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Generalized-Ensemble Algorithms for Studying Protein Folding

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Book cover Water and Biomolecules

Part of the book series: Biological and Medical Physics, Biomedical ((BIOMEDICAL))

Abstract

Conventional simulations of biomolecular systems will get trapped in states of local-minimum energy. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other parameter space. From only one simulation run, one can obtain accurate canonical-ensemble averages of physical quantities as functions of temperature and other parameters of the sytem by the single-histogram and/or multiple-histogram reweighting techniques. In this article, we review the generalized-ensemble algorithms. Two well-known methods, namely, multicanonical algorithm and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present further extensions of the above two methods.

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References

  1. U.H.E. Hansmann, Y. Okamoto, in Annual Reviews of Computational Physics VI, ed. by D. Stauffer (World Scientific, Singapore, 1999), pp. 129–157

    Google Scholar 

  2. A. Mitsutake, Y. Sugita, Y. Okamoto, Biopolymers (Peptide Science) 60, 96–123 (2001)

    Article  CAS  Google Scholar 

  3. Y. Sugita, Y. Okamoto, in Lecture Notes in Computational Science and Engineering, ed. by T. Schlick, H.H. Gan (Springer-Verlag, Berlin, 2002), pp. 304–332; e-print: cond-mat/0102296

    Google Scholar 

  4. Y. Okamoto, J. Mol. Graphics Mod. 22, 425–439 (2004); e-print: cond-mat/ 0308360

    Article  CAS  Google Scholar 

  5. H. Kokubo, Y. Okamoto, Mol. Sim. 32, 791–801 (2006)

    Article  CAS  Google Scholar 

  6. S.G. Itoh, H. Okumura, Y. Okamoto, Mol. Sim. 33, 47–56 (2007)

    Article  CAS  Google Scholar 

  7. Y. Sugita, A. Mitsutake, Y. Okamoto, in Lecture Notes in Physics, ed. by W. Janke (Springer-Verlag, Berlin, 2008), pp. 369–407; e-print: arXiv:0707.3382v1 [cond-mat.stat-mech]

    Google Scholar 

  8. A.M. Ferrenberg, R.H. Swendsen, Phys. Rev. Lett. 61, 2635–2638 (1988); 63, 1658 (1989)

    Article  PubMed  CAS  Google Scholar 

  9. A.M. Ferrenberg, R.H. Swendsen, Phys. Rev. Lett. 63, 1195–1198 (1989)

    Article  PubMed  CAS  Google Scholar 

  10. S. Kumar, D. Bouzida, R.H. Swendsen, P.A. Kollman, J.M. Rosenberg, J. Comput. Chem. 13, 1011–1021 (1992)

    Article  CAS  Google Scholar 

  11. B.A. Berg, T. Neuhaus, Phys. Lett. B 267, 249–253 (1991)

    Article  Google Scholar 

  12. B.A. Berg, T. Neuhaus, Phys. Rev. Lett. 68, 9–12 (1992)

    Article  PubMed  Google Scholar 

  13. B.A. Berg, Fields Institute Communications 26, 1–24 (2000); also see e-print: cond-mat/9909236

    Google Scholar 

  14. W. Janke, Physica A 254, 164–178 (1998)

    Article  CAS  Google Scholar 

  15. J. Lee, Phys. Rev. Lett. 71, 211–214 (1993); 71, 2353 (1993)

    Article  PubMed  CAS  Google Scholar 

  16. M. Mezei, J. Comput. Phys. 68, 237–248 (1987)

    Article  Google Scholar 

  17. C. Bartels, M. Karplus, J. Phys. Chem. B 102, 865–880 (1998)

    Article  CAS  Google Scholar 

  18. G.M. Torrie, J.P. Valleau, J. Comput. Phys. 23, 187–199 (1977)

    Article  Google Scholar 

  19. J.S. Wang, R.H. Swendsen, J. Stat. Phys. 106, 245–285 (2002)

    Article  Google Scholar 

  20. F. Wang, D.P. Landau, Phys. Rev. Lett. 86, 2050–2053 (2001)

    Article  PubMed  CAS  Google Scholar 

  21. F. Wang, D.P. Landau, Phys. Rev. E 64, 056101 (2001)

    Article  CAS  Google Scholar 

  22. Q. Yan, R. Faller, J.J. de Pablo, J. Chem. Phys. 116, 8745–8749 (2002)

    Article  CAS  Google Scholar 

  23. S. Trebst, D.A. Huse, M. Troyer, Phys. Rev. E 70 046701 (2004)

    Article  CAS  Google Scholar 

  24. B.A. Berg, T. Celik, Phys. Rev. Lett. 69, 2292–2295 (1992)

    Article  PubMed  Google Scholar 

  25. B.A. Berg, U.H.E. Hansmann, T. Neuhaus, Phys. Rev. B 47, 497–500 (1993)

    Article  Google Scholar 

  26. W. Janke, S. Kappler, Phys. Rev. Lett. 74, 212–215 (1995)

    Article  PubMed  CAS  Google Scholar 

  27. B.A. Berg, W. Janke, Phys. Rev. Lett. 80, 4771–4774 (1998)

    Article  CAS  Google Scholar 

  28. N. Hatano, J.E. Gubernatis, Prog. Theor. Phys. (Suppl.) 138, 442–447 (2000)

    Article  CAS  Google Scholar 

  29. B.A. Berg, A. Billoire, W. Janke, Phys. Rev. B 61, 12143–12150 (2000)

    Article  CAS  Google Scholar 

  30. U.H.E. Hansmann, Y. Okamoto, J. Comput. Chem. 14, 1333–1338 (1993)

    Article  CAS  Google Scholar 

  31. U.H.E. Hansmann, Y. Okamoto, Physica A 212, 415–437 (1994)

    Article  CAS  Google Scholar 

  32. M.H. Hao, H.A. Scheraga, J. Phys. Chem. 98, 4940–4948 (1994)

    Article  CAS  Google Scholar 

  33. Y. Okamoto, U.H.E. Hansmann, J. Phys. Chem. 99, 11276–11287 (1995)

    Article  CAS  Google Scholar 

  34. N.B. Wilding, Phys. Rev. E 52, 602–611 (1995)

    Article  CAS  Google Scholar 

  35. A. Kolinski, W. Galazka, J. Skolnick, Proteins 26, 271–287 (1996)

    Article  PubMed  CAS  Google Scholar 

  36. N. Urakami, M. Takasu, J. Phys. Soc. Jpn. 65, 2694–2699 (1996)

    Article  CAS  Google Scholar 

  37. S. Kumar, P. Payne, M. Vásquez, J. Comput. Chem. 17, 1269–1275 (1996)

    Article  CAS  Google Scholar 

  38. U.H.E. Hansmann, Y. Okamoto, F. Eisenmenger, Chem. Phys. Lett. 259, 321–330 (1996)

    Article  CAS  Google Scholar 

  39. U.H.E. Hansmann, Y. Okamoto, Phys. Rev. E 54, 5863–5865 (1996)

    Article  CAS  Google Scholar 

  40. U.H.E. Hansmann, Y. Okamoto, J. Comput. Chem. 18, 920–933 (1997)

    Article  CAS  Google Scholar 

  41. H. Noguchi, K. Yoshikawa, Chem. Phys. Lett. 278, 184–188 (1997)

    Article  CAS  Google Scholar 

  42. N. Nakajima, H. Nakamura, A. Kidera, J. Phys. Chem. B 101, 817–824 (1997)

    Article  CAS  Google Scholar 

  43. C. Bartels, M. Karplus, J. Comput. Chem. 18, 1450–1462 (1997)

    Article  CAS  Google Scholar 

  44. J. Higo, N. Nakajima, H. Shirai, A. Kidera, H. Nakamura, J. Comput. Chem. 18, 2086–2092 (1997)

    Article  CAS  Google Scholar 

  45. Y. Iba, G. Chikenji, M. Kikuchi, J. Phys. Soc. Jpn. 67, 3327–3330 (1998)

    Article  Google Scholar 

  46. A. Mitsutake, U.H.E. Hansmann, Y. Okamoto, J. Mol. Graphics Mod. 16, 226–238; 262–263 (1998)

    Google Scholar 

  47. U.H.E. Hansmann, Y. Okamoto, J. Phys. Chem. B 103, 1595–1604 (1999)

    Article  CAS  Google Scholar 

  48. H. Shimizu, K. Uehara, K. Yamamoto, Y. Hiwatari, Mol. Sim. 22, 285–301 (1999)

    Article  CAS  Google Scholar 

  49. S. Ono, N. Nakajima, J. Higo, H. Nakamura, Chem. Phys. Lett. 312, 247–254 (1999)

    Article  CAS  Google Scholar 

  50. A. Mitsutake, Y. Okamoto, J. Chem. Phys. 112, 10638–10647 (2000)

    Article  CAS  Google Scholar 

  51. K. Sayano, H. Kono, M.M. Gromiha, and A. Sarai, J. Comput. Chem. 21, 954–962 (2000)

    Article  CAS  Google Scholar 

  52. F. Yasar, T. Celik, B.A. Berg, H. Meirovitch, J. Comput. Chem. 21, 1251–1261 (2000)

    Article  CAS  Google Scholar 

  53. A. Mitsutake, M. Kinoshita, Y. Okamoto, F. Hirata, Chem. Phys. Lett. 329, 295–303 (2000)

    Article  CAS  Google Scholar 

  54. M.S. Cheung, A.E. Garcia, J.N. Onuchic, Proc. Natl. Acad. Sci. U.S.A. 99, 685–690 (2002)

    Article  PubMed  CAS  Google Scholar 

  55. N. Kamiya, J. Higo, H. Nakamura, Protein Sci. 11, 2297–2307 (2002)

    Article  PubMed  CAS  Google Scholar 

  56. S.W. Jang, Y. Pak, S.M. Shin, J. Chem. Phys. 116, 4782–4786 (2002)

    Article  CAS  Google Scholar 

  57. J.G. Kim, Y. Fukunishi, H. Nakamura, Phys. Rev. E 67, 011105 (2003)

    Article  CAS  Google Scholar 

  58. N. Rathore, T.A. Knotts IV, J.J. de Pablo, J. Chem. Phys. 118, 4285–4290 (2003)

    Article  CAS  Google Scholar 

  59. T. Terada, Y. Matsuo, A. Kidera, J. Chem. Phys. 118, 4306–4311 (2003)

    Article  CAS  Google Scholar 

  60. B.A. Berg, H. Noguchi, Y. Okamoto, Phys. Rev. E 68, 036126 (2003)

    Article  CAS  Google Scholar 

  61. M. Bachmann, W. Janke, Phys. Rev. Lett. 91, 208105 (2003)

    Article  PubMed  CAS  Google Scholar 

  62. H. Okumura, Y. Okamoto, Chem. Phys. Lett. 383, 391–396 (2004)

    Article  CAS  Google Scholar 

  63. H. Okumura, Y. Okamoto, Chem. Phys. Lett. 391, 248–253 (2004)

    Article  CAS  Google Scholar 

  64. S.G. Itoh, Y. Okamoto, Chem. Phys. Lett. 400, 308–313 (2004)

    Article  CAS  Google Scholar 

  65. S.G. Itoh, Y. Okamoto, Phys. Rev. E 76, 026705 (2007)

    Article  CAS  Google Scholar 

  66. T. Munakata, S. Oyama, Phys. Rev. E 54, 4394–4398 (1996)

    Article  CAS  Google Scholar 

  67. K. Hukushima, K. Nemoto, J. Phys. Soc. Jpn. 65, 1604–1608 (1996)

    Article  CAS  Google Scholar 

  68. K. Hukushima, H. Takayama, K. Nemoto, Int. J. Mod. Phys. C 7, 337–344 (1996)

    Article  Google Scholar 

  69. C.J. Geyer, in Computing Science and Statistics: Proc. 23rd Symp. on the Interface, ed. by E.M. Keramidas (Interface Foundation, Fairfax Station, 1991), pp. 156–163

    Google Scholar 

  70. R.H. Swendsen, J.-S. Wang, Phys. Rev. Lett. 57, 2607–2609 (1986)

    Article  PubMed  Google Scholar 

  71. K. Kimura, K. Taki, in Proc. 13th IMACS World Cong. on Computation and Appl. Math. (IMACS '91), ed. by R. Vichnevetsky, J.J.H. Miller, vol. 2, pp. 827–828

    Google Scholar 

  72. D.D. Frantz, D.L. Freeman, J.D. Doll, J. Chem. Phys. 93, 2769–2784 (1990)

    Article  CAS  Google Scholar 

  73. M.C. Tesi, E.J.J. van Rensburg, E. Orlandini, S.G. Whittington, J. Stat. Phys. 82, 155–181 (1996)

    Article  Google Scholar 

  74. E. Marinari, G. Parisi, J.J. Ruiz-Lorenzo, in Spin Glasses and Random Fields, ed. by A.P. Young (World Scientific, Singapore, 1998), pp. 59–98

    Google Scholar 

  75. Y. Iba, Int. J. Mod. Phys. C 12, 623–656 (2001)

    Article  Google Scholar 

  76. U.H.E. Hansmann, Chem. Phys. Lett. 281, 140–150 (1997)

    Article  CAS  Google Scholar 

  77. Y. Sugita, Y. Okamoto, Chem. Phys. Lett. 314, 141–151 (1999)

    Article  CAS  Google Scholar 

  78. A. Irbäck, E. Sandelin, J. Chem. Phys. 110, 12256–12262 (1999)

    Article  Google Scholar 

  79. M.G. Wu, M.W. Deem, Mol. Phys. 97, 559–580 (1999)

    Article  CAS  Google Scholar 

  80. Y. Sugita, A. Kitao, Y. Okamoto, J. Chem. Phys. 113, 6042–6051 (2000)

    Article  CAS  Google Scholar 

  81. C.J. Woods, J.W. Essex, M.A. King, J. Phys. Chem. B 107, 13703–13710 (2003)

    Article  CAS  Google Scholar 

  82. Y. Sugita, Y. Okamoto, Chem. Phys. Lett. 329, 261–270 (2000)

    Article  CAS  Google Scholar 

  83. A. Mitsutake, Y. Okamoto, Chem. Phys. Lett. 332, 131–138 (2000)

    Article  CAS  Google Scholar 

  84. D. Gront, A. Kolinski, J. Skolnick, J. Chem. Phys. 113, 5065–5071 (2000)

    Article  CAS  Google Scholar 

  85. G.M. Verkhivker, P.A. Rejto, D. Bouzida, S. Arthurs, A.B. Colson, S.T. Freer, D.K. Gehlhaar, V. Larson, B.A. Luty, T. Marrone, P.W. Rose, Chem. Phys. Lett. 337, 181–189 (2001)

    Article  CAS  Google Scholar 

  86. H. Fukunishi, O. Watanabe, S. Takada, J. Chem. Phys. 116, 9058–9067 (2002)

    Article  CAS  Google Scholar 

  87. A. Mitsutake, Y. Sugita, Y. Okamoto, J. Chem. Phys. 118, 6664–6675 (2003)

    Article  CAS  Google Scholar 

  88. A. Mitsutake, Y. Sugita, Y. Okamoto, J. Chem. Phys. 118, 6676–6688 (2003)

    Article  CAS  Google Scholar 

  89. A. Sikorski, P. Romiszowski, Biopolymers 69, 391–398 (2003)

    Article  PubMed  CAS  Google Scholar 

  90. C.Y. Lin, C.K. Hu, U.H.E. Hansmann, Proteins 52, 436–445 (2003)

    Article  PubMed  CAS  Google Scholar 

  91. G. La Penna, A. Mitsutake, M. Masuya, Y. Okamoto, Chem. Phys. Lett. 380, 609–619 (2003)

    Article  CAS  Google Scholar 

  92. M. Falcioni, M.W. Deem, J. Chem. Phys. 110, 1754–1766 (1999)

    Article  CAS  Google Scholar 

  93. Q. Yan, J.J. de Pablo, J. Chem. Phys. 111, 9509–9516 (1999)

    Article  CAS  Google Scholar 

  94. T. Nishikawa, H. Ohtsuka, Y. Sugita, M. Mikami, Y. Okamoto, Prog. Theor. Phys. (Suppl.) 138, 270–271 (2000)

    Article  CAS  Google Scholar 

  95. D.A. Kofke, J. Chem. Phys. 117, 6911–6914 (2002)

    Article  CAS  Google Scholar 

  96. T. Okabe, M. Kawata, Y. Okamoto, M. Mikami, Chem. Phys. Lett. 335, 435–439 (2001)

    Article  CAS  Google Scholar 

  97. Y. Ishikawa, Y. Sugita, T. Nishikawa, Y. Okamoto, Chem. Phys. Lett. 333, 199–206 (2001)

    Article  CAS  Google Scholar 

  98. A.E. Garcia, K.Y. Sanbonmatsu, Proteins 42, 345–354 (2001)

    Article  PubMed  CAS  Google Scholar 

  99. R.H. Zhou, B.J. Berne, R. Germain, Proc. Natl. Acad. Sci. U.S.A. 98, 14931–14936 (2001)

    Article  PubMed  CAS  Google Scholar 

  100. A.E. Garcia, K.Y. Sanbonmatsu, Proc. Natl. Acad. Sci. U.S.A. 99, 2782–2787 (2002)

    Article  PubMed  CAS  Google Scholar 

  101. R.H. Zhou, B.J. Berne, Proc. Natl. Acad. Sci. U.S.A. 99, 12777–12782 (2002)

    Article  PubMed  CAS  Google Scholar 

  102. M. Feig, A.D. MacKerell, C.L. Brooks III, J. Phys. Chem. B 107, 2831–2836 (2003)

    Article  CAS  Google Scholar 

  103. Y.M. Rhee, V.S. Pande, Biophys. J. 84, 775–786 (2003)

    Article  PubMed  CAS  Google Scholar 

  104. D. Paschek, A.E. Garcia, Phys. Rev. Lett. 93, 238105 (2004)

    Article  PubMed  CAS  Google Scholar 

  105. D. Paschek, S. Gnanakaran, A.E. Garcia, Proc. Natl. Acad. Sci. USA 102, 6765–6770 (2005)

    Article  PubMed  CAS  Google Scholar 

  106. J.W. Pitera, W. Swope, Proc. Natl. Acad. Sci. U.S.A. 100, 7587–7592 (2003)

    Article  PubMed  CAS  Google Scholar 

  107. M.K. Fenwick, F.A. Escobedo, Biopolymers 68, 160–177 (2003)

    Article  PubMed  CAS  Google Scholar 

  108. A. Mitsutake, Y. Okamoto, J. Chem. Phys. 121, 2491–2504 (2004)

    Article  PubMed  CAS  Google Scholar 

  109. M.K. Fenwick, F.A. Escobedo, J. Chem. Phys. 119, 11998–12010 (2003)

    Article  CAS  Google Scholar 

  110. K. Murata, Y. Sugita, Y. Okamoto, Chem. Phys. Lett. 385, 1–7 (2004)

    Article  CAS  Google Scholar 

  111. A.K. Felts, Y. Harano, E. Gallicchio, R.M. Levy, Proteins 56, 310 (2004)

    Article  PubMed  CAS  Google Scholar 

  112. A. Mitsutake, M. Kinoshita, Y. Okamoto, F. Hirata, J. Phys. Chem. B 108, 19002–19012 (2004)

    Article  CAS  Google Scholar 

  113. A. Baumketner, J.E. Shea, Biophys. J. 89, 1493 (2005)

    Article  PubMed  CAS  Google Scholar 

  114. T. Yoda, Y. Sugita, Y. Okamoto, Proteins 66, 846–859 (2007)

    Article  PubMed  CAS  Google Scholar 

  115. A.E. Roitberg, A. Okur, C. Simmerling, J. Phys. Chem. B 111, 2415–2418 (2007)

    Article  PubMed  CAS  Google Scholar 

  116. T.W. Whitfield, L. Bu, J.E. Straub, Physica A 305, 157–171 (2002)

    Article  Google Scholar 

  117. W. Kwak, U.H.E. Hansmann, Phys. Rev. Lett. 95, 138102 (2005)

    Article  PubMed  CAS  Google Scholar 

  118. N. Metropolis, A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller, E. Teller, J. Chem. Phys. 21, 1087–1092 (1953)

    Article  CAS  Google Scholar 

  119. S. Nosé, Mol. Phys. 52, 255–268 (1984)

    Article  Google Scholar 

  120. S. Nosé, J. Chem. Phys. 81, 511–519 (1984)

    Article  Google Scholar 

  121. H.C. Andersen, J. Chem. Phys. 72, 2384 (1980)

    Article  CAS  Google Scholar 

  122. I.R. McDonald, Mol. Phys. 23, 41 (1972)

    Article  CAS  Google Scholar 

  123. H. Okumura, Y. Okamoto, Phys. Rev. E 70, 026702 (2004)

    Article  CAS  Google Scholar 

  124. H. Okumura, Y. Okamoto, J. Phys. Soc. Jpn. 73, 3304–3311 (2004)

    Article  CAS  Google Scholar 

  125. H. Okumura, Y. Okamoto, J. Comput. Chem. 27, 379–395 (2006)

    Article  PubMed  CAS  Google Scholar 

  126. B.A. Berg, C. Muguruma, Y. Okamoto, Phys. Rev. B 75, 092202 (2007)

    Article  CAS  Google Scholar 

  127. C. Muguruma, Y. Okamoto, B.A. Berg, Phys. Rev. E 78, 041113 (2008)

    Article  CAS  Google Scholar 

  128. L. Pauling, J. Am. Chem. Soc. 57, 2680 (1935)

    Article  CAS  Google Scholar 

  129. W.F. Giauque, M. Ashley, Phys. Rev. 43, 81 (1933)

    Article  CAS  Google Scholar 

  130. National Institute of Standards and Technology (NIST) at http://physics.nist. gov/cuu/

  131. W.F. Giauque, J.W. Stout, J. Am. Chem. Soc. 58, 1144 (1936)

    Article  CAS  Google Scholar 

  132. L. Onsager, M. Dupuis, Re. Scu. Int. Fis. ‘Enrico Fermi’ 10, 294 (1960)

    Google Scholar 

  133. J.F. Nagle, J. Math. Phys. 7, 1484 (1966)

    Article  CAS  Google Scholar 

  134. O. Haida, T. Matsuo, H. Suga, and S. Seki, J. Chem. Thermodynamics 6, 815 (1974)

    Article  CAS  Google Scholar 

  135. B.A. Berg, 2005 (unpublished).

    Google Scholar 

  136. Y. Sugita, Y. Okamoto, Biophys. J. 88, 3180–3190 (2005)

    Article  PubMed  CAS  Google Scholar 

  137. K.R. Shoemaker, P.S. Kim, E.J. York, J.M. Stewart, R.L. Baldwin, Nature 326, 563–567 (1987)

    Article  PubMed  CAS  Google Scholar 

  138. K.R. Shoemaker, R. Fairman, D.A. Schultz, A.D. Robertson, E.J. York, J.M. Stewart, R.L. Baldwin, Biopolymers 29, 1–11 (1990)

    Article  PubMed  CAS  Google Scholar 

  139. P.J. Kraulis, J. Appl. Crystallogr. 24, 946–950 (1991)

    Article  Google Scholar 

  140. E.A. Merritt, D.J. Bacon, Methods Enzymol. 277, 505–524 (1997)

    Article  PubMed  CAS  Google Scholar 

  141. J. Wang, P. Cieplak, P.A. Kollman, J. Comput. Chem. 21, 1049–1074 (2000)

    Article  CAS  Google Scholar 

  142. T. Yoda, Y. Sugita, Y. Okamoto, Chem. Phys. Lett. 386, 460–467 (2004)

    Article  CAS  Google Scholar 

  143. W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, M.L. Klein, J. Chem. Phys. 79, 926–935 (1983)

    Article  CAS  Google Scholar 

  144. H. Okumura, Y. Okamoto, Bull. Chem. Soc. Jpn. 80, 1114–1123 (2007)

    Article  CAS  Google Scholar 

  145. H. Okumura, Y. Okamoto, J. Phys. Chem. B 112, 12038–12049 (2008)

    Article  PubMed  CAS  Google Scholar 

  146. P.A. Kollman, R. Dixon, W. Cornell, T. Fox, C. Chipot, A. Pohorille, in Computer Simulation of Biomolecular Systems, Vol. 3, ed. by A. Wilkinson, P. Weiner, W.F. van Gunsteren (Kluwer, Dordrecht, 1997), pp. 83–96

    Google Scholar 

  147. H. Okumura, S.G. Itoh, Y. Okamoto, J. Chem. Phys. 126, 084103 (2007)

    Article  PubMed  CAS  Google Scholar 

  148. S.D. Bond, B.J. Leimkuhler, B.B. Laird, J. Comput. Phys. 151, 114 (1999)

    Article  CAS  Google Scholar 

  149. S. Nosé, J. Phys. Soc. Jpn. 70, 75 (2001)

    Article  Google Scholar 

  150. T.F. Miller, M. Eleftheriou, P. Pattnaik, A. Ndirango, D. Newns, G.J. Martyna, J. Chem. Phys. 116, 8649 (2002)

    Article  CAS  Google Scholar 

  151. B.A. Berg, Introduction to Monte Carlo Simulations and Their Statistical Analysis, (World Scientific, Singapore, 2004)

    Google Scholar 

  152. T. Takekiyo, T. Imai, M. Kato, Y. Taniguchi, Biopolymers 73, 283 (2004)

    Article  PubMed  CAS  Google Scholar 

  153. H. Kokubo, Y. Okamoto, Chem. Phys. Lett. 383, 397–402 (2004)

    Article  CAS  Google Scholar 

  154. H. Kokubo, Y. Okamoto, J. Chem. Phys. 120, 10837–10847 (2004)

    Article  PubMed  CAS  Google Scholar 

  155. H. Kokubo, Y. Okamoto, J. Phys. Soc. Jpn. 73, 2571–2585 (2004)

    Article  CAS  Google Scholar 

  156. H. Kokubo, Y. Okamoto, Chem. Phys. Lett. 392, 168–175 (2004)

    Article  CAS  Google Scholar 

  157. A. Krogh, B. Larsson, G.v. Heijne, E.L.L. Sonnhammer, J. Mol. Biol. 305, 567 (2001)

    Article  PubMed  CAS  Google Scholar 

  158. D.T. Jones, W.R. Taylor, J.M. Thornton, Biochemistry 33, 3038 (1994)

    Article  PubMed  CAS  Google Scholar 

  159. T. Hirokawa, S. Boon-Chieng, S. Mitaku, Bioinformatics 14, 378 (1998)

    Article  PubMed  CAS  Google Scholar 

  160. G.E. Tusnady, I. Simon, J. Mol. Biol. 283, 489 (1998)

    Article  PubMed  CAS  Google Scholar 

  161. W.E. Reiher III, Theoretical Studies of Hydrogen Bonding, Ph.D. Thesis, Department of Chemistry, Harvard University, Cambridge, MA, USA, 1985

    Google Scholar 

  162. E. Neria, S. Fischer, M. Karplus, J. Chem. Phys. 105, 1902 (1996)

    Article  CAS  Google Scholar 

  163. R.A. Sayle, E.J. Milner-White, Trends. Biochem. Sci. 20, 374 (1995)

    Article  PubMed  CAS  Google Scholar 

  164. A. Mitsutake, Y. Sugita, T. Yoda, T. Nishikawa, Y. Okamoto, in preparation.

    Google Scholar 

  165. G.A. Kaminski, R.A. Friesner, J. Tirado-Rives, W.L. Jorgensen, J. Phys. Chem. B 105, 474 (2001)

    Article  CAS  Google Scholar 

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Okamoto, Y. (2009). Generalized-Ensemble Algorithms for Studying Protein Folding. In: Kuwajima, K., Goto, Y., Hirata, F., Kataoka, M., Terazima, M. (eds) Water and Biomolecules. Biological and Medical Physics, Biomedical . Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-88787-4_4

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