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Energy conversion efficiency of feedback pulsing ratchet

Yan Ming-Yue Zhang Xu Liu Chen-Hao Huang Ren-Zhong Gao Tian-Fu Zheng Zhi-Gang

Energy conversion efficiency of feedback pulsing ratchet

Yan Ming-Yue, Zhang Xu, Liu Chen-Hao, Huang Ren-Zhong, Gao Tian-Fu, Zheng Zhi-Gang
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  • Biomolecular motors are a big family of protein, and play a very important role in transporting the organelles within cells. They can also convert chemical energy into mechanical energy. In order to study the dynamic mechanism of molecular motors in depth, a great many of Brownian ratchet models such as double-temperature ratchet, feedback control ratchet, and hand-over-hand ratchet have been proposed. By investigating different kinds of ratchets, it is better to comprehend the directed transport of Brownian particles and obtain an insight into the transport process in biomedicine. Especially, the investigation of Brownian ratchets can also be used for improving the accurate drug delivery and effectively utilizing the medicine.Until now, the directed transport of ratchet has aoused the interest of researchers. It is found that a certain driving phase can lead to the current reversal of the underdamped ratchets in theory. A large number of experiments have shown that most of the biomolecular motors in cells are enzyme protein macromolecules and they can carry the “cargos” to implement the directed transport. Interestingly, molecular motors have high efficiency usually, and some of them can even reach an efficiency close to 100% in experiment. Nevertheless, it is found that the energy conversion of Brownian motors is low as indicated by calculating the rate between the effective work of particles and the input energy of ratchets. According to a comparison between the experimental results and theoretical analyses, it is well known that the efficiency of ratchets is still far from the actual motor efficiency measured experimentally. Therefore, how to increase the efficiency of molecular motor which is pulled by loads is still a very important research topic. Owing to the fact that the molecular motors are influenced by the cellular environment during the hydrolysis of ATP in the organism, the catalytic cycles of the coupled motor proteins are out of phase. This gives us an inspiration for establishing the corresponding feedback pulsing ratchet.Due to the effect of the feedback pulse on coupled ratchets, the directed transport character of pulsing ratchets when they drag loads is explored in the present work. And the directed transport, diffusion and energy conversion efficiency of coupled particles are discussed systematically. It can be observed that the directed transport of the feedback pulsing ratchets would be futher facilitated by adjusting suitable free length and coupling strength. Meanwhile, the energy conversion efficiency of coupled particles can obtain a maximum value under a certain free length and coupling strength. In particular, there is the current reversal in an evolutive cycle under a certain pulse. Moreover, the diffusion of coupled particles can be suppressed effectively by modulating the pulsing phase, thus the corresponding directed transport of pulsing ratchets can be facilitated. In addition, the energy conversion of feedback ratchets can also be improved if the load is appropriate. The current reserval obtained in this paper can be applied to the particle separation. On the other hand, these results provide some great experimental inspirations in the aspect of medical delivery.
      Corresponding author: Gao Tian-Fu, tianfugao@synu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 11475022, 11347003), the Teaching Research Program of Thermodynamics and Statistical Physics in the Institution of Higher Education, the Natural Science Foundation of Liaoning Province, China (Grant No. 20180550149), and the Scientific Research Funds of Huaqiao University, China.
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    [2]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120507

    [3]

    Zhang H W, Wen S T, Zhang H T, Li Y X, Chen G R 2012 Chin. Phys. B 21 078701

    [4]

    Munárriz J, Mazo J J, Falo F 2008 Phys. Rev. E 77 031915

    [5]

    Tutu H, Ouchi K, Horita T 2017 Phys. Rev. E 95 062103

    [6]

    Vorotnikov D 2017 Discr. Cont. Dyn. Syst. Ser. B 16 963

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    Reimann P 2002 Phys. Rep. 361 57

    [8]

    Rozenbaum V M, Yang D Y, Lin S H, Tsong T Y 2006 Physica A 363 211

    [9]

    Nara Y, Niemi H, Steinheimer J, Stöcker H 2017 Phys. Lett. B 769 024915

    [10]

    Mateos J L, Arzola A V, Volke-Seplveda K 2011 Phys. Rev. Lett. 106 168104

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    Minucci S, Pelicci P G 2006 Nat. Rev. Cancer 6 38

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    Palmigiano A, Santaniello F, Cerutti A, Penkov D, Purushothaman D 2018 Sci. Rep. 8 3198

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    Linke H 2002 Appl. Phys. A:Mater. Sci. Process. 75 167

    [14]

    van den Heuvel M G L, Dekker C 2007 Science 317 333

    [15]

    Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106

    [16]

    Qin T Q, Wang F, Yang B, Luo M K 2015 Acta Phys. Sin. 64 120501 (in Chinese) [秦天齐, 王飞, 杨博, 罗懋康 2015 物理学报 64 120501]

    [17]

    Sahoo M, Jayannavar A M 2017 Physica A 465 40

    [18]

    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 物理学报 62 040501]

    [19]

    Dinis L, Quintero R N 2015 Phys. Rev. E 91 032920

    [20]

    Wang H Y, Bao J D 2013 Physica A 06 037

    [21]

    Cubero D, Renzoni F 2016 Phys. Rev. Lett. 116 010602

    [22]

    Shu Y G, Ouyang Z C (in Chinese) [舒咬根, 欧阳钟灿 2007 物理 36 735]

    [23]

    Li M, Ouyang Z C, Shu Y G 2016 Acta Phys. Sin. 18 188702 (in Chinese) [黎明, 欧阳钟灿, 舒咬根 2016 物理学报 18 188702]

    [24]

    Xie P, Chen H 2018 Phys. Chem. Chem. Phys. 20 4752

    [25]

    Nutku F, Aydiner E 2015 Chin. Phys. B 24 040501

    [26]

    Zeng C H, Wang H 2012 Chin. Phys. B 21 050502

    [27]

    Delacruz E M, Ostap E M, Sweeney H L 2001 J. Biol. Chem. 276 32373

    [28]

    Nishikawa S, Homma K, Komori Y, Iwaki M, Wazawa T, Hikikoshi Iwone A, Saito J, Ikebe R, Katayama E, Yanagida T 2002 Biochem. Biophys. Res. Commun. 290 311

    [29]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120502

    [30]

    Colomés E, Zhan Z, Marian D, Oriols X 2017 Phys. Rev. B 96 075135

    [31]

    Gao T F, Chen J C 2009 J. Phys. A:Math. Theor. 42 065002

    [32]

    Stella L, Lorenz C D, Kantorovich L 2014 Phys. Rev. B 89 1

    [33]

    Li G, Tu Z C 2016 Sci. China:Phys. Mech. Astron. 59 640501

    [34]

    Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102

    [35]

    Wang H Y, Bao J D 2007 Physica A 374 33

    [36]

    Fan L M, L M T, Huang R Z, Gao T F, Zheng Z G 2017 Acta Phys. Sin. 66 010501 (in Chinese) [范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚 2017 物理学报 66 010501]

    [37]

    Lu S C, Ou Y L, Ai B Q 2017 Physica A 482 501

    [38]

    Ai B Q, He Y F, Zhong W R 2014 J. Chem. Phys. 141 194111

  • [1]

    Xie P 2010 Int. J. Biol. Sci. 6 665

    [2]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120507

    [3]

    Zhang H W, Wen S T, Zhang H T, Li Y X, Chen G R 2012 Chin. Phys. B 21 078701

    [4]

    Munárriz J, Mazo J J, Falo F 2008 Phys. Rev. E 77 031915

    [5]

    Tutu H, Ouchi K, Horita T 2017 Phys. Rev. E 95 062103

    [6]

    Vorotnikov D 2017 Discr. Cont. Dyn. Syst. Ser. B 16 963

    [7]

    Reimann P 2002 Phys. Rep. 361 57

    [8]

    Rozenbaum V M, Yang D Y, Lin S H, Tsong T Y 2006 Physica A 363 211

    [9]

    Nara Y, Niemi H, Steinheimer J, Stöcker H 2017 Phys. Lett. B 769 024915

    [10]

    Mateos J L, Arzola A V, Volke-Seplveda K 2011 Phys. Rev. Lett. 106 168104

    [11]

    Minucci S, Pelicci P G 2006 Nat. Rev. Cancer 6 38

    [12]

    Palmigiano A, Santaniello F, Cerutti A, Penkov D, Purushothaman D 2018 Sci. Rep. 8 3198

    [13]

    Linke H 2002 Appl. Phys. A:Mater. Sci. Process. 75 167

    [14]

    van den Heuvel M G L, Dekker C 2007 Science 317 333

    [15]

    Ai B Q, He Y F, Zhong W R 2011 Phys. Rev. E 83 051106

    [16]

    Qin T Q, Wang F, Yang B, Luo M K 2015 Acta Phys. Sin. 64 120501 (in Chinese) [秦天齐, 王飞, 杨博, 罗懋康 2015 物理学报 64 120501]

    [17]

    Sahoo M, Jayannavar A M 2017 Physica A 465 40

    [18]

    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 物理学报 62 040501]

    [19]

    Dinis L, Quintero R N 2015 Phys. Rev. E 91 032920

    [20]

    Wang H Y, Bao J D 2013 Physica A 06 037

    [21]

    Cubero D, Renzoni F 2016 Phys. Rev. Lett. 116 010602

    [22]

    Shu Y G, Ouyang Z C (in Chinese) [舒咬根, 欧阳钟灿 2007 物理 36 735]

    [23]

    Li M, Ouyang Z C, Shu Y G 2016 Acta Phys. Sin. 18 188702 (in Chinese) [黎明, 欧阳钟灿, 舒咬根 2016 物理学报 18 188702]

    [24]

    Xie P, Chen H 2018 Phys. Chem. Chem. Phys. 20 4752

    [25]

    Nutku F, Aydiner E 2015 Chin. Phys. B 24 040501

    [26]

    Zeng C H, Wang H 2012 Chin. Phys. B 21 050502

    [27]

    Delacruz E M, Ostap E M, Sweeney H L 2001 J. Biol. Chem. 276 32373

    [28]

    Nishikawa S, Homma K, Komori Y, Iwaki M, Wazawa T, Hikikoshi Iwone A, Saito J, Ikebe R, Katayama E, Yanagida T 2002 Biochem. Biophys. Res. Commun. 290 311

    [29]

    Li C P, Chen H B, Zheng Z G 2017 Front. Phys. 12 120502

    [30]

    Colomés E, Zhan Z, Marian D, Oriols X 2017 Phys. Rev. B 96 075135

    [31]

    Gao T F, Chen J C 2009 J. Phys. A:Math. Theor. 42 065002

    [32]

    Stella L, Lorenz C D, Kantorovich L 2014 Phys. Rev. B 89 1

    [33]

    Li G, Tu Z C 2016 Sci. China:Phys. Mech. Astron. 59 640501

    [34]

    Zheng Z G, Cross M C, Hu G 2002 Phys. Rev. Lett. 89 154102

    [35]

    Wang H Y, Bao J D 2007 Physica A 374 33

    [36]

    Fan L M, L M T, Huang R Z, Gao T F, Zheng Z G 2017 Acta Phys. Sin. 66 010501 (in Chinese) [范黎明, 吕明涛, 黄仁忠, 高天附, 郑志刚 2017 物理学报 66 010501]

    [37]

    Lu S C, Ou Y L, Ai B Q 2017 Physica A 482 501

    [38]

    Ai B Q, He Y F, Zhong W R 2014 J. Chem. Phys. 141 194111

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  • Citation:
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Publishing process
  • Received Date:  31 May 2018
  • Accepted Date:  11 July 2018
  • Published Online:  05 October 2018

Energy conversion efficiency of feedback pulsing ratchet

    Corresponding author: Gao Tian-Fu, tianfugao@synu.edu.cn
  • 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
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant Nos. 11475022, 11347003), the Teaching Research Program of Thermodynamics and Statistical Physics in the Institution of Higher Education, the Natural Science Foundation of Liaoning Province, China (Grant No. 20180550149), and the Scientific Research Funds of Huaqiao University, China.

Abstract: Biomolecular motors are a big family of protein, and play a very important role in transporting the organelles within cells. They can also convert chemical energy into mechanical energy. In order to study the dynamic mechanism of molecular motors in depth, a great many of Brownian ratchet models such as double-temperature ratchet, feedback control ratchet, and hand-over-hand ratchet have been proposed. By investigating different kinds of ratchets, it is better to comprehend the directed transport of Brownian particles and obtain an insight into the transport process in biomedicine. Especially, the investigation of Brownian ratchets can also be used for improving the accurate drug delivery and effectively utilizing the medicine.Until now, the directed transport of ratchet has aoused the interest of researchers. It is found that a certain driving phase can lead to the current reversal of the underdamped ratchets in theory. A large number of experiments have shown that most of the biomolecular motors in cells are enzyme protein macromolecules and they can carry the “cargos” to implement the directed transport. Interestingly, molecular motors have high efficiency usually, and some of them can even reach an efficiency close to 100% in experiment. Nevertheless, it is found that the energy conversion of Brownian motors is low as indicated by calculating the rate between the effective work of particles and the input energy of ratchets. According to a comparison between the experimental results and theoretical analyses, it is well known that the efficiency of ratchets is still far from the actual motor efficiency measured experimentally. Therefore, how to increase the efficiency of molecular motor which is pulled by loads is still a very important research topic. Owing to the fact that the molecular motors are influenced by the cellular environment during the hydrolysis of ATP in the organism, the catalytic cycles of the coupled motor proteins are out of phase. This gives us an inspiration for establishing the corresponding feedback pulsing ratchet.Due to the effect of the feedback pulse on coupled ratchets, the directed transport character of pulsing ratchets when they drag loads is explored in the present work. And the directed transport, diffusion and energy conversion efficiency of coupled particles are discussed systematically. It can be observed that the directed transport of the feedback pulsing ratchets would be futher facilitated by adjusting suitable free length and coupling strength. Meanwhile, the energy conversion efficiency of coupled particles can obtain a maximum value under a certain free length and coupling strength. In particular, there is the current reversal in an evolutive cycle under a certain pulse. Moreover, the diffusion of coupled particles can be suppressed effectively by modulating the pulsing phase, thus the corresponding directed transport of pulsing ratchets can be facilitated. In addition, the energy conversion of feedback ratchets can also be improved if the load is appropriate. The current reserval obtained in this paper can be applied to the particle separation. On the other hand, these results provide some great experimental inspirations in the aspect of medical delivery.

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