高分子链穿过纳米孔的计算机模拟
摘要
生物高分子链通过纳米小孔的现象在生物领域中广泛存在。研究此现象的动力学行为,不仅有助于人们更好地理解生命过程,而且对医学、物理学、化学以及生物科技也有重要的意义。近年来人们从各个方面对这一动力学过程做了大量的研究,并取得了丰硕的研究成果。本论文结合当前进展,用计算机模拟的方法,对高分子链经纳米小孔移位的动力学行为进行了研究。
高分子链由于无规热运动或者在外力驱动下可以经过一个远小于高分子链尺寸的小孔从cis空间移位到trans空间。我们首先考察了对高分子链经吸附膜上的小孔移位的动力学过程。我们发现,移位时间τ与链节与小孔的相互作用参数ε有关。当链-孔相互作用参数ε较小时,我们有τ～ε-2；当ε为中等大小时,τ达到最小；之后τ随ε增大而增大。同时我们也考察了移位时间随链长N和随孔中驱动力F的变化关系,得到τ～N2+v和τ～F-δ,在F很小的区域指数δ约为0,对于较大的F指数δ约为0.9。我们还定性上解释了上述模拟结果。其次我们研究了高分子链经排斥膜上的小孔移位的动力学过程,考察了链-孔相互作用对高分子链移位的影响。当链-孔之间仅有相互排斥作用时,移位时间跟孔中驱动力之间的关系为τ～F-δ,其中F较大时δ≈0.86,移位时间跟链长的关系满足τ～Nα,标度指数α=1.38,这一结果跟已有结论很符合。对于链-孔有相互吸引作用的情况,我们发现了长链的移位时间跟链长的关系也满足τ～Nα,但我们第一次发现α=1。
Transport of biopolymers through nanopores is ubiquitous in biology. Studying the dynamics of polymer translocating through nanopores is not only helpful to better understand the life processes, but also important for medicine, physics, chemical industry and biotechnology, etc. A lot of meaningful researches on this topic have been done and many interesting results have been reported. In this dissertation we report our work on studying the translocation of polymer through nanopores with computer simulation technique.
With thermal random motion or under the external driving force, polymer chain can translocate a nanopore which is far less than the size of the polymer chain from the cis space to trans space. Firstly, we investigate the dynamics process of polymer chain translocating through a nanopore in an adsorption membrane. We find that the translocation timeτis dependent on the polymer-pore interactionε-At smallε,τdecreases withεwith a relationτ～ε-2; r is minimum at moderateε; and at lastτincreases withεat largeε. Meanwhile we also do research on the dependence of the translocation time on chain length and driving force. We obtainτ～N2+v andτ-F-δ, where the exponentδis about 0 in small F region and 0.9 at higher F. We also qualitatively explain the above simulation result. Secondly, we investigate the dynamics process of the polymer translocation through a nanopore in a repulsion membrane, and examining the effect of the polymer-pore interaction on the translocation time. For a repulsive pore, there is a relationτ～F-δwithδabout 0.86 at moderate F, and there is a relationτ～Nαwith a about 1.38, which is consistent with already existed conclusions. While for an attractive pore, we findτ～Nαwithα=1 for long chain, which is firstly found in our simulation.
高分子链由于无规热运动或者在外力驱动下可以经过一个远小于高分子链尺寸的小孔从cis空间移位到trans空间。我们首先考察了对高分子链经吸附膜上的小孔移位的动力学过程。我们发现,移位时间τ与链节与小孔的相互作用参数ε有关。当链-孔相互作用参数ε较小时,我们有τ～ε-2；当ε为中等大小时,τ达到最小；之后τ随ε增大而增大。同时我们也考察了移位时间随链长N和随孔中驱动力F的变化关系,得到τ～N2+v和τ～F-δ,在F很小的区域指数δ约为0,对于较大的F指数δ约为0.9。我们还定性上解释了上述模拟结果。其次我们研究了高分子链经排斥膜上的小孔移位的动力学过程,考察了链-孔相互作用对高分子链移位的影响。当链-孔之间仅有相互排斥作用时,移位时间跟孔中驱动力之间的关系为τ～F-δ,其中F较大时δ≈0.86,移位时间跟链长的关系满足τ～Nα,标度指数α=1.38,这一结果跟已有结论很符合。对于链-孔有相互吸引作用的情况,我们发现了长链的移位时间跟链长的关系也满足τ～Nα,但我们第一次发现α=1。
Transport of biopolymers through nanopores is ubiquitous in biology. Studying the dynamics of polymer translocating through nanopores is not only helpful to better understand the life processes, but also important for medicine, physics, chemical industry and biotechnology, etc. A lot of meaningful researches on this topic have been done and many interesting results have been reported. In this dissertation we report our work on studying the translocation of polymer through nanopores with computer simulation technique.
With thermal random motion or under the external driving force, polymer chain can translocate a nanopore which is far less than the size of the polymer chain from the cis space to trans space. Firstly, we investigate the dynamics process of polymer chain translocating through a nanopore in an adsorption membrane. We find that the translocation timeτis dependent on the polymer-pore interactionε-At smallε,τdecreases withεwith a relationτ～ε-2; r is minimum at moderateε; and at lastτincreases withεat largeε. Meanwhile we also do research on the dependence of the translocation time on chain length and driving force. We obtainτ～N2+v andτ-F-δ, where the exponentδis about 0 in small F region and 0.9 at higher F. We also qualitatively explain the above simulation result. Secondly, we investigate the dynamics process of the polymer translocation through a nanopore in a repulsion membrane, and examining the effect of the polymer-pore interaction on the translocation time. For a repulsive pore, there is a relationτ～F-δwithδabout 0.86 at moderate F, and there is a relationτ～Nαwith a about 1.38, which is consistent with already existed conclusions. While for an attractive pore, we findτ～Nαwithα=1 for long chain, which is firstly found in our simulation.
引文
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[3]Darnell J, Lodish H and Baltimore D Molecular Cell Biology (Scientific American Books, New York,1995)
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[8]Slonkina E and Kolomeisky A B 2003 J. Chem. Phys.118 10371
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[10]Luo K F and Metzler R 2010 J. Chem. Phys.133 75101
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[12]Meller A, Nivon L, and Branton D 2001 Phys. Rev. Lett.86 3435
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[15]Muthukumar M 2003 J. Chem. Phys.118,5174
[16]Luo K F, Ala-Nissila T, Ying S C and Bhatacharya A 2007 Phys. Rev. Lett.99 148102
[17]Tian P and Smith G D 2003 J. Chem. Phys.119,11475
[18]Luo M B 2007 Polymer 48,7679
[19]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. Lett.100, 058101
[20]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. E 78, 061911
[21]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. E 78. 061918
[22]Krasilnikov O V, Rodrigues C G and Bezrukov S M 2006 Phys. Rev. Lett.97, 018301
[23]Sebastian K L and Paul A K R 2000 Phys. Rev. E 62 927
[24]Sung W and Park P J 1996 Phys. Rev. Lett.77 783
[25]Sun L Z, Cao W P and Luo MB 2010 Phys. Chem. Chem. Phys.12 13318
[26]Muthukumar M 1999 J. Chem. Phys. 111 10371
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[28]Chern S S, Cardenas A E and Coalson R D 2001 J. Chem. Phys.1157772
[29]Slokina E and Kolomeishy A 2003 J. Chem. Phys.118 7112
[30]Luo K F, Ala-Nissila T and Ying S C 2006 J. Chem. Phys.124 034714
[31]Luo K F, Huopaniemi I, Ala-Nissila A and Ying S C 2006 J. Chem. Phys.124 114704
[32]Loebl H C, Randel R, Goodwin S P and Matthai C C 2003 Phys. Rev. E 67 041913
[33]Huopaniemi I, Luo K F, Ala-Nissila T and Ying S C 2006 J. Chem. Phys.125 124901
[34]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2007 J. Chem. Phys.126 145101
[35]Huopaniemi I, Luo K F, Ala-Nissila T and Ying S C 2007 Phys. Rev. E 75 061912
[36]Luo K F, Metzler R, Ala-Nissila T and Ying S C 2009 Phys. Rev. E 80 021907
[37]Kim SH, Panwar AS, Kumar S, Ahn KH and Lee SJ 2004 J. Chem. Phys.121 9116
[38]Tian P and Smith G D 2003 J. Chem. Phys.119 11475
[39]Matysiak S, Montesi A, Pasquali M, Kolomeisky A B and Clementi C 2006 Phys. Rev. Lett.96 118103
[40]Nanper D Polymer Stabilization of Colloidal Dispersions, London,1983
[41]Goddard E, Goddard, Vincent B Polymer Adsorption and Dispersion Stability, Washington, D.C., Americal Chemical Society,1984
[42]Andrade J D Surface and Interfacial Aspects of Biomedical Polymers, New York, Plenum,1985
[43]Yau W W, Kirkl and Bly D, In Modern Size ExclusionChromatography, New York, Wiley,1979
[44]Wu S In Polymer Interfaces and Adhesion, New York, Dekker,1982
[45]Akeson M, Branton D, Kasianowicz J J, Brandin E and Deamer D W 1999 Biophys. J.77,3227
[46]Kantor Y and Kardar M 2004 Phys. Rev. E 69,021806
[47]Lubensky D K and Nelson D R 1999 Biophys. J.77,1824
[48]Cao W P, Sun L Z, Wang C and Luo M B 2011 Int. J. Mod. Phys. B 25 3345
[49]Luo K F, Ala-Nissila T, Ying S C and Metzler R 2009 Europhys. Lett.88 68006
[50]Bhattacharya A, Morrison W H, Luo K F, Ala-Nissila T, Ying S C, Milchev A and Binder K 2009 Eur. Phys. J.29423
[51]Sun LZ, Cao W P and Luo M B 2009 J. Chem. Phys.131194904
[2]Alberts B and Bray D Molecular biology of the cell (Grand, New York,1994)
[3]Darnell J, Lodish H and Baltimore D Molecular Cell Biology (Scientific American Books, New York,1995)
[4]Driselkelmann B 1994 Microbiol. Rev.58 293
[5]Chang D C Guide to Electroporation and Electrofusion (Academic, New York 1992)
[6]Han J, Turner S W and Craighead H G 1999 Phys. Rev. Lett.83 7112
[7]Turner S W P, Calodi M and Craighead H G 2002 Phys. Rev. Lett.88 128103
[8]Slonkina E and Kolomeisky A B 2003 J. Chem. Phys.118 10371
[9]Meirovitch H 1988 J. Chem. Phys.892514
[10]Luo K F and Metzler R 2010 J. Chem. Phys.133 75101
[11]Kasianowicz J J, Brandin E D and Deamer D 1996 Proc. Natl. Acad. Sci. USA, 93 13770
[12]Meller A, Nivon L, and Branton D 2001 Phys. Rev. Lett.86 3435
[13]Meller A, Nivon L, Brandin E, Golovchenko J A and Branton D 2000 Proc. Natl. Acad. Sci. U.S.A.97 1079
[14]Meller A and Branton D 2002 Electrophoresis 23 2583
[15]Muthukumar M 2003 J. Chem. Phys.118,5174
[16]Luo K F, Ala-Nissila T, Ying S C and Bhatacharya A 2007 Phys. Rev. Lett.99 148102
[17]Tian P and Smith G D 2003 J. Chem. Phys.119,11475
[18]Luo M B 2007 Polymer 48,7679
[19]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. Lett.100, 058101
[20]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. E 78, 061911
[21]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2008 Phys. Rev. E 78. 061918
[22]Krasilnikov O V, Rodrigues C G and Bezrukov S M 2006 Phys. Rev. Lett.97, 018301
[23]Sebastian K L and Paul A K R 2000 Phys. Rev. E 62 927
[24]Sung W and Park P J 1996 Phys. Rev. Lett.77 783
[25]Sun L Z, Cao W P and Luo MB 2010 Phys. Chem. Chem. Phys.12 13318
[26]Muthukumar M 1999 J. Chem. Phys. 111 10371
[27]Risken H The Fokker-Planck Equation (Springer-Verlay, Berlin,1984)
[28]Chern S S, Cardenas A E and Coalson R D 2001 J. Chem. Phys.1157772
[29]Slokina E and Kolomeishy A 2003 J. Chem. Phys.118 7112
[30]Luo K F, Ala-Nissila T and Ying S C 2006 J. Chem. Phys.124 034714
[31]Luo K F, Huopaniemi I, Ala-Nissila A and Ying S C 2006 J. Chem. Phys.124 114704
[32]Loebl H C, Randel R, Goodwin S P and Matthai C C 2003 Phys. Rev. E 67 041913
[33]Huopaniemi I, Luo K F, Ala-Nissila T and Ying S C 2006 J. Chem. Phys.125 124901
[34]Luo K F, Ala-Nissila T, Ying S C and Bhattacharya A 2007 J. Chem. Phys.126 145101
[35]Huopaniemi I, Luo K F, Ala-Nissila T and Ying S C 2007 Phys. Rev. E 75 061912
[36]Luo K F, Metzler R, Ala-Nissila T and Ying S C 2009 Phys. Rev. E 80 021907
[37]Kim SH, Panwar AS, Kumar S, Ahn KH and Lee SJ 2004 J. Chem. Phys.121 9116
[38]Tian P and Smith G D 2003 J. Chem. Phys.119 11475
[39]Matysiak S, Montesi A, Pasquali M, Kolomeisky A B and Clementi C 2006 Phys. Rev. Lett.96 118103
[40]Nanper D Polymer Stabilization of Colloidal Dispersions, London,1983
[41]Goddard E, Goddard, Vincent B Polymer Adsorption and Dispersion Stability, Washington, D.C., Americal Chemical Society,1984
[42]Andrade J D Surface and Interfacial Aspects of Biomedical Polymers, New York, Plenum,1985
[43]Yau W W, Kirkl and Bly D, In Modern Size ExclusionChromatography, New York, Wiley,1979
[44]Wu S In Polymer Interfaces and Adhesion, New York, Dekker,1982
[45]Akeson M, Branton D, Kasianowicz J J, Brandin E and Deamer D W 1999 Biophys. J.77,3227
[46]Kantor Y and Kardar M 2004 Phys. Rev. E 69,021806
[47]Lubensky D K and Nelson D R 1999 Biophys. J.77,1824
[48]Cao W P, Sun L Z, Wang C and Luo M B 2011 Int. J. Mod. Phys. B 25 3345
[49]Luo K F, Ala-Nissila T, Ying S C and Metzler R 2009 Europhys. Lett.88 68006
[50]Bhattacharya A, Morrison W H, Luo K F, Ala-Nissila T, Ying S C, Milchev A and Binder K 2009 Eur. Phys. J.29423
[51]Sun LZ, Cao W P and Luo M B 2009 J. Chem. Phys.131194904