RSS feeds
РусскийEnglish
Issue 12, 2024
Volume year page
Issues Authors PACS Subscription For authors

Issues

 / 

1997

 / 

February

←  →

Reviews of topical problems


Disordered polymers


Institute for Biochemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119334, Russian Federation

A single polymer macromolecule is considered with disorder types such as branches, knots, and heterogeneous sequences of chemical units. In all cases, simple theoretical approaches are employed to gain useful physical insights. For branched polymers, a simple Flory-type theory is described by means of which the difference between the universality classes for molecules with quenched and annealed branches is demonstrated. For knots, another Flory-type theory is suggested to describe the swelling and/or collapse of a quenched topology ring or the size distribution for the annealed case. To consider heteropolymers, the Random Energy Model borrowed from the spin glass theory is systematically employed. This allows a simple yet rigorous description of both the freezing transition of a random sequence globule and the use of the canonical ensemble for designing sequences with energy-optimized ground state conformation. Along with the analytical theory, computer tests for the freezing and design processes are discussed. The sequence design scheme is shown to yield a specific prediction concerning the character of correlations in protein sequences. Statistical tests confirming this prediction are described.

Fulltext pdf (678 KB)
Fulltext is also available at DOI: 10.1070/PU1997v040n02ABEH000192
PACS: 36.20.−r, 64.70.−p, 87.10.+e, 87.10.-v (all)
DOI: 10.1070/PU1997v040n02ABEH000192
URL: https://ufn.ru/en/articles/1997/2/b/
A1997WT28000002
Citation: Grosberg A Yu "Disordered polymers" Phys. Usp. 40 125–158 (1997)
BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Гросберг А Ю «Неупорядоченные полимеры» УФН 167 129–166 (1997); DOI: 10.3367/UFNr.0167.199702b.0129

References (157) ↓ Cited by (36) Similar articles (20)

  1. Lifshits I M Zh. Eksp. Teor. Fiz. 55 2408 (1968) [Sov. Phys. JETP28 1280 (1968)]
  2. Doi M, Edwards S F The Theory of Polymer Dynamics (Oxford: Oxford University Press, 1987)
  3. De Gennes P G Scaling Concepts in Polymer Physics (Ithaca, NY: Cornell University Press, 1979) [Translated into Russian (Moscow: Mir, 1982)]
  4. Lifshits I M, Gredeskul S A, Pastur L A Vvedenie v Teoriyu Neuporyadochennykh Sistem (Introduction to the Theory of Disordered Systems, Moscow: Nauka, 1982) [Translated into English (New York: Wiley & Sons, 1988)]
  5. Anfinsen C Science181 223 (1973)
  6. Derrida B Phys. Rev. Lett.45 79 (1980)
  7. Bryngelson J D, Wolynes P G Proc. Nat. Acad. Sci. USA 84 7524 (1987)
  8. Wolynes P G, in Spin Glass Ideas in Biology (Ed. D Stein, Singapore: World Scientific, 1991) p. 1
  9. Shakhnovich E, Gutin A Biophys. Chem. 34 (3) 187 (1989)
  10. Pande V S, Grosberg A Yu, Tanaka T Biophys. J. (in press)
  11. Ptitsyn O B, Volkenstein M V J. Biomolec. Struct. and Dynamics4 137 (1986)
  12. Shakhnovich E, Gutin A Proc. Nat. Acad. Sci. USA90 7195 (1993)
  13. Pande V S, Grosberg A Yu, Tanaka T Proc. Nat. Acad. Sci. USA91 12976 (1994)
  14. Pande V S, Grosberg A Yu, Tanaka T Proc. Nat. Acad. Sci. USA91 12972 (1994)
  15. Panyukov S, Rabin Y Phys. Rep. 269 1 (1996)
  16. Bates F, Fredrickson G H Ann. Rev. Phys. Chem. 41 525 (1990)
  17. Erukhimovich I, Khokhlov A Polymer Sci. 35 1522 (1993)
  18. Binder K Adv. Polymer Sci. 112181 (1994)
  19. Grosberg A Yu, Kaganova E M, Molchanov S A Biofizika29 30 (1984) [Biophysics 29 27 (1984)]
  20. Grosberg A Yu J. Stat. Phys. 38149 (1985)
  21. Grosberg A Yu, Kaganova E M Dokl. Acad. Nauk294 838 (1987); [Sov. Phys. Dokl. 36 474 (1987)]
  22. Grosberg A Yu, Shakhnovich E I Zh. Exp. Theor. Fiz. 91 837 (1986) [Sov. Phys. JETP64 493 (1986)]
  23. Grosberg A Yu, Shakhnovich E I Zh. Eksp. Teor. Fiz. 91 2159 (1986) [Sov. Phys. JETP64 1284 (1986)]
  24. Grosberg A Yu, Shakhnovich E I Biofizika31 1045 (1986) [Biophysics 31 1139 (1986)]
  25. Joanny J-F J. de Phys II 41281 (1994)
  26. Garel T et al. Europhys Lett.89 (1989)
  27. Grosberg A Yu, Izrailev S F, Nechaev S K Phys. Rev. E 501912 (1994)
  28. Sommer J-U, Daoud M Europhys. Lett.32407 (1995)
  29. De Gennes P G "Chrysanthemums": Weak Micellisation Preprint (1995)
  30. Vedenov A A, Dykhne A M, Frank-Kamenetskiî M D Usp. Fiz. Nauk105 479 (1971) [Sov. Phys. Usp.14 715 (1972)]
  31. Azbel M Ya Biopolymers1961, 81, 95, 1311 (1980); Azbel M et al. Biopolymers211687 (1982)
  32. Grosberg A Yu, Khokhlov A R Statisticheskaya Fizika Makromolekul (Statistical Physics of Macromolecules, Moscow: Nauka, 1989) [Translated into English (New York: AIP Press, 1994)]
  33. Trifonov E N, Tan R K Z, Harvey S C, in Structure and Expression (Eds M H Sarma, R H Sarma, Schenectady, NY: Adenin Press, 1988) p. 243
  34. Bednar J et al. J. Mol. Biol. 254579 (1995)
  35. Higgs P G, Joanny J-F J. Chem. Phys. 941543 (1991)
  36. Kantor Y, Li, Kardar M Phys. Rev. Lett.6961 (1992); Kantor Y, Kardar M Europhys. Lett. 27643 (1994); Kantor Y, Kardar M, Li H Phys. Rev. E491383 (1994); Kantor Y, Kardar M Phys. Rev. E 511299 (1995); Kantor Y, Kardar M Phys. Rev. E 52835 (1995); Ertas D, Kantor Y Phys. Rev. E (1996, in press)
  37. Wittmer J, Johner A, Joanny J F Europhys. Lett.24263 (1993)
  38. Dobrynin A V, Rubinstein M J. de Phys. II5677 (1995)
  39. Gutin A M, Shakhnovich E I Phys. Rev. E 50 R3322 (1994)
  40. Grosberg A Yu Biofizika29 569 (1984) [Biophysics 29 (1984)]
  41. Garel T, Leibler L, Orland H J. de Phys. II42139 (1994)
  42. Marko J F, Siggia E D Macromolecules 27981 (1994); Science265506 (1994); Phys. Rev. E522912 (1995)
  43. Frank-Kamenetskiî M D Samaya Glavnaya Molekula (Unraveling, Moscow: Nauka, 1989) [Translated into English (New York: DNA, VCH, 1993)]
  44. Zimm B H, Stockmayer W H J. Chem. Phys.171301 (1949)
  45. Gutin A M, Grosberg AYu, Shakhnovich E I Macromolecules261293 (1993)
  46. Isaacson J, Lubensky T C J. de Phys. Lett.41 L469 (1980)
  47. Daoud M et al. Macromolecules 16 1833 (1983)
  48. Parisi G, Sourlas N Phys. Rev. Lett. 46 871 (1981)
  49. Daoud M, Joanny J-F J. de Phys. 42 1359 (1981)
  50. Gaunt D, Flesia S J. Phys. A 24 3655 (1991); Janse van Rensburg E, Madras N J. Phys. A 25 303 (1992)
  51. Shi-Min Cui, Zheng Yu Chen Phys. Rev. E525084 (1995)
  52. Shi-Min Cui, Zheng Yu Chen Phys. Rev. E536238 (1996)
  53. Grosberg A Yu, Gutin A M, Shakhnovich E I Macromolecules283718 (1995)
  54. Kelvin, Lord Trans. Roy. Soc. of Edinburg25217 (1868)
  55. Wu F Y Rev. Mod. Phys.64 1099 (1992); 65577 (1993)
  56. Kauffman L H Knots and Physics (Singapore: World Scientific, 1991)
  57. Atiyah M The Geometry and Physics of Knots (Cambridge: University Press, 1990) [Translated into Russian (Moscow: Mir, 1995)]
  58. Moffatt H K Nature (London) 347 367 (1990)
  59. Frisch H L, Wasserman E J. Am. Chem. Soc. 83 3789 (1961)
  60. Delbrück M Mathematical Problems in the Biological Sciences, Proc. of Symposium in Applied Mathematics(American Mathematical Society, Providence RI) 1455 (1962)
  61. Liang C, Mislow K J. Am. Chem. Soc.11611189 (1994); 1163588 (1994); J. Math. Chem.15245 (1994)
  62. Sumners D W, Whittington S G J. Phys. A 211689 (1988)
  63. Pippenger N Discrete Appl. Math.25273 (1989)
  64. Nechaev S K J. Phys. A 213659 (1988)
  65. Nechaev S Statistics of Knots and Entangled Random Walks(Singapore: World Scientific, 1996)
  66. Nechaev S K, Grosberg A Yu, Vershik A M J. Phys. A 292411 (1996)
  67. Edwards S F Proc. Phys. Soc.91513 (1967)
  68. Prager S, Frisch H L J. Chem. Phys. 461475 (1967)
  69. Khokhlov A R, Nechaev S K Phys. Lett. A112156 (1985)
  70. Vologodskiî A V, Lukashin A V, Frank-Kamenetskiî M D Zh. Eksp. Teor. Fiz.67 1875 (1974) [Sov. Phys. JETP40 932 (1975)]
  71. Koniaris K, Muthukumar M Phys. Rev. Lett.662211 (1991)
  72. Deguchi T, Tsurusaki K J. of Knot Theory and its Ramifications 3 321 (1994)
  73. Grosberg A Yu, Feigel A, Rabin Y Phys. Rev. E(in press)
  74. Grosberg A Yu, Nechaev S K Adv. Polymer Sci. 106 1 (1993)
  75. Drossel B, Kardar M Phys. Rev. E 53 5861 (1996)
  76. Frank-Kamenetskiî M D, Vologodskiî A V Phys. Usp.134 641 (1981) [Sov. Phys. Usp.24 679 (1981)]; Vologodskiî A V Topology and Physics of Circular DNA (Boca Raton: CRC Press, 1992)
  77. Tait P G Scientific Papers1273 (1898)
  78. Rolfsen D Knots and Links(Berkeley: Publish or Perish Press, 1976)
  79. Atiyah M Rev. Mod. Phys.67977 (1995)
  80. Crowell R H, Fox R H Introduction to Knot Theory (Ginna, Boston, 1963) [Translated into Russian (Moscow: Mir, 1965)]
  81. Jones V F R Bull. Am. Math. Soc.12103 (1985)
  82. Katritch V et al. Nature (1996, in press)
  83. Klenin K V et al. J. Biomolec. Struct. and Dynamics 5 1173 (1988)
  84. Liu L F, Depew R E, Wang J C J. Molec. Biology 106 439 (1976)
  85. Rybenkov V V, Cozzarelli N R, Vologodskii A V Proc. Nat. Acad. Sci. USA 90 5307 (1993)
  86. Shaw S Y, Wang J C Science260533 (1993)
  87. Tesi M C et al. J. Phys. A 27 347 (1994)
  88. Grosberg A Yu, Nechaev S K J. Phys. A 25 4659 (1992); Europhys. Lett.20613 (1992)
  89. Grosberg A Yu, Nechaev S K, Shakhnovich E I J. de Phys. 49 2095 (1988)
  90. Jianpeng Ma, Straub J E, Shakhnovich E I J. Chem. Phys. 103 2615 (1995)
  91. Timoshenko E et al. J. Chenm. Phys.(in press)
  92. Chu B, Ying Q, Grosberg A Yu Macromolecules 28 180 (1995)
  93. Chu B, Ying Q Macromolecules 29 1824 (1996)
  94. Grosberg A Yu, Kuznetsov D V Macromolecules 26 4249 (1993)
  95. Ganazzoli F, Ferla R La, Allegra G Macromolecules 28 5285 (1995)
  96. Grosberg A Yu et al. Europhys. Lett. 23 373 (1993)
  97. Sikorav J -L, Jannink G C.R. Acad. Sci. Paris 316 751 (1993)
  98. Sikorav J -L, Church G M J. Mol. Biol. 222 1085 (1991)
  99. Janse van Rensburg E J, Whittington S G J. Phys. A 24 3935 (1991)
  100. Cates M E, Deutsch J M J. de Phys. 47 2121 (1986)
  101. Semenov A N J. de Phys. 49 175 (1988)
  102. De Gennes P G Macromolecules 17 703 (1984); reprinted in Simple Views on Condensed Matter(Singapore: World Scientific, 1992) p. 215
  103. Rabin Y, Grosberg A Yu, Tanaka T Europhys. Lett. 32 505 (1995)
  104. Frauenfelder H, Wolynes P G Physics Today 47 (2) 58 (1994)
  105. Goldanskii V I Tunneling Phenomena in Chemical Physics (New York: Gordon and Breach Sci. Publ., 1989)
  106. Finkelstein A V, Gutin A M, Badretdinov A Ya FEBS Lett. 325 23 (1993)
  107. Finkelstein A V, Badretdinov A Ya, Gutin A M Proteins 23 142 (1995)
  108. Finkelstein A V, Gutin A M, Badretdinov A Ya Proteins 23 151 (1995)
  109. Miyazawa S, Jernigan R Macromolecules 18 534 (1985)
  110. Godzik A, Kolinski A, Skolnick J Protein Sci. (BNW) 10 2107 (1995)
  111. Goldenfeld N Lectures on phase transitions and the renormalization group(Reading, Mass.: Addison-Wesley Press, 1992)
  112. Lau K F, Dill K A Macromolecules223986 (1989)
  113. Obukhov S P Phys. Rev. A422015 (1990)
  114. Garel T, Leibler L, Orland H J. de Phys. II 4 2139 (1994)
  115. Li H et al. Science 273 666 (1996)
  116. 27.8° is indeed the correct value of electro-weak mixing angle. The author hopes that the reader did not lose his sense of humor...
  117. Mezard M, Parisi G, Virasoro M Spin Glass Theory and Beyond(Singapore: World Scientific, 1987)
  118. Koukiou F J. Phys. A26L1207 (1993)
  119. Pande V S, Grosberg A Yu, Tanaka T Phys. Rev. Lett.763987 (1996)
  120. Hecht M H et al. Science249884 (1990)
  121. Editorial commentary Science2691821 (1995)
  122. Pande V S, Grosberg A Yu, Tanaka T J. Chem. Phys.(in press)
  123. Pande V S, Grosberg A Yu, Tanaka T Phys. Rev. E513381 (1995)
  124. Sfatos C D, Gutin A M, Shakhnovich E I Phys. Rev. E48465 (1993)
  125. Shakhnovich E, Gutin A J. Chem. Phys.935967 (1990)
  126. Pande V S et al. J. Phys. A 276231 (1994)
  127. Flory P Principles of Polymer Chemistry(Ithaca: Cornell University Press, 1953)
  128. Garel T, Orland H, Thirumalai D Preprint (1995)
  129. Gutin A M, Shakhnovich E I J. Chem. Phys988174 (1993)
  130. Bryngelson J D J. Chem. Phys.1006038 (1994)
  131. Yue K, Dill K A Proc. Nat. Acad. Sci. USA 894163 (1992)
  132. Abkevich V, Gutin A, Shakhnovich E J. Mol. Biol.252460 (1995)
  133. Ramanathan S, Shakhnovich E I Phys. Rev. E501303 (1994)
  134. Pande V S, Grosberg A Yu, Tanaka T Macromolecules282218 (1995)
  135. Shakhnovich E I Phys. Rev. Lett. 723907 (1994)
  136. Derrida B J. de Phys. Lett.46L401 (1985)
  137. Plotkin S S, Wang J, Wolynes P G Phys. Rev. E536271 (1996)
  138. Pande V S, Grosberg A Yu, Tanaka T J. Chem. Phys.1018246 (1994)
  139. Pande V S, Grosberg A Yu, Tanaka T J. Chem. Phys.1039482 (1995)
  140. Grosberg A Yu, Khokhlov A R Fizika v Mire Polimerov (Physics in the World of Polymers, Moscow: Nauka, 1989)
  141. Monod J Chance and Necessity: an Essay on the Natural Philosophy of Modern Biology(New York: Vintage Books, 1971)
  142. Tupygin A Yu, Chechetkin V R Zh. Eksp. Teor. Fiz. 106 335 (1994) [JETP79186 (1994)]
  143. Chechetkin V R, Turygin A Yu Phys. Lett. A19975 (1995); J. Theor. Biol. 175 477 (1995); 178205 (1996)
  144. Lifshitz I M Zh. Eksp. Teor. Fiz. 65 1100 (1973) [Sov. Phys. JETP 38 546 (1974)]
  145. Peng C -K et al. Nature 356 168 (1992)
  146. Bairoch A, Boeckmann B Nucleic Acids Res. 20 2019 (1992)
  147. Pande V S Ph. D. Thesis (MIT, 1995)
  148. Strait B J, Dewey G Phys. Rev. E 52 6588 (1995)
  149. Eigen M, Schuster P The Hypercycle, a Principle of Natural Self-Organization(Berlin, New York: Springer Verlag, 1979); Eigen M, Winkler R Laws of the Game: How the Principles of Nature Govern Chance(New York: Harper & Row, 1983); Eigen M, Winkler-Oswatitsch R Steps Towards Life: a Perspective on Evolution(Oxford New York: Oxford University Press, 1992)
  150. Dyson F Origins of Life(Combridge: Cambridge University Press, 1985)
  151. Grosberg A Yu, Khokhlov A R On the Unsolved Problems in Statistical Physics of Macromolecules (Pouschino: NCBI, 1985)
  152. Gutin A, Abkevich V, Shakhnovich E Proc. Nat. Acad. Sci. USA921282 (1995); Abkevich V, Gutin A, Shakhnovich E Proc. Nat. Acad. Sci. USA 93 830 (1996)
  153. Shakhnovich E, Abkevich V, Ptitsyn O Nature(London) 37996 (1996)
  154. Onuchic J N et al. Proc. Nat. Acad. Sci. USA923626 (1995)
  155. Shakhnovich E Phys. Rev. E(in press)
  156. Romanovskiî Yu M, Stepanova N V, Chernavskiî D S Matematichesraya Biofizika (Mathematical Biophysics, Moscow: Nauka, 1984)
  157. Blumenfeld L A, Tikhonov A N Biophysical Thermodynamics of Intracellular Processes(Berlin: Springer-Verlag, 1994)
© 1918–2024 Uspekhi Fizicheskikh Nauk
Email: ufn@ufn.ru Editorial office contacts About the journal Terms and conditions