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Macrotransport analysis of effective mobility of biomolecules in periodic nano-filter polar arrays

Li Zi-Rui Liao Ning-Bo Zhou Yu-Qing Xue Wei Liu Mou-Bin

Macrotransport analysis of effective mobility of biomolecules in periodic nano-filter polar arrays

Li Zi-Rui, Liao Ning-Bo, Zhou Yu-Qing, Xue Wei, Liu Mou-Bin
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  • Transport of anisotropic biomolecules and/or charged Brownian particles in periodic porous media is of great importance in the fields of biomedicine, water treatment, and environmental engineering etc. In this paper, we present the modeling of transport of biomolecules in periodic polar arrays based on a numerical analysis of effective mobility. Anisotropic biomolecules are transformed to point-sized Brownian particles through introduction of configurational entropy, and the effective charge and effective transport parameters are calculated using macrotransport theory. As an example, the mobility of short dsDNA fragments in a nano-polar array is calculated. It is demonstrated that when the sizes of the gaps between the nano-poles are similar to or smaller than the size of biomolecules, the configurational entropy has a significant effect on the effective velocity. Difference in configurational entropy in the confined space dominates the partitioning of the molecules. In addition, as the effect of entropic barrier decreases with the strength of external electric field, relatively low voltage is preferred in order to achieve better selectivity.
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11372229).
    [1]

    Han J, Fu J, Schoch R B 2008 Lab. Chip. 8 23

    [2]

    Fu J, Mao P, Han J 2005 Appl. Phys. Lett. 87 263902

    [3]

    Fu J, Yoo J, Han J 2006 Phys. Rev. Lett. 97 018103

    [4]

    Fu J, Schoch R B, Stevens A L, Tannenbaum S R, Han J 2007 Nat. Nano. 2 121

    [5]

    Mao P, Han J 2009 Lab. Chip. 9 586

    [6]

    Han J, Turner S W, Craighead H G 1999 Phys. Rev. Lett. 83 1688

    [7]

    Han J, Craighead H G 2000 Science 288 1026

    [8]

    Dorfman K D 2010 Rev. Mod. Phys. 82 2903

    [9]

    Stein D, Kruithof M, Dekker C 2004 Phys. Rev. Lett. 93 035901

    [10]

    Gao L, Wu J, Gao D, Wu J 2007 Appl. Phys. Lett. 91 113902

    [11]

    Wu J, Zhao S L, Gao L, Wu J, Gao D 2011 Lab. Chip 11 4036

    [12]

    Wu J, Zhao S L, Gao L, Wu J, Gao D 2013 J. Phys. Chem. B 117 2267

    [13]

    Fang Z L, Fang Q 2001 Mod. Sci. Instrum. 4 3 (in Chinese) [方肇伦, 方群 2001 现代科学仪器 4 3]

    [14]

    Lin B C, Qin J H 2005 Chinese J. Chromatogr. 23 456 (in Chinese) [林炳承, 秦建华 2005 色谱 23 456]

    [15]

    Qin J H, Feng Y S,Lin B C 2003 Chinese J. Chromatogr. 21 464 (in Chinese) [秦建华, 冯应升, 林炳承 2003 色谱 21 464]

    [16]

    Zhang Z X, Shen Z, Zhao H, Li B, Song S P, Hu J, Lin B C, Li M Q 2005 Acta. Chim. Sin. 63 1743 (in Chinese) [张志祥, 沈铮, 赵辉, 李宾, 宋世平, 胡钧, 林炳承, 李民乾 2005 化学学报 63 1743]

    [17]

    Zhou X M, Li D Z, Shen Z, Liu W, Li G R, Lin B C 2005 Chem. J. Chinese. U. 26 1252 (in Chinese) [周小棉, 李大志, 沈铮, 刘伟, 李桂茹, 林炳承 2005 高等学校化学学报 26 1252]

    [18]

    Yao B, He Q H, Du W B, Shi X T, Fang Q 2009 Chinese J. Chromatogr. 27 662 (in Chinese) [姚波, 何巧红, 杜文斌, 石晓彤, 方群 2009 色谱 27 662]

    [19]

    Rodbard D, Chrambach A 1970 Proc. Nat. Acad. Sci. 65 970

    [20]

    Zhang J L, Jiang J G, Jiang X G, Huang Y N 2007 Acta Phys. Sin. 56 5088 (in Chiniese) [张晋鲁, 蒋建国, 蒋新革, 黄以能 2007 物理学报 56 5088]

    [21]

    Jiang S C, Zhang L X, Xia A C, Chen H P, Cheng J 2010 Chin. Phys. B 19 018106

    [22]

    Cao X Z, Merlitz H, Sommer J U, Wu C X 2012 Chin. Phys. B 21 118202

    [23]

    Fayad G N,Hadjiconstantinou N G 2010 Microfluid. Nanofluid. 8 521

    [24]

    Li H X, Qiang HF 2009 Adv. Mech. 39 165 (in Chinese) [李红霞, 强洪夫 2009 力学进展 39 165]

    [25]

    Zhou L W, Liu M B, Chang J Z 2012 Acta Polym. Sin. 7 720 (in Chinese) [周吕文, 刘谋斌, 常建忠 2012 高分子学报 7 720]

    [26]

    Chen S, Shang Z, Zhao Y, Wang D 2010 J. Tongji Univ. (Nat. Sci.) 38 767 (in Chinese) [陈硕, 尚智, 赵岩, 王丹 2010 同济大学学报 (自然科学版) 38 767]

    [27]

    Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少锋, 汪久根 2013 物理学报 62 124701]

    [28]

    Wang Y, Xie Y J, Yang H Y, Zhang X Y 2010 Chinese J. Chem. Phys. 3 313 (in Chinese) [王瑶, 谢永军, 杨海洋, 张兴元 2010 化学物理学报 3 313]

    [29]

    Xie Y J, Shi Q W, Wang X P, Zhu P P, Yang H Y, Zhang X Y 2005 Acta Phys. Sin. 53 2796 (in Chinese) [谢永军, 石勤伟, 王晓平, 朱平平, 杨海洋, 张兴元 2005 物理学报 53 2796]

    [30]

    Su J Y, Zhang L X 2008 Chin. Phys. B 17 3115

    [31]

    Xu L M, He L L, Cheng J 2011 J. Zhejiang Univ. (Sci. Edn.) 5 009 (in Chinese) [徐李梅, 何林李, 成军 2011 浙江大学学报 (理学版) 5 009]

    [32]

    Allison S A, Li Z, Reed D, Stellwagen N C 2002 Electrophoresis 23 2678

    [33]

    Gao H L, Zhou K L, Wang C, Li S J, Zhang H, Xia X H 2012 Electrochemistry 18 229 (in Chinese) [高红丽, 周凯琳, 王琛, 李素娟, 章慧, 夏兴华 2012 电化学 18 229]

    [34]

    Li Z R, Liu G R, Chen Y Z, Wang J S, Bow H, Cheng Y, Han J 2008 Electrophoresis 29 329

    [35]

    Li Z R, Liu G R, Han J, Cheng Y, Chen Y Z, Wang J S, Hadjiconstantinou N G 2009 Phys. Rev. E 80 041911

    [36]

    Brenner H, Edwards D 1993 Macrotransport Processes (Boston MA: Butterworth Heinemann) p1

    [37]

    Dorfman K D, Brenner H 2002 Phys. Rev. E 65 021103

    [38]

    Yariv E, Dorfman K D 2007 Phys. Fluids. 19 037101

    [39]

    Dorfman K D 2010 Chem. Eng. Commu. 197 39

    [40]

    Wang X, Drazer G 2009 Phys. Fluids. 21 102002

    [41]

    Bernate J A, Drazer G 2011 J. Colloid. Interface. Sci. 356 341

    [42]

    Li Z R, Liu G R, Han J, Chen Y Z, Wang J S, Hadjiconstantinou N G 2009 Anal. Bioanal. Chem. 34 427

    [43]

    Berg H C 1993 Random walks in biology (Princeton: Princeton University Press) p1

    [44]

    Rubenstein M, Colby R H 2003 Polymer Physics (New York: Oxford University Press) p1

    [45]

    Stellwagen N C, Gelfi C, Righetti P G 1997 Biopolymers 42 687

    [46]

    Tirado M M, Martinez C L, Garcia de la Torre J J 1984 Chem. Phys. 81 2047

    [47]

    Li Z R, Liu G R, Hadjiconstantinou N G, Han J, Wang J S, Chen Y Z 2011 Electrophoresis 32 506

  • [1]

    Han J, Fu J, Schoch R B 2008 Lab. Chip. 8 23

    [2]

    Fu J, Mao P, Han J 2005 Appl. Phys. Lett. 87 263902

    [3]

    Fu J, Yoo J, Han J 2006 Phys. Rev. Lett. 97 018103

    [4]

    Fu J, Schoch R B, Stevens A L, Tannenbaum S R, Han J 2007 Nat. Nano. 2 121

    [5]

    Mao P, Han J 2009 Lab. Chip. 9 586

    [6]

    Han J, Turner S W, Craighead H G 1999 Phys. Rev. Lett. 83 1688

    [7]

    Han J, Craighead H G 2000 Science 288 1026

    [8]

    Dorfman K D 2010 Rev. Mod. Phys. 82 2903

    [9]

    Stein D, Kruithof M, Dekker C 2004 Phys. Rev. Lett. 93 035901

    [10]

    Gao L, Wu J, Gao D, Wu J 2007 Appl. Phys. Lett. 91 113902

    [11]

    Wu J, Zhao S L, Gao L, Wu J, Gao D 2011 Lab. Chip 11 4036

    [12]

    Wu J, Zhao S L, Gao L, Wu J, Gao D 2013 J. Phys. Chem. B 117 2267

    [13]

    Fang Z L, Fang Q 2001 Mod. Sci. Instrum. 4 3 (in Chinese) [方肇伦, 方群 2001 现代科学仪器 4 3]

    [14]

    Lin B C, Qin J H 2005 Chinese J. Chromatogr. 23 456 (in Chinese) [林炳承, 秦建华 2005 色谱 23 456]

    [15]

    Qin J H, Feng Y S,Lin B C 2003 Chinese J. Chromatogr. 21 464 (in Chinese) [秦建华, 冯应升, 林炳承 2003 色谱 21 464]

    [16]

    Zhang Z X, Shen Z, Zhao H, Li B, Song S P, Hu J, Lin B C, Li M Q 2005 Acta. Chim. Sin. 63 1743 (in Chinese) [张志祥, 沈铮, 赵辉, 李宾, 宋世平, 胡钧, 林炳承, 李民乾 2005 化学学报 63 1743]

    [17]

    Zhou X M, Li D Z, Shen Z, Liu W, Li G R, Lin B C 2005 Chem. J. Chinese. U. 26 1252 (in Chinese) [周小棉, 李大志, 沈铮, 刘伟, 李桂茹, 林炳承 2005 高等学校化学学报 26 1252]

    [18]

    Yao B, He Q H, Du W B, Shi X T, Fang Q 2009 Chinese J. Chromatogr. 27 662 (in Chinese) [姚波, 何巧红, 杜文斌, 石晓彤, 方群 2009 色谱 27 662]

    [19]

    Rodbard D, Chrambach A 1970 Proc. Nat. Acad. Sci. 65 970

    [20]

    Zhang J L, Jiang J G, Jiang X G, Huang Y N 2007 Acta Phys. Sin. 56 5088 (in Chiniese) [张晋鲁, 蒋建国, 蒋新革, 黄以能 2007 物理学报 56 5088]

    [21]

    Jiang S C, Zhang L X, Xia A C, Chen H P, Cheng J 2010 Chin. Phys. B 19 018106

    [22]

    Cao X Z, Merlitz H, Sommer J U, Wu C X 2012 Chin. Phys. B 21 118202

    [23]

    Fayad G N,Hadjiconstantinou N G 2010 Microfluid. Nanofluid. 8 521

    [24]

    Li H X, Qiang HF 2009 Adv. Mech. 39 165 (in Chinese) [李红霞, 强洪夫 2009 力学进展 39 165]

    [25]

    Zhou L W, Liu M B, Chang J Z 2012 Acta Polym. Sin. 7 720 (in Chinese) [周吕文, 刘谋斌, 常建忠 2012 高分子学报 7 720]

    [26]

    Chen S, Shang Z, Zhao Y, Wang D 2010 J. Tongji Univ. (Nat. Sci.) 38 767 (in Chinese) [陈硕, 尚智, 赵岩, 王丹 2010 同济大学学报 (自然科学版) 38 767]

    [27]

    Xu S F, Wang J G 2013 Acta Phys. Sin. 62 124701 (in Chinese) [许少锋, 汪久根 2013 物理学报 62 124701]

    [28]

    Wang Y, Xie Y J, Yang H Y, Zhang X Y 2010 Chinese J. Chem. Phys. 3 313 (in Chinese) [王瑶, 谢永军, 杨海洋, 张兴元 2010 化学物理学报 3 313]

    [29]

    Xie Y J, Shi Q W, Wang X P, Zhu P P, Yang H Y, Zhang X Y 2005 Acta Phys. Sin. 53 2796 (in Chinese) [谢永军, 石勤伟, 王晓平, 朱平平, 杨海洋, 张兴元 2005 物理学报 53 2796]

    [30]

    Su J Y, Zhang L X 2008 Chin. Phys. B 17 3115

    [31]

    Xu L M, He L L, Cheng J 2011 J. Zhejiang Univ. (Sci. Edn.) 5 009 (in Chinese) [徐李梅, 何林李, 成军 2011 浙江大学学报 (理学版) 5 009]

    [32]

    Allison S A, Li Z, Reed D, Stellwagen N C 2002 Electrophoresis 23 2678

    [33]

    Gao H L, Zhou K L, Wang C, Li S J, Zhang H, Xia X H 2012 Electrochemistry 18 229 (in Chinese) [高红丽, 周凯琳, 王琛, 李素娟, 章慧, 夏兴华 2012 电化学 18 229]

    [34]

    Li Z R, Liu G R, Chen Y Z, Wang J S, Bow H, Cheng Y, Han J 2008 Electrophoresis 29 329

    [35]

    Li Z R, Liu G R, Han J, Cheng Y, Chen Y Z, Wang J S, Hadjiconstantinou N G 2009 Phys. Rev. E 80 041911

    [36]

    Brenner H, Edwards D 1993 Macrotransport Processes (Boston MA: Butterworth Heinemann) p1

    [37]

    Dorfman K D, Brenner H 2002 Phys. Rev. E 65 021103

    [38]

    Yariv E, Dorfman K D 2007 Phys. Fluids. 19 037101

    [39]

    Dorfman K D 2010 Chem. Eng. Commu. 197 39

    [40]

    Wang X, Drazer G 2009 Phys. Fluids. 21 102002

    [41]

    Bernate J A, Drazer G 2011 J. Colloid. Interface. Sci. 356 341

    [42]

    Li Z R, Liu G R, Han J, Chen Y Z, Wang J S, Hadjiconstantinou N G 2009 Anal. Bioanal. Chem. 34 427

    [43]

    Berg H C 1993 Random walks in biology (Princeton: Princeton University Press) p1

    [44]

    Rubenstein M, Colby R H 2003 Polymer Physics (New York: Oxford University Press) p1

    [45]

    Stellwagen N C, Gelfi C, Righetti P G 1997 Biopolymers 42 687

    [46]

    Tirado M M, Martinez C L, Garcia de la Torre J J 1984 Chem. Phys. 81 2047

    [47]

    Li Z R, Liu G R, Hadjiconstantinou N G, Han J, Wang J S, Chen Y Z 2011 Electrophoresis 32 506

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  • Received Date:  22 June 2013
  • Accepted Date:  19 July 2013
  • Published Online:  05 November 2013

Macrotransport analysis of effective mobility of biomolecules in periodic nano-filter polar arrays

  • 1. College of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou 325035, China;
  • 2. Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, China
Fund Project:  Project supported by the National Natural Science Foundation of China (Grant No. 11372229).

Abstract: Transport of anisotropic biomolecules and/or charged Brownian particles in periodic porous media is of great importance in the fields of biomedicine, water treatment, and environmental engineering etc. In this paper, we present the modeling of transport of biomolecules in periodic polar arrays based on a numerical analysis of effective mobility. Anisotropic biomolecules are transformed to point-sized Brownian particles through introduction of configurational entropy, and the effective charge and effective transport parameters are calculated using macrotransport theory. As an example, the mobility of short dsDNA fragments in a nano-polar array is calculated. It is demonstrated that when the sizes of the gaps between the nano-poles are similar to or smaller than the size of biomolecules, the configurational entropy has a significant effect on the effective velocity. Difference in configurational entropy in the confined space dominates the partitioning of the molecules. In addition, as the effect of entropic barrier decreases with the strength of external electric field, relatively low voltage is preferred in order to achieve better selectivity.

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