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The Brownian motion in a harmonic trap is studied by magnetic tweezers experiment and computer simulation. The results of the experiment and simulation validate the theory. Then the theory is used to analyze the experimental results including the effect of persistent length of DNA on the displacement distribution of the bead and the error in force measurements. It can be concluded that the variation of the persistent length affects more the Brownian motion along the DNA chain than in the other direction; under a small force, a considerable error of the force measurement will occur.
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Keywords:
- Brownian motion /
- hamonic trap /
- magnetic tweezers /
- DNA
[1] Einstein A 1956 Investigations on the Theory of the Brownian Movement (Dover Pubns) p1
[2] Robert M M 2009 Brownian Motion: Fluctuations, Dynamics, and Applications (NY: Oxford University Press) p46
[3] Hao B L 2011 Physics 40 1 (in Chinese) [郝柏林 2011 物理 40 1]
[4] Uhlenbeck G E, Ornstein L S 1930 Phys. Rev. 36 823
[5] Wang M C, Uhlenbeck G E 1945 Rev. Mod. Phys. 17 323
[6] Berg-Sorensen K, Flyvbjerg H 2004 Rev. Sci. Instrum. 75 594
[7] Strick T R, Allemand J F, Bensimon D, Croquette V 1998 Biophys. J. 74 2016
[8] Ran S Y, Wang X L, Fu W B, Lai Z H, Wang W C, Liu X Q, Mai Z H, Li M 2006 Chin. Phys. Lett. 23 504
[9] Ran S Y, Wang X L, Fu W B, Wang W C, Li M 2008 Chin. Sci. Bull. 53 836
[10] Wang X L, Zhang X H, Wei K J, Sun B, Li M 2008 Acta Phys. Sin. 57 3905 (in Chinese) [王晓玲, 张兴华, 魏孔吉, 孙博, 李明 2008 物理学报 57 3905]
[11] Ran S Y, Wang Y W, Yang G C 2011 Physics Experimentation 31(7) 1 (in Chinese) [冉诗勇, 王艳伟, 杨光参 2011 物理实验 31(7) 1]
[12] Jiang Y Q, Guo H L, Liu C X, Li Z L, Cheng B Y, Zhang D Z, Jia S T 2004 Acta Phys. Sin. 53 1721 (in Chinese) [降雨强, 郭红莲, 刘春香, 李兆霖, 程丙英, 张道中, 贾锁堂 2004 物理学报 53 1721]
[13] Ran S Y, Sun B, Li M 2007 Physics 36 228 (in Chinese) [冉诗勇, 孙博, 李明 2007 物理 36 228]
[14] Hinterdorfer P, Van Oijen A 2009 Handbook of single-molecule biophysics (Springer Verlag) p1
[15] Reif F 1965 Fundamentals of Statistical and Thermal Physics (New York: McGraw-Hill) p249
[16] Wang C T 1991 Statistical Physics p343 (in Chinese) [王诚泰 1991 统计物理学(清华大学出版社) 第343页]
[17] Marko J F, Siggia E D 1995 Macromolecules 28 8759
[18] Lin B, Yu J, Rice S A 2000 Phys. Rev. E 62 3909
[19] Leuba S H, Karymov M A, Tomschik M, Ramjit R, Smith P, Zlatanova J 2003 Proc. Natl. Acad. Sci. 100 495
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[1] Einstein A 1956 Investigations on the Theory of the Brownian Movement (Dover Pubns) p1
[2] Robert M M 2009 Brownian Motion: Fluctuations, Dynamics, and Applications (NY: Oxford University Press) p46
[3] Hao B L 2011 Physics 40 1 (in Chinese) [郝柏林 2011 物理 40 1]
[4] Uhlenbeck G E, Ornstein L S 1930 Phys. Rev. 36 823
[5] Wang M C, Uhlenbeck G E 1945 Rev. Mod. Phys. 17 323
[6] Berg-Sorensen K, Flyvbjerg H 2004 Rev. Sci. Instrum. 75 594
[7] Strick T R, Allemand J F, Bensimon D, Croquette V 1998 Biophys. J. 74 2016
[8] Ran S Y, Wang X L, Fu W B, Lai Z H, Wang W C, Liu X Q, Mai Z H, Li M 2006 Chin. Phys. Lett. 23 504
[9] Ran S Y, Wang X L, Fu W B, Wang W C, Li M 2008 Chin. Sci. Bull. 53 836
[10] Wang X L, Zhang X H, Wei K J, Sun B, Li M 2008 Acta Phys. Sin. 57 3905 (in Chinese) [王晓玲, 张兴华, 魏孔吉, 孙博, 李明 2008 物理学报 57 3905]
[11] Ran S Y, Wang Y W, Yang G C 2011 Physics Experimentation 31(7) 1 (in Chinese) [冉诗勇, 王艳伟, 杨光参 2011 物理实验 31(7) 1]
[12] Jiang Y Q, Guo H L, Liu C X, Li Z L, Cheng B Y, Zhang D Z, Jia S T 2004 Acta Phys. Sin. 53 1721 (in Chinese) [降雨强, 郭红莲, 刘春香, 李兆霖, 程丙英, 张道中, 贾锁堂 2004 物理学报 53 1721]
[13] Ran S Y, Sun B, Li M 2007 Physics 36 228 (in Chinese) [冉诗勇, 孙博, 李明 2007 物理 36 228]
[14] Hinterdorfer P, Van Oijen A 2009 Handbook of single-molecule biophysics (Springer Verlag) p1
[15] Reif F 1965 Fundamentals of Statistical and Thermal Physics (New York: McGraw-Hill) p249
[16] Wang C T 1991 Statistical Physics p343 (in Chinese) [王诚泰 1991 统计物理学(清华大学出版社) 第343页]
[17] Marko J F, Siggia E D 1995 Macromolecules 28 8759
[18] Lin B, Yu J, Rice S A 2000 Phys. Rev. E 62 3909
[19] Leuba S H, Karymov M A, Tomschik M, Ramjit R, Smith P, Zlatanova J 2003 Proc. Natl. Acad. Sci. 100 495
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