and human error in the experiment. Therefore, in order to further study the influences of error factors on feedback control ratchets, Cao's research group (Feito M, Cao F J 2007 Eur. Phys. J. B 59 63) pioneered the idea of error probability and discussed the transport behavior of feedback ratchets in the presence of error probability.Based on Cao's error ratchet model, in this paper the temperature factor in introduced to further control the feedback ratchets, and the directed transport characteristics of the coupled Brownian particles in the temperature feedback ratchets are studied. The effects of temperature factor, phase difference and temperature frequency on the directed transport of coupled Brownian particles are discussed in detail. It is found that the temperature factor does not always reduce the directed transport of Brownian particles. There is a minimum value which means that the temperature factor can enhance the directed transport of the feedback ratchets within a certain change interval. In addition, in a small temperature amplitude range, the directed transport of the coupled particles exhibits a multi-peak structure with the change of temperature frequency. It is means that the appropriate temperature change frequency can enhance the directed transport of the feedback ratchets multiple times. The conclusions obtained in this paper can not only inspire experimental selection of appropriate temperature feedback information to optimize the directed transport of the Brownian ratchets, but also provide theoretical references for analyzing and processing the experimental data, especially error analysis.

Keywords:

Authors and contacts

1.
College of Physical Science and Technology, Shenyang Normal University, Shenyang 110034, China
2.
College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China

Corresponding author: Gao Tian-Fu, tianfugao@synu.edu.cn ; Zheng Zhi-Gang, zgzheng@hqu.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11875135, 11347003), the High-level Talent Support Program of Shenyang Normal University, China, and the Postgraduate Education Reform Project of Shenyang Normal University, China (Grant No. YJSJG320210100).

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References

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Cited By

图 1 (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随温度相位差$ \theta $的变化曲线, 其中$ \omega = 0.1{\text{π}} $, $A = $$ 1.0$, $ {T_0} = 0.7 $

Figure 1. Curves of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the phase different of temperature $ \theta $, where $ \omega = 0.1{\text{π}} $, $ A = 1.0 $, $ {T_0} = 0.7 $.

DownLoad: Full-Size Img PowerPoint

图 2 (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随临界温度$ {T_{\text{C}}} $的变化曲线, 其中$ \omega = 0.1{\text{π}} $, $A = $$ 1.0$, $ \theta = 0.2{\text{π}} $

Figure 2. Curves of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the critical temperature ${T_{\rm{C}}}$, where $ \omega = 0.1{\text{π}} $, $ A = 1.0 $, $ \theta = 0.2{\text{π}} $.

DownLoad: Full-Size Img PowerPoint

图 3 (a) 质心平均速度$\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) 质心扩散系数$ {D_{{\text{eff}}}} $和 (c) $ Pe $数随温度频率$ \omega $的变化曲线, 其中$ {T_0} = 0.7 $, $\theta = $$ 0.2{\text{π}}$, $ {\alpha _i} = 0.8 $

Figure 3. Curve of (a) the center-of-mass mean velocity $\left\langle {{V_{{\rm{cm}}}}} \right\rangle $, (b) the center-of-mass diffusion coefficient $ {D_{{\text{eff}}}} $ and (c) $ Pe $ number varying with the temperature frequency $ \omega $, where $ {T_0} = 0.7 $, $ \theta = 0.2{\text{π}} $, $ {\alpha _i} = 0.8 $.

DownLoad: Full-Size Img PowerPoint

[1]	舒咬根, 欧阳钟灿 2007 物理 36 735 Google Scholar Shu Y G, Ouyang Z C 2007 Physics 36 735 Google Scholar
[2]	Xie P 2010 Int. J. Biol. Sci 6 665
[3]	Oster G, Wang H 2003 Trends Cell Biol 13 114 Google Scholar
[4]	国家自然科学基金委员会, 中国科学院 2020 中国学科发展战略·软凝聚态物理学(下) (北京: 科学出版社) 第1037页 National Natural Science Foundation of China, Chinese Academy of Sciences 2020 Chinese Subject Development Strategy· Soft Condensed Matter Physics (Part 2) (Beijing: Science Press) p1037 (in Chinese)
[5]	Palmigiano A, Santaniello F, Cerutti A, Penkov D, Purushothama D 2018 Sci. Rep. 8 3198 Google Scholar
[6]	Linke H 2002 Appl. Phys. A 75 167 Google Scholar
[7]	van den Heuvel M G L, Dekker C 2007 Science 317 333 Google Scholar
[8]	Zhang H W, Wen S T, Zhang H T, Li Y X, Chen G R 2012 Chin. Phys. B 21 078701 Google Scholar
[9]	Doering C R 1995 Nuovo Cimento 17 685 Google Scholar
[10]	Astumian R D, Bier M 1994 Phys. Rev. Lett. 72 1766 Google Scholar
[11]	Gao T F, Chen J C 2009 J. Phys. A: Math. Theor. 42 065002 Google Scholar
[12]	Reimann P 2002 Phys. Rep. 361 57 Google Scholar
[13]	Rosalie L W, Fabrice M K P 2016 Physica A 460 326 Google Scholar
[14]	Pawel R, Felix M 2010 Phys. Rev. E 81 061120 Google Scholar
[15]	Feito M, Cao F J 2006 Phys. Rev. E 74 041109 Google Scholar
[16]	范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚 2017 物理学报 66 010501 Google Scholar Fan L M, Lv M T, Gao T F, Huang R Z, Zheng Z G 2017 Acta. Phys. Sin. 66 010501 Google Scholar
[17]	Feito M, Cao F J 2007 Phys. Rev. E 76 061113 Google Scholar
[18]	Feito M, Cao F J 2008 Physica A 387 4553 Google Scholar
[19]	Wang H Y, Bao J D 2007 Physica A 374 33 Google Scholar
[20]	Feito M, Baltanas J P, Cao F J 2009 Phys. Rev. E 80 031128 Google Scholar
[21]	Rousselet J, Salome L, Ajdari A, Prost J 1994 Nature 370 446 Google Scholar
[22]	Feito M, Cao F J 2007 Eur. Phys. J. B 59 63 Google Scholar
[23]	Dan D, Jayannavarar A M, Menon G I 2003 Physica A 318 40 Google Scholar
[24]	王莉芳, 高天附, 黄仁忠, 郑玉祥 2013 物理学报 62 070502 Google Scholar Wang L F, Gao T F, Huang R Z, Zheng Y X 2013 Acta. Phys. Sin. 62 070502 Google Scholar
[25]	Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120507 Google Scholar
[26]	Cao F J, Feito M, Touchette H 2007 Physica A 388 113
[27]	Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102 Google Scholar
[28]	Mateos J L 2004 Fluctuation Noise Lett 4 161 Google Scholar
[29]	Lindner B, Schimanasky-Geier L 2002 Phys. Rev. Lett. 89 230602 Google Scholar
[30]	Wang H Y, Bao J D 2005 Physica A 357 373 Google Scholar

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Vol. 70, Issue 19 - 2021-10-05

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