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Techniques and Applications of Langevin Dynamics Simulations

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The Molecular Dynamics of Liquid Crystals

Part of the book series: NATO ASI Series ((ASIC,volume 431))

Abstract

A review of Langevin dynamics simulations, with emphasis on the practical details, is presented. The topics include (i) parametrisation of the friction constant and related hydrodynamic theory; (ii) choice of algorithms and estimation of systematic and statistical error; (iii) calculation of transition rates from time correlation functions and the Kramers theory of barrier crossing; (iv) reorientational correlation functions; (v) application to lipid bilayers, including the analysis of NMR spin-lattice relaxation times from simulations. Topics (ii)-(iv) are illustrated with simulations of a particle in a harmonic potential, a particle in a bistable potential, and a dimer in a Maier-Saupe potential, respectively. The FORTRAN programs for these examples are included.

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References

  1. Chandrasekhar, S. (1943) Rev. Mod. Phys., 15 1.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Zwanzig, R. (1969) Ann. Rev. of Phys. Chem., 15 325.

    Article  Google Scholar 

  3. Allen, M. P. and Tildesley, D. J. (1987) Computer Simulation of Liquids, Clarendon Press, Oxford.

    MATH  Google Scholar 

  4. Brooks, C. L., Pettitt, B. M. and Karplus, M. (1988) Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics, Wiley-Interscience, New York.

    Google Scholar 

  5. Brooks, B. R. (1987) Supercomputer Research in Chemistry and Chemical Engineering, K. F. Jensen and D. G. Truhlar (eds.), ACS Symposium Series, 353 American Chemical Society, Washington, DC, p. 123.

    Google Scholar 

  6. Pastor, R. W., Venable, R. M. and Karplus, M. (1988) J. chem. Phys., 89 1112.

    Article  ADS  Google Scholar 

  7. Levine, Y. K., Partington, P. and Roberts, G. C. K. (1973) Molec. Phys., 25 497.

    Article  ADS  Google Scholar 

  8. London, R. E. and Avitabile, J. (1977) J. Am. Chem. Soc., 99 7765.

    Article  Google Scholar 

  9. Wittebort, R. J. and Szabo, A. (1978) J. chem, Phys., 69 1722.

    Article  ADS  Google Scholar 

  10. Gent, M. P. N. and Prestagard, J. H. (1977) J. Mag. Res., 25 243.

    Google Scholar 

  11. Bocian, D. F. and Chan, S. I. (1978) Ann. Rev. of Phys. Chem., 29 307.

    Article  ADS  Google Scholar 

  12. Szabo, A. (1986) Ann. New York Acad. Sci., 482 44.

    Article  ADS  Google Scholar 

  13. Pastor, R. W., Venable, R. M., Karplus, M. and Szabo, A. (1988) J. chem. Phys., 89 1128.

    Article  ADS  Google Scholar 

  14. Rommel, E., Noack, F., Meier, P. and Kothe, G. (1988) J. chem. Phys., 92 2981.

    Article  Google Scholar 

  15. Brown, M. F. (1982) J. chem. Phys., 77 1576.

    Article  ADS  Google Scholar 

  16. Brown, M. F. (1984) J. chem. Phys., 80 2808.

    Article  ADS  Google Scholar 

  17. Brown, M. F., Ribeiro, A. A. and Williams, G. D. (1983) Proc. Natl. Acad, Sci. USA, 80 4325.

    Article  ADS  Google Scholar 

  18. Pace, R. J. and Chan, S. I. (1982) J. chem. Phys., 76 4228.

    Article  ADS  Google Scholar 

  19. Pace, R. J. and Chan, S. I. (1982) J. chem. Phys., 76 4228.

    Article  ADS  Google Scholar 

  20. Hynes, J. T. (1985) Theory of Chemical Reaction Dynamics, Vol. 4, M. Baer (ed.), CRC Press. Boca Raton, Chap. 4.

    Google Scholar 

  21. Kubo, R. (1966) Rep. Progr. Phys., 29 255.

    Article  ADS  Google Scholar 

  22. Zwanzig, R. and Bixon, M. (1970) Phys. Rev., A 2 2005.

    Article  ADS  Google Scholar 

  23. Harp, G. D. and Berne, B. J. (1970) Phys. Rev., A 2 975.

    Article  ADS  Google Scholar 

  24. Adelman, S. A. and Brooks III, C. L. (1982) J. Chem. Phys., 86 1511.

    Article  Google Scholar 

  25. Berkowitz, M., Morgan, J. D. and McCammon, J. A. (1983) J. chem. Phys., 78 3256.

    Article  ADS  Google Scholar 

  26. Grote, R. F. and Hynes, J. T. (1981) J. chem. Phys., 75 2191.

    Article  MathSciNet  ADS  Google Scholar 

  27. Tully, J. C. (1980) Ann. Rev. of Phys. Chem., 31 319.

    Article  ADS  Google Scholar 

  28. Montgomery, J. A., Holmgren, S. L. and Chandler, S. L. (1980) J. chem. Phys., 73 3688.

    Article  ADS  Google Scholar 

  29. Gordon, R. G. (1966) J. chem. Phys., 44 1830.

    Article  ADS  Google Scholar 

  30. Skinner, J. L. and Wolynes, P. G. (1980) J. chem Phys., 72 4913.

    Article  MathSciNet  ADS  Google Scholar 

  31. Bull, T. E. and Egan, W. (1984) J. chem. Phys., 81 3181.

    Article  ADS  Google Scholar 

  32. Einstein, A. (1956) Investigations on the Theory of Brownian Movement, Dover, New York.

    MATH  Google Scholar 

  33. Yamakawa, H. (1971) Modern Theory of Polymer Solutions, Harper and Row, New York.

    Google Scholar 

  34. Cantor, C. R. and Schimmel, P. R. (1980) Biophysical Chemistry, Part II: Techniques for the Study of Biological Structure and Function, W. H. Freeman and Co., San Francisco.

    Google Scholar 

  35. Teller, D. C., Swanson, E. and de Haen, C. (1979) Methods in Enzymology, 61 p. 103.

    Article  Google Scholar 

  36. Venable, R. M. and Pastor, R. W. (1988) Biopolymers, 27 1001.

    Article  Google Scholar 

  37. Hu, C. and Zwanzig, R. (1974) J. chem. Phys., 60, 4354.

    Article  ADS  Google Scholar 

  38. Berne, B. J. and Pecora, R. (1976) Dynamic Light Scattering, Wiley, New York.

    Google Scholar 

  39. Murdy, J. S. and Cotts, R. M. (1970) J. chem. Phys., 53 4724.

    Article  ADS  Google Scholar 

  40. Garcia de la Torre, J. and Bloomfield, V. A. (1981) Quart. Rev. of Biophys., 14 81.

    Article  Google Scholar 

  41. Kirkwood, J. G. and Riseman, J. (1948) J. chem. Phys., 16 565.

    Article  ADS  Google Scholar 

  42. Paul, E. and Mazo, R. M. (1968) J. chem. Phys., 48 1405.

    Article  ADS  Google Scholar 

  43. Zimm, B. H. (1980) Macromolecules, 13 592.

    Article  ADS  Google Scholar 

  44. Garcia de la Torre, J., Jimenez, A. and Freire, J. J. (1982) Macromolecules, 15 148.

    Article  ADS  Google Scholar 

  45. Evans, G. T. and Knauss, D. C. (1980) J. chem. Phys., 72 1504.

    Article  ADS  Google Scholar 

  46. Levy, R. M., Karplus, M. and Wolynes, P. G. (1981) J. Am. Chem. Soc., 103 5998.

    Article  Google Scholar 

  47. Lee, B. and Richards, F. M. (1971) J. Mol. Biol., 55 379.

    Article  Google Scholar 

  48. Pastor, R. W. and Karplus, M. (1988) J. Phys. Chem., 92 2636.

    Article  Google Scholar 

  49. Brooks, C. L., Brunger, A. and Karplus, M. (1985) Biopolymers, 24 843.

    Article  Google Scholar 

  50. Ermak, D. L. and McCammon, J. A. (1978) J. chem. Phys., 69 1352.

    Article  ADS  Google Scholar 

  51. Pear, M. R. and McCammon, J. A. (1981) J. chem Phys., 74 6922.

    Article  ADS  Google Scholar 

  52. Ladanyi, B. M. and Hynes, J. T. (1982) J. chem. Phys., 77 4739.

    Article  ADS  Google Scholar 

  53. Pastor, R. W. and Zwanzig, R. (1989) J. chem. Phys., 90 5729.

    Article  ADS  Google Scholar 

  54. Verlet, L. (1967) Phys. Rev., 159 98.

    Article  ADS  Google Scholar 

  55. van Gunsteren, W. F. and Berendsen, H. J. C. (1982) Mol. Phys., 45 637.

    Article  ADS  Google Scholar 

  56. Brunger, A., Brooks, C. B. and Karplus, M. (1984) Chem. Phys. Lett., 105 495.

    Article  ADS  Google Scholar 

  57. van Gunsteren, W. F. and Berendsen, H. J. C. (1986) Proceedings of the Enrico Fermi School on Molecular-Dynamics Simulation of Statistical-Mechanical Systems, G. Ciccotti and W. G. Hoover (eds.), North-Holland, Amsterdam, p.43.

    Google Scholar 

  58. Pastor, R. W., Brooks, B. R. and Szabo, A. (1988) Mol. Phys., 65 1409.

    Article  ADS  Google Scholar 

  59. Ryckaert, J. P. and Bellemans, A. (1975) Chem. Phys. Lett., 30 123.

    Article  ADS  Google Scholar 

  60. Pastor R. W. and Karplus, M. (1989) J. chem. Phys., 91 211.

    Article  ADS  Google Scholar 

  61. Ediden, M. (1974) Ann. Rev. Biophys. and Bioeng., 3 179.

    Article  Google Scholar 

  62. Lakowicz, J. R. (1981) Spectroscopy in Biochemistry, Vol 1, J. E. Bull (ed.), CRC Press, p. 195.

    Google Scholar 

  63. Ermak, D. and Buckholtz, H. (1980) J. Comput. Phys., 35 169.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  64. Allen M. P. (1982) Mol. Phys., 47 599.

    Article  ADS  Google Scholar 

  65. van Gunsteren, W. F. and Berendsen, H. J. C. (1988) Molecular Simulation, 1 173–185.

    Article  Google Scholar 

  66. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T. (1986) Numerical Recipies, Cambridge University Press, New York.

    Google Scholar 

  67. Bloomfield, P. (1976) Fourier Analysis on Time Series: An Introduction, John Wiley and Sons, New York.

    Google Scholar 

  68. Agarwal, R. C. and Cooley, J. W. (1986) IBM J. Res. Develop., 30 145.

    Article  MathSciNet  Google Scholar 

  69. Venable, R. M. and Pastor, R. W. unpublished results.

    Google Scholar 

  70. Jacucci, G. and Rahman, A. (1984) Nuovo Cimento, D4 317.

    Google Scholar 

  71. Swope, W. C., Anderson, H. C., Berens, P. H. and Wilson, K. R. (1982) J. chem. Phys., 76 637.

    Article  ADS  Google Scholar 

  72. Straatsma, T. P., Berendsen, H. J. C. and Stain, A. J. (1986) Mol. Phys., 57 89.

    Article  ADS  Google Scholar 

  73. Zwanzig, R. and Aliwadi, N. K. (1969) Phys. Rev., 182 280.

    Article  MathSciNet  ADS  Google Scholar 

  74. Lee, S. and Karplus, M. (1984) J. chem. Phys., 81 6106.

    Article  ADS  Google Scholar 

  75. Go, N. and Kano, F. (1981) J. chem. Phys., 75 4166.

    Article  ADS  Google Scholar 

  76. Pastor, R. W. and Szabo, A. Computer Simulations of Liquid Crystals, G. R. Luckhurst (ed.), Kluwar Academic Publishing, in the press.

    Google Scholar 

  77. Kramers, H. A. (1940) Physica (The Hague), 7 284.

    Article  MathSciNet  ADS  MATH  Google Scholar 

  78. Mel’nikov, V. I. and Meshkov, S. V. (1986) J. chem. Phys., 85 1018.

    Article  ADS  Google Scholar 

  79. Berne, B. J., Borkovec, M. and Straub, J. E. (1988) J. Phys. Chem., 92 3711.

    Article  Google Scholar 

  80. Hanggi, P., Talkare, P. and Borkovec, M. (1990) Rev. Modern Phys., 62 251.

    Article  MathSciNet  ADS  Google Scholar 

  81. Chandler, D. (1987) Introduction to Modern Statistical Mechanics, Oxford University Press, New York.

    Google Scholar 

  82. Zhou, H-X. (1989) Chem. Phys. Lett., 164 285.

    Article  ADS  Google Scholar 

  83. Eyring, H. (1935) J. chem. Phys., 3, 107.

    Article  ADS  Google Scholar 

  84. Loncharich, R. J., Brooks, B. R. and Pastor, R. W. (1992) Biopolymers, Vol. 32 p. 523.

    Article  Google Scholar 

  85. Chandler, D. (1978) J. chem. Phys., 68 2959.

    Article  ADS  Google Scholar 

  86. Northrup, S. H. and Hynes, J. T. (1980) J. chem. Phys., 73 2700.

    Article  MathSciNet  ADS  Google Scholar 

  87. Helfand, E., Wasserman, Z. R. and Weber, T. A. (1980) Macromolecules, 13, 526.

    Article  ADS  Google Scholar 

  88. Huntress, W. T. (1968) J. chem. Phys., 48 3524.

    Article  ADS  Google Scholar 

  89. Evans, G. T. (1977) J. chem. Phys., 67 2911.

    Article  ADS  Google Scholar 

  90. Hubbard, P. S. (1963) Phys. Rev., 131 1155.

    Article  ADS  Google Scholar 

  91. Rychaert, J. P., Ciccotti, G. and Berendsen, H. J. C. (1977) J. Comput. Phys., 23, 327.

    Article  ADS  Google Scholar 

  92. Maier, W. and Saupe, A. (1959) Z. Naturforsch, Tiel A, 14 882.

    ADS  Google Scholar 

  93. de Gennes, P. G. (1974) The Physics and Chemistry of Liquid Crystals, Clarendon Press, Oxford.

    Google Scholar 

  94. Luckhurst, G. R. and Gray, G. W. (1979) The Physics and Chemistry of Liquid Crystals, Academic Press.

    Google Scholar 

  95. Emsley, J. W., Luckhurst, G. R. and Stockley, C. P. (1982) Proc. R. Soc. Lond., A 381 117.

    ADS  Google Scholar 

  96. Marcelja, S. (1974) Biochem. Biophys. Acta., 367 165.

    Article  Google Scholar 

  97. Martinez, M. C. L. and Garcia de la Torre, J. (1987) Biophys J., 52 303.

    Article  Google Scholar 

  98. Davis, J. H. (1983) Biochem. Biophys. Acta, 737 117.

    Google Scholar 

  99. Torchia, D. A. (1984) Ann. Rev. Biophys. Bioeng., 13 125–144.

    Article  Google Scholar 

  100. Seelig, J. and MacDonald, P. M. (1987) Acc. of Chem. Res., 20 221.

    Article  Google Scholar 

  101. Pastor, R. W., Venable, R. M. and Karplus, M. (1991) Proc. Natl. Acad. Sci. USA, 88 892.

    Article  ADS  Google Scholar 

  102. Pastor, R. W. (1990) Molecular Description of Biological Membrane Components by Computer Aided Conformational Analysis, R. Brasseur (ed.), CRC Press, p. 171.

    Google Scholar 

  103. Cevc, G. and Marsh, D. (1987) Phospholipid Bilayers, John Wiley and Sons, New York.

    Google Scholar 

  104. Seelig, A. and Seelig, J. (1974) Biochemistry, 13 4839.

    Article  Google Scholar 

  105. Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc., 104 4546.

    Article  Google Scholar 

  106. Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc., 104 4559.

    Article  Google Scholar 

  107. Szabo, A. (1984) J. chem. Phys., 81 150.

    Article  ADS  Google Scholar 

  108. Venable, R. M., Zhang, Y., Hardy, B. J. and Pastor, R. W. (1993) Science, Vol. 262 p. 223.

    Article  ADS  Google Scholar 

  109. Lipari, G. and Szabo, A. (1980) Biophys. J., 30 489.

    Article  ADS  Google Scholar 

  110. Artymiuk, P. J., Blake, C. C. F., Grace, D. E. P., Oatley, S. J., Phillips, D. C., Sternberg, M. E. (1979) Nature, 280 563.

    Article  ADS  Google Scholar 

  111. Kuntz, I. D. and Kauzmann, W. (1974) Advances in Protein Chemistry, 28 236.

    Article  Google Scholar 

  112. Cross, A. J. and Fleming, G. R. (1986) Biophys. J., 50 507.

    Article  ADS  Google Scholar 

  113. Hayduk, W. and Cheng, S. C. (1971) Engineering Science, 26 635.

    Article  Google Scholar 

  114. Pollack, G. L. and Enyeart, (1985) J. J., Phys. Rev., A 31 980.

    Article  ADS  Google Scholar 

  115. Vold, R. R., Vold, R. L. and Szeverenyi, N. M. (1979) J. Chem. Phys., 70 5213.

    Article  ADS  Google Scholar 

  116. De Loof, H., Segrest, J. P., Harvey, S. and Pastor, R. W. (1991) Biochemistry, 30 2099.

    Article  Google Scholar 

  117. Levy, R. M., Karplus, M. and McCammon, J. A. (1979) Chem. Phys. Lett., 65 4.

    Article  ADS  Google Scholar 

  118. Skolnick, J. and Helfand, E. (1980) J. chem. Phys., 72 5489.

    Article  ADS  Google Scholar 

  119. Helfand, E. (1984) Science, 226 647.

    Article  ADS  Google Scholar 

  120. McCammon, J. A., Northrup, S. H. and Allison, S. A. (1986) J. chem. Phys., 90 3901.

    Article  Google Scholar 

  121. Case, D. A. (1988) Prog. in Biophys. and Mol. Biol., 56 39.

    Google Scholar 

  122. Turq, P., Lantelme, F. and Friedman, H. L. (1977) J. chem. Phys., 66 3039.

    Article  ADS  Google Scholar 

  123. Schlick, T. and Peskin, C. S. (1989) Comm. on Pure and Appl. Math., 42 1141.

    Article  MathSciNet  MATH  Google Scholar 

  124. Zhang, G. and Schlick, T. (1993) J. Comp. Chem, Vol. 14 1212.

    Article  Google Scholar 

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Pastor, R.W. (1994). Techniques and Applications of Langevin Dynamics Simulations. In: Luckhurst, G.R., Veracini, C.A. (eds) The Molecular Dynamics of Liquid Crystals. NATO ASI Series, vol 431. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-1168-3_5

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  • DOI: https://doi.org/10.1007/978-94-011-1168-3_5

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