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A knotted polymer chain passing through a pore is investigated by molecule dynamics method. In this paper, we take 31 knot as an example. It is found that, during the process of translocation, the size of the knot fluctuates until the knot is unknotted. In addition, the effect of the knot on the translocation velocity of the knotted chain is also discussed. For the given external force, the average translocation time τ satisfies the scaling relation:τ～N α, and the scaling exponent α increases with the external force f. For short knotted polymer chains, the average translocation time τ decreases when the external force f increases. However, for very long knotted polymer chains, the average translocation time τ increases when the external force f increases. In the meantime, the position of knot in a knotted polymer chain also affects the average translocation time τ strongly. The closer the knot approaches the first translocated monomer, the longer the average translocation time. This investigation can provide some insights into the translocation of knotted polymer chains (especially knotted DNA) through the nanopore, and help us understand the translocation behavior of biomacromolecules.
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Keywords:
- molecule dynamics method /
- knotted polymer chain /
- translocation time /
- unknotted
[1] Mansfield M L 1994 Macromolecules 27 5924
[2] Lua R, Borovinskiy A L, Grosberg A Y 2004 Polymer 45 717
[3] Virnau P, Kantor Y, Kardar M 2005 J. Am. Chem. Soc. 127 15102
[4] Matthews R, Louis A A, Yeomans J M 2009 Phys. Rev. Lett. 102 088101
[5] Murzin A G, Brenner S E, Hubbard T, Chothia C 1995 J. Mol. Biol. 247 536
[6] Wang X H, Shen Y, Zhang L X 2009 Chin. Phys. B 18 1684
[7] Atiyah M F 1990 The Geometry and Physics of Knots (Cambridge: Cambridge University Press) p291
[8] Katritch V, Bednar J, Michoud D, Scharein R G, Dubochet J, Stasiak A 1996 Nature 384 142
[9] Katritch V, Olson W K, Pieranski P, Dubochet J, Stasiak A 1997 Nature 388 148
[10] Virnau P, Mirny L A, Kardar M 2006 PLoS Comput. Biol. 2 1074
[11] Han J, Turner S W, Craighead H G 1999 Phys. Rev. Lett. 83 1688
[12] Turner S W P, Cabodi M, Craighead H G 2002 Phys. Rev. Lett. 88 128103
[13] Grigoriev S M, Muro C, Dejean L M, Campo M L, Martinez-Caballero S, Kinnally K W 2004 Int. Rev. Cytol. 238 227
[14] Szabo I, Bathori G, Tombola F, Brini M, Coppola A, Zoratti M 1997 J. Biol. Chem. 272 25275
[15] Hanss B, Leal-Pinto E, Bruggeman L A, Copeland T D, Klotman P E 1998 Proc. Natl. Acad. Sci. U.S.A. 95 1921
[16] Tseng Y L, Liu J J, Hong R L 2002 Mol. Pharmacol. 62 864
[17] Kasianowicz J J, Brandin E, Branton D, Deamer D 1996 Proc. Natl. Acad. Sci. U.S.A. 93 13770
[18] Meller A, Nivon L, Brandin E, Golovchenko J, Branton D 2000 Proc. Natl. Acad. Sci. U.S.A. 97 1079
[19] Jiang S C, Zhang L X, Xia A G, Chen H P, Cheng J 2010 Chin. Phys. B 19 018106
[20] Ali I, Marenduzzo D, Yeomans J M 2006 Phys. Rev. Lett. 96 208102
[21] Ali I, Marenduzzo D, Yeomans J M 2008 Biophys. J. 94 4159
[22] Li Y L, Luo C L 2002 Acta Phys. Sin. 51 2589 (in Chinese) [李延龄、罗成林 2002 51 2589]
[23] Zhang X R, Shen Z G, Chen J F, Wang W C 2003 Acta Phys. Sin. 52 163 (in Chinese) [张现仁、沈志刚、陈建峰、汪文川 2003 52 163]
[24] Xie Y J, Shi Q W, Wang X P, Zhu P P, Yang H Y, Zhang X Y 2004 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 2004 53 2796]
[25] Luo K F, Ala-Nissila T, Ying S C, Bhattacharya A 2008 Phys. Rev. Lett. 100 058101
[26] Jiang S C, Zhang L X, Xia A G, Chen H P 2009 Acta Phys. Sin. 59 4337 (in Chinese) [江绍钏、章林溪、夏阿根、陈宏平 2010 59 4337]
[27] Luo K F, Ala-Nissila Nissila T A, Ying S C, Bhattacharya A 2007 Phys. Rev. Lett. 99 148102
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[1] Mansfield M L 1994 Macromolecules 27 5924
[2] Lua R, Borovinskiy A L, Grosberg A Y 2004 Polymer 45 717
[3] Virnau P, Kantor Y, Kardar M 2005 J. Am. Chem. Soc. 127 15102
[4] Matthews R, Louis A A, Yeomans J M 2009 Phys. Rev. Lett. 102 088101
[5] Murzin A G, Brenner S E, Hubbard T, Chothia C 1995 J. Mol. Biol. 247 536
[6] Wang X H, Shen Y, Zhang L X 2009 Chin. Phys. B 18 1684
[7] Atiyah M F 1990 The Geometry and Physics of Knots (Cambridge: Cambridge University Press) p291
[8] Katritch V, Bednar J, Michoud D, Scharein R G, Dubochet J, Stasiak A 1996 Nature 384 142
[9] Katritch V, Olson W K, Pieranski P, Dubochet J, Stasiak A 1997 Nature 388 148
[10] Virnau P, Mirny L A, Kardar M 2006 PLoS Comput. Biol. 2 1074
[11] Han J, Turner S W, Craighead H G 1999 Phys. Rev. Lett. 83 1688
[12] Turner S W P, Cabodi M, Craighead H G 2002 Phys. Rev. Lett. 88 128103
[13] Grigoriev S M, Muro C, Dejean L M, Campo M L, Martinez-Caballero S, Kinnally K W 2004 Int. Rev. Cytol. 238 227
[14] Szabo I, Bathori G, Tombola F, Brini M, Coppola A, Zoratti M 1997 J. Biol. Chem. 272 25275
[15] Hanss B, Leal-Pinto E, Bruggeman L A, Copeland T D, Klotman P E 1998 Proc. Natl. Acad. Sci. U.S.A. 95 1921
[16] Tseng Y L, Liu J J, Hong R L 2002 Mol. Pharmacol. 62 864
[17] Kasianowicz J J, Brandin E, Branton D, Deamer D 1996 Proc. Natl. Acad. Sci. U.S.A. 93 13770
[18] Meller A, Nivon L, Brandin E, Golovchenko J, Branton D 2000 Proc. Natl. Acad. Sci. U.S.A. 97 1079
[19] Jiang S C, Zhang L X, Xia A G, Chen H P, Cheng J 2010 Chin. Phys. B 19 018106
[20] Ali I, Marenduzzo D, Yeomans J M 2006 Phys. Rev. Lett. 96 208102
[21] Ali I, Marenduzzo D, Yeomans J M 2008 Biophys. J. 94 4159
[22] Li Y L, Luo C L 2002 Acta Phys. Sin. 51 2589 (in Chinese) [李延龄、罗成林 2002 51 2589]
[23] Zhang X R, Shen Z G, Chen J F, Wang W C 2003 Acta Phys. Sin. 52 163 (in Chinese) [张现仁、沈志刚、陈建峰、汪文川 2003 52 163]
[24] Xie Y J, Shi Q W, Wang X P, Zhu P P, Yang H Y, Zhang X Y 2004 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 2004 53 2796]
[25] Luo K F, Ala-Nissila T, Ying S C, Bhattacharya A 2008 Phys. Rev. Lett. 100 058101
[26] Jiang S C, Zhang L X, Xia A G, Chen H P 2009 Acta Phys. Sin. 59 4337 (in Chinese) [江绍钏、章林溪、夏阿根、陈宏平 2010 59 4337]
[27] Luo K F, Ala-Nissila Nissila T A, Ying S C, Bhattacharya A 2007 Phys. Rev. Lett. 99 148102
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