摘要
高分子与表面相互作用的临界点实质是一个相变的临界点,相变现象是一个物理和材料领域的典型问题,对这问题尽管已经研究多年,但全面掌握至今仍是一个难题。高分子穿过膜上纳米孔的现象普遍存在于生命过程;利用电泳法,依据高分子的运动检测分离生物高分子是分离高分子的一个常用方法,如何提高分离的效率是当今生物应用技术领域一个需要解决的问题。本文研究了高分子与表面相互作用的相变临界点,并将这个相变临界现象与生物高分子在跨膜运输和电泳中的扩散运动结合起来研究。它既有助于理解高分子在生物系统中的运输机制,又为设计更好的分离装置探索了一条新的途径。
本文的主要工作如下:
A.本文将相变临界现象与生物高分子的扩散运动结合起来研究,既研究了高分子与表面的静态作用及这个作用的临界点,也研究了这个临界点附近高分子的扩散运动。根据高分子的运动情况得到的临界点与静态方法得到的一致,为研究临界点附近的性质提出了动态研究的新方法。
B.我们用完全计数法枚举了有限链长吸附高分子的构象,从而得到了有限链长吸附高分子构象数的精确值。我们将完全计数法得到的数值分析归纳为函数关系,并将其推广到长链高分子,第一次将吸附高分子的构象数用一般的函数关系表达。
C.考虑高分子与膜的相互作用,我们研究了分子穿过膜的动态。通过分析高分子穿过膜的时间和膜两边的分子单元的分布,我们发现高分子穿过膜的动态随相互作用能量的变化有一个临界点。
D.大量的研究团体正致力于改良传统的凝胶电泳,设计、制作精细的微观分离系统以提高分离高分子的效率。一种熵陷阱纳米阵列装置被设计和制造出来用于分离长的DNA分子。我们在这种熵陷阱纳米阵列装置中,考虑系统的界面与分子的相互作用,并研究了这个相互作用对系统检测分子的影响。我们发现分子与界面的作用不同,分子的运动相差很大,因此可利用这种作用对高分子进行分辨检测,从而提高系统对分子分辨的效率。
The critical point of interaction between macromolecules and surfaces is actually a critical point of the phase transition. The phenomenon of phase transition is a typical issue in physics and material study. Even though the problem has been studied for many years, it has not been understood thoroughly. The translocation of macromolecules through nanopores in nuclear and cellular membranes is commonly observed in processes of living. The electrophoresis is a standard method for the separation of macromolecules by length. How to improve the efficiency of separation is now a problem faced by researchers in the field of biological technology. In this paper, we study the critical point of interaction between macromolecules and surfaces, the critical phenomenon in translocation of biopolymer through membranes and the critical phenomenon of macromolecular transport in electrophoresis. It provides insight into the mechanisms of macromolecular transport in biological systems and also explores a new method in designing better separation techniques for biopolymers.
The main innovations in this paper are:
A. We relate the critical phenomenon of phase transition with the transport of biopolymers. Not only the static interaction between macromolecules and surfaces and the critical point of the interaction we study, but also we research the macromolecular transport near the critical point. The critical point obtained by dynamic method is consistent with that obtained by static method, so the dynamic method can be a new technique to study the property near the critical point.
B. We enumerate exactly all configurations of tethered chains with different chain length, so we get the exact number of the configurations. By analyzing the dependence of the number of configurations on the chain length and the number of contacts, we get the function relationship which is extrapolated to longer chain. This is the first time that the dependence of the number of the configurations on the chain length and the number of contacts is expressed by a function.
C. Taking account of the interaction between macromolecules and surfaces, we study the translocation of polymers through membranes. Analyzing the time of the translocation and the distribution of polymer monomers, we find there is a critical point while the time and the distribution change with the interaction energy changing.
D. Many researchers have been committed themselves to improve the traditional gel electrophoresis, design and make better separation systems. A nanofluidic channel array device, consisting of many entropic traps, was designed and fabricated for the separation of long DNA molecules. We take account of the interaction between molecules and surfaces of the entropic traps system. We find that molecules moves quit differently because of the different interaction, so the molecules may be separated efficiently.
引文
1. de Gennes, P. G.,Scaling Concept in Polymer Physics, Cornell University Press (1979).
2. Ising, E., Z. Physik 31: 253(1925).
3. Onsager, L., Phys. Rev. 65: 117(1944).
4. Kadanoff, L. P., Physics 2: 263(1966).
5. Wilson, K. G.,Phys. Rev. Lett. 26: 584(1972).
6. Eisenriegler, E., Kremer, K. and Binder, K., J. Chem. Phys. 77, 6296 (1982).
7. Hammersly, J. M., Torrie, G. M., and Whittington, S. G.,J. Phys. A 15, 539 (1982).
8. Meirovitch, H. and Livne, S., J. Chem. Phys. 88,4507 (1988).
9. Livne, S., and Meirovitch, H., J. Chem. Phys. 88, 4498 (1988).
10. Metzger, S., Müller, M., Binder, K. and Baschnagel, J., Macromol. Theory Simul. 11,985(2002).
11. Frisch, H. L., Simha, R. and Eirich, F. R., J. Chem. Phys. 21, 365 (1953).
12. Van Rensburg, E. J. J. and Rechnitzer, A. R., J. Phys. A 37, 6875 (2004).
13. Gong Y. C. and Wang, Y. M., Macromolecules 35, 7492 (2002).
14. Eisenriegler, E., Polymers near Surfaces, World Scientific, Singapore 1993.
15. Le Guillou, J. C. and Zinn-Justin, J., Phys. Rev. Lett. 39, 95(1977).
16. Diehl, H. W., and Dietrich, S., Phys. Rev. B 24, 2878(1981).
17. Hegger, R. and Grassberger, P., J. Phys. A 27,4069(1994).
18. Simon, S. M. and Blobel, G.,Cell 65, 371 (1991).
19. Alberts, B. and Bray, D., Molecular Biology of the Cell, Grand, New York, 1994.
20. Darnell, J., Lodish, H. and Baltimore, D., Molecular Cell Biology, Scientific 11. American Books, New York, 1995.
21. Driselkelmann, B., Microbiol. Rev. 58, 293 (1994).
22. Han, J. Turner S. W. and Craighead, H. G.,Phys. Rev. Lett. 83, 1688 (1999).
23. Turner, S. W., Calodi, M. and Craighead, H. G.,Phys. Rev. Lett. 88, 128103 (2002).
24. Whittington, S. G.,J. Chem. Phys. 63, 779 (1975).
25. Sudor, J. and Novotny, M.,V., Anal. Chem. 66: 2446(1994).
26. Kim, Y. and Morris, M.D., Anal. Chem. 66: 3081(1994).
27. Kim, Y. and Morris, M.D., Anal. Chem. 67: 784(1995).
28. Mitnik, L., Heller, C., Port, J. and Viovy, J.L., Science 267: 219(1995).
29. Burke, D.T., Burns, M.A., Mastrangelo, C., Genome Res. 7: 189 (1997).
30. Burns, M.A. et al, Science 282: 484 (1998).
31. Volkmuth, W.D. and Austin, R.H., Nature 358,600(1992).
32. Volkmuth, W.D. et al, Phys. Rev. Lett. 72: 2117(1994).
33. Duke, T.A.J., Austin, R.H., Cox, E.C. and Chan, S.S., Electrophoresis 17: 1075 (1996).
34. Turner, S.W., Perez, A.M., Lopez, A. and Craighead, H.G., J. Vac. Sci. Technol. B 16:3835(1998).
35. Chou, H.P., Spence, C. and Scherer, A. and Quake, S., Proc.Natl. Acad. Sci. U.S.A. 96:11(1999).
36. Chou, C.F. et al, Proc. Natl. Acad. Sci. U.S.A. 96:13762 (1999).
37. Han, J. and Craighead, H.G., J. Vac. Sci. Technol. A 17: 2142 (1999).
38. Madabhushi, R.S. et al, Electrophoresis 18: 104(1997).
39. Bakajin, O. B., Duke, T. A. J., Chou, C. F., Chan, S. S., Austin, R. H. and Cox, E.C., Phys. Rev. Lett. 80: 2737 (1998).
40. Doyle, P. S., Bibette, J., Bancaud, A. and Viovy, J.-L., Science 295,2237(2002).
41. Olson, D. J., Johnson, J. M., Patel, P. D., Shaqfeh, E. S. G.,Boxer, S. G. and Fuller, G. G., Langmuir 17: 7396 (2001).
42. Sevick, E. M. and Williams, D. R. M., Phys. Rev. Lett. 76: 2595 (1996).
43. Patel, P. D. and Shaqfeh, E. S. G.,J. Chem. Phys. 118: 2941 (2003).
44. Flomenbom O. and Klafter, J., Phys. Rev. E 68: 041910 (2003).
45. Ambjornsson, T., Apell, S. P. and Konkoli, Z., J. Chem. Phys. 117: 4063(2002).
46. Sebastian, K.L., Paul, A.K.R. Phys. Rev. E 62: 927(2000)
47. Kong, C. Y. and Muthukumar, M., Electrophoresis 23: 2697(2002).
48. Vlovy, J.-L., Rev. Mod. Phys. 72: 813(2000).
49. Russel, W. B., Saville, D. A. and Schowalter, W. R., Colloidal dispersions( Cambridge University Press, New York, 1989).
50. Marko, J. F. and Siggia, E. D., Macromolecules 28: 8759 (1995).
51. Long, D. and Viovy, J. L., Phys. Rev. E 53: 803 (1996).
52. Panwar, A. S. and Kumar, S., J. Chem. Phys. 118: 925 (2003).
53. Ertas, D., Phys. Rev. Lett. 80: 1548(1998).
54. Duke, T. A. J., Austin, R. H., Phys. Rev. Lett. 80: 1552(1998).
55. Derényi, I., Astumian, R. D., Phys. Rev. E 58: 7781(1998).
56. Hammond, R. W., Bader, J. S., Henck, S. A., Deem, M. W., McDermott, G. A., Bustillo, J. M., Rothberg, J. M., Electrophoresis 21: 74(2000).
57. van Oudenaarden, A., Boxer, S. G., Science 285: 1046(1999).
58 . Griess, G. A., Rogers, E., Serwer, P., Electrophoresis 22: 981(2001).
59. Slater, G. W., Guo, H. L. and Nixon, G. I., Phys. Rev. Lett. 78, 1170(1997).
60. Han, J. and Craighead, H. G.,Science 288 , 1026(2000).
61. Kuhn, W., Kolloid-Z 68, 2(1934).
62. Flory, P. J., Principles of Polymer Chemistry, Cornell University Press (1953).
63. Silberberg, A., J. Chem. Phys. 46,1105(1967).
64. Clayfield, E. J. and Lumb, E. C, J. Colloid Interface Sci. 22, 285(1966).
65. McCrackin, F. L., J. Chem. Phys. 47,1980(1967).
66. Lax, M., Macromolecules 7, 660(1974).
67. Mark, P. and Windwer, S., Macromolecules 7, 690(1974).
68. Luo, M. B., J. Chem. Phys 128, 044912 (2008).
69. Kasianowicz, J. J., Brandin, E., Branton, D. and Deamer, D., Proc. Natl. Acad. Sci. USA 93, 13770(1996).
70. Meller, A., Nivon, L. and Branton, D., Phys. Rev. Lett. 86, 3435(2001).
71. Meller, A. and Branton, D., Electrophoresis 23, 2583(2002).
72. Chen, P., Gu, J. J., Brandin, E., Kim, Y. R., Wang, Q. and Brandon, D., Nano Lett. 4, 2293(2004).
73. Henrickson, S. E., Misakian, M., Robertson. 3. and Kasianowicz, J. J., Phys. Rev. Lett. 85, 3057(2000).
74. Nakane, J., Akeson, M. and Marziali, A., Electrophoresis 23,2592(2002).
75. Sung, W. and Park, P. J, Phys. Rev. Lett. 77, 783(1996).
76. Dimarzio, E. A. and Mandell, A. L., J. Chem. Phys. 107, 5510(1997).
77. Muthukumar, M., J. Chem. Phys. 111, 10371(1999).
78. Lubensky, D. K. and Nelson, D. R., BioPhys. J. 77, 1824(1999).
79. Boehm, R. E., Macromolecules 32, 7645( 1999).
80. Tian, P. and Smith, G.D., J. Chem. Phys. 119,11475(2003).
81. Slonkina, E. and Kolomeisky, A. B., J. Chem. Phys. 118, 7112(2003).
82. Chem, S. S., Cardenas, A. E., Coalson, R. D., J. Chem. Phys. 115, 7772(2001).
83. Muthukumar, M., Phys. Rev. Lett. 86, 3188(2001).
84. Milchev, A., Binder, K. and Bhattacharya, A. J., J. Chem. Phys. 121, 6042 (2004).
85. Milchev, A. and Binder, K., Comput Phys. Commun 169,107(2005).
86. Lansac, Y., Maiti, P. K. and Glaser, M. A., Polymer 45,3099(2004).
87. Chen, C-M, Physica A 350, 95(2005).
88. Luo, M. B., Polymer 46, 5730(2005).
89. Gu, F. and Wang, H. J., Chin. Phys. Lett. 22,2549(2005).
90. Ding, K. J., Cai, D. Q., Zhan, F. R., Wu, L. J. and Yu, Z. L., Chin. Phys. 15, 940(2006).
91. Shen, Y. and Zhang, L. X., Polymer 48, 3593(2005).
92. He, Y. D., Qian, H. J., Lu, Z. Y. and Li, Z. S., Polymer 48, 3601(2007).
93. Han, J. and Craighead, H. G.,Anal. Chem. 74, 394(2002).
94. Tessier, F., Labrie, J. and Slater, G.W., Macromolecules 35: 4791 (2002).
95. Chen, Z. and Escobedo F. A., Mol. Simul. 29: 417(2003).
96. Streek, M., Schmid, F., Duong, T. T. and Ros, A., J. Biotechnol. 112: 79(2004).
97. Panwar, A. S. and Kumar, S., Macromolecules 39: 1279(2006).
98. Park, P. J. and Sung, W, J. Chem. Phys. Ill: 5259 (1999).
99. Barbert, M. N., Guttmann, A. J., Middlemiss, K. M., Torrie, G.M. and Whittington, S. G., J. Phys. A, 11, 1833 (1978).
100. Ishinable, T., J. Chem. Phys.77, 3171 (1982).
101. 冯端 等, 《金属物理学--第三卷相变》, 科学出版社, 2000.
102. Mishra, P. K., Kumar, S. and Singh, Y., Physica A 323,453 (2003)
103. Ziebarth, J.D., Wang, Y.M., Polotsky, A. and Luo, M.B., Macromolecules 40: 3498(2007).
104. You, S. and van Rensburg, E. J. J., Phys. Rev. E. 64, 046101 (2001).
105. Descas, R., Sommer, J.U. and Blumen, A. J., Chem. Phys. 120, 8831 (2004).
106. Fisher, M. E. and Barber, M. N., Phys. Rev. Lett. 28: 1516(1972).
107. Suzuki, M. Prog. Theoret. Phys. 58: 1142(1977).
108. Brézin, E., J. Phys. (Paris) 43: 15(1982).
109. Domb, C. and Lebowitz, J. L., Phase Transitions and Critical Phenomena Vol.8, ed. by Academic Press Inc.(London)Ltd.
110. Ferdinand, A. E. and Fisher, M. E., Phys. Rev. 185: 832(1969).
111. Nauenberg, M., J. Phys. A8: 925(1975).
112. Lee, J-R., Phys. Rev. B 49: 3317(1994).
113. Carmesin, I. and Kremer, K., Macromolecules 21: 2819(1988).
114. Metzger, S., Müller, M., Binder, K. and Baschnagel, J., J. Chem. Phys. 118: 8489 (2003 ) .
115. Luo, M.B. and Huang, J.H., Euro. Polym. J. 39: 135 (2003 ) .
116. Singer, S.J. Annu. Rev. Cell Biol. 6: 247(1990).
117. Schatz, G.and Dobberstein, B. Science 271: 1519(1996).
118. Chang, D.C., Guide to Electroporation and Electrofusion (Academic, New York 1992).
119. Zimm, B.H. and Leven, S.D., Q. Rev. Biophys 25: 171(1992).
120. Kasianowicz, J.J., Henrickson, S.E., Weetall, H.H., Robertson, B., Anal Chem 73: 2268(2001).
121. Luo, M.B., Polymer 48: 7679(2007).
122. Doi, M. and Edwards, S.F., The Theory of Polymer Dynamics(Clarendon Press, Oxford, 1986).
123. Yoon, H and Deutsch, JM, J. Chem. Phys. 102: (9090)1995.
124. Dubbeldam, J.L.A., Milchev, A, Rostiashvilil, V.G. and Vilgis, T.A. Euro. Phys. Lett. 79:18002(2007).
125. Huopaniemi, I., Luo, K., Ala-Nissila, T. and Ying, T., J. Chem. Phys. 125: 124901 (2006).
126. Wei, D.S., Yang, W., Jin, X.G. and Liao, Q, J. Chem. Phys. 126: 204901 (2007).
127. Muthukumar, M., J. Chem. Phys. 118:15(2003).
128. Picu, R.C. and Rakshit, A., J. Chem. Phys. 127: 144909 (2007).
129. Meller, A, J. Phys.: Condens. Matter 15: R581(2003).
130. Dohoney, K.M., and Gelles, J, Nature 409:370( 2001).
131. Dubbeldam, J.L.A, Milchev, A., Rostiashvili, V.G. and Vilgis, T.A., Phys. Rev E 76: 010801(2007).
132. Loebl, H.C., Randel, R., Goodwin, S.P. and Matthai, C.C., Phys. Rev.67: 041913(2003).
133. Lam, PM, Liu F and Ou-Yang ZC, Phys. Rev. 74: 011911(2006).
134. Luo, K.F., Ala-Nissila, T., Ying, S.C. and Bhattacharya, A., Phys. Rev. Lett. 99:148102(2007).
135. Chen, Y.C., Wang, C., Zhou, Y.L., Luo, M.B., J. Chem. Phys. 130: 54902(2009).
136. Kramers. H. A., Physica 7: 284(1940)
137. Kim, S. H., Panwar, A. S., Kumer, S., Ahn, K. H. and Lee, S. J., J. Chem. Phys. 121:9116(2004).