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A generalized-Yvon-Born-Green method for coarse-grained modeling

Advances, Challenges, and Insight

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  • A. Representation of Molecular Systems Across Scales
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Abstract

The Yvon-Born-Green (YBG) integral equation is a basic result of liquid state theory that relates the pair potential of a simple fluid to the resulting equilibrium two- and three-body correlation functions. Quite recently, we derived a more general form that can be applied to complex molecular systems. This generalized-YBG (g-YBG) theory provides not only an exact relation between a given potential and the resulting equilibrium correlation functions, but also a remarkably powerful framework for directly solving the statistical mechanics inverse problem of determining potentials from equilibrium structure ensembles. In the context of coarse-grained (CG) modeling, the g-YBG theory determines a variationally optimal approximation to the many-body potential of mean force directly (i.e., noniteratively) from structural correlation functions and, in particular, allows “force-matching” without forces. While our initial efforts numerically validated the g-YBG theory with relatively simple systems, our more recent efforts have considered increasingly complex systems, such as peptides and polymers. This minireview summarizes this progress and the resulting insight, as well as discusses the outstanding challenges and future directions for the g-YBG theory.

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References

  1. C.N. Likos, Phys. Rep. 348, 267 (2001)

    Article  ADS  Google Scholar 

  2. J.P. Hansen, C.I. Addison, A.A. Louis, J. Phys.: Condens. Matter 17, S3185 (2005)

    ADS  Google Scholar 

  3. J.P. Hansen, I.R. McDonald, Theory of Simple Liquids, 2nd edn. (Academic Press, San Diego, CA USA, 1990)

  4. R. Evans, Adv. Phys. 28, 143 (1979)

    Article  ADS  Google Scholar 

  5. H.C. Andersen, D. Chandler, J. Chem. Phys. 57, 1918 (1972)

    Article  ADS  Google Scholar 

  6. H.C. Andersen, D. Chandler, J. Chem. Phys. 57, 1930 (1972)

    Article  ADS  Google Scholar 

  7. K.S. Schweizer, J.G. Curro, Phys. Rev. Lett. 58, 246 (1987)

    Article  ADS  Google Scholar 

  8. K.S. Schweizer, J.G. Curro, Adv. Chem. Phys. 93, 1 (1997)

    Google Scholar 

  9. M.G. Guenza, J. Phys.: Condens. Matter 20, 033101 (2008)

    ADS  Google Scholar 

  10. J. McCarty, I.Y. Lyubimov, M.G. Guenza, J. Phys. Chem. B 113, 11876 (2009)

    Article  Google Scholar 

  11. T.L. Hill, Statistical Mechanics: Principles and Selected Applications (Dover reprint, 1987)

  12. D. Henderson (ed.), Fundamentals of Inhomogeneous Fluids (Marcel Dekker, Inc., 1992)

  13. K.E. Gubbins, Chem. Phys. Lett. 76, 329 (1980)

    Article  MathSciNet  ADS  Google Scholar 

  14. S.G. Whittington, L.G. Dunfield, J. Phys. A: Math., Nucl., Gen. 6, 484 (1973)

    Article  ADS  Google Scholar 

  15. M.P. Taylor, J.E.G. Lipson, J. Chem. Phys. 100, 518 (1993)

    Article  ADS  Google Scholar 

  16. M.P. Taylor, J.E.G. Lipson, J. Chem. Phys. 102, 2118 (1995)

    Article  ADS  Google Scholar 

  17. P. Attard, J. Chem. Phys. 102, 5411 (1995)

    Article  ADS  Google Scholar 

  18. J.W. Mullinax, W.G. Noid, Phys. Rev. Lett. 103, 198104 (2009)

    Article  ADS  Google Scholar 

  19. J.W. Mullinax, W.G. Noid, J. Phys. Chem. C 114, 5661 (2010)

    Article  Google Scholar 

  20. J.W. Mullinax, W.G. Noid, J. Chem. Phys. 133, 124107 (2010)

    Article  ADS  Google Scholar 

  21. J.W. Mullinax, W.G. Noid, Proc. Natl. Acad. Sci. USA 107, 19867 (2010)

    Article  ADS  Google Scholar 

  22. C.R. Ellis, J.F. Rudzinski, W.G. Noid, Macromol. Theory Sim. 20, 478 (2011)

    Article  Google Scholar 

  23. J.F. Rudzinski, W.G. Noid, J. Chem. Phys. 135, 214101 (2011)

    Article  ADS  Google Scholar 

  24. J.F. Rudzinski, W.G. Noid, J. Phys. Chem. B 116, 8621 (2012)

    Article  Google Scholar 

  25. W.G. Noid, Methods Mol. Biol. 924, 487 (2013)

    Article  Google Scholar 

  26. J.F. Rudzinski, W.G. Noid, J. Phys. Chem. B 118, 8295 (2014)

    Article  Google Scholar 

  27. T.L. Hill, An Introduction to Statistical Thermodynamics (Addison Wesley Publishing Company, 1997)

  28. W.G. Noid, J.W. Chu, G.S. Ayton, G.A. Voth, J. Phys. Chem. B 111, 4116 (2007)

    Article  Google Scholar 

  29. W.G. Noid, J.W. Chu, G.S. Ayton, V. Krishna, S. Izvekov, G.A. Voth, A. Das, H.C. Andersen, J. Chem. Phys. 128, 244114 (2008)

    Article  ADS  Google Scholar 

  30. W.G. Noid, P. Liu, Y.T. Wang, J.W. Chu, G.S. Ayton, S. Izvekov, H.C. Andersen, G.A. Voth, J. Chem. Phys. 128, 244115 (2008)

    Article  ADS  Google Scholar 

  31. G. Ciccotti, R. Kapral, E. Vanden-Eijnden, Chem. Phys. Chem. 6, 1809 (2005)

    Google Scholar 

  32. M. Mechelke, M. Habeck, J. Chem. Theor. Comp. 9(12), 5685 (2013)

    Article  Google Scholar 

  33. H.H. Rugh, Phys. Rev. Lett. 78, 772 (1997)

    Article  ADS  Google Scholar 

  34. O.G. Jepps, G. Ayton, D.J. Evans, Phys. Rev. E 62, 4757 (2000)

    Article  ADS  Google Scholar 

  35. W.G. Noid, J. Chem. Phys. 139(9), 090901 (2013)

    Article  ADS  Google Scholar 

  36. S. Izvekov, G.A. Voth, J. Phys. Chem. B 109, 2469 (2005)

    Article  Google Scholar 

  37. S. Izvekov, G.A. Voth, J. Chem. Phys. 123, 134105 (2005)

    Article  ADS  Google Scholar 

  38. F. Ercolessi, J.B. Adams, Europhys. Lett. 26, 583 (1994)

    Article  ADS  Google Scholar 

  39. J.G. Kirkwood, J. Chem. Phys. 3(5), 300 (1935)

    Article  ADS  MATH  Google Scholar 

  40. A. Liwo, S. Oldziej, M.R. Pincus, R.J. Wawak, S. Rackovsky, H.A. Scheraga, J. Comp. Chem. 18, 849 (1997)

    Article  Google Scholar 

  41. N.G. van Kampen, Stochastic Processes in Physics and Chemistry, 3rd edn. (North-Holland, 2007)

  42. A.J. Chorin, O.H. Hald, R. Kupferman, Proc. Natl. Acad. Sci. USA 97, 2968 (2000)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  43. A.J. Chorin, Multiscale Model. Simul. 1, 105 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  44. A.J. Chorin, O.H. Hald, Stochastic Tools in Mathematics and Science (Springer, New York, NY USA, 2006)

  45. W. Tschop, K. Kremer, J. Batoulis, T. Burger, O. Hahn, Acta Poly. 49, 61 (1998)

    Article  Google Scholar 

  46. F. Müller-Plathe, Chem. Phys. Chem. 3, 754 (2002)

    Google Scholar 

  47. M.S. Shell, J. Chem. Phys. 129, 144108 (2008)

    Article  ADS  Google Scholar 

  48. A. Chaimovich, M.S. Shell, Phys. Rev. E 81 (2010)

  49. A. Chaimovich, M.S. Shell, J. Chem. Phys. 134, 094112 (2011)

    Article  ADS  Google Scholar 

  50. S. Kullback, R.A. Leibler, Ann. Math. Stat. 22, 79 (1951)

    Article  MathSciNet  MATH  Google Scholar 

  51. A.P. Lyubartsev, A. Laaksonen, Phys. Rev. E 52, 3730 (1995)

    Article  ADS  Google Scholar 

  52. T. Murtola, M. Karttunen, I. Vattulainen, J. Chem. Phys. 131, 055101 (2009)

    Article  ADS  Google Scholar 

  53. A. Lyubartsev, A. Mirzoev, L.J. Chen, A. Laaksonen, Faraday Disc. 144, 43 (2010)

    Article  ADS  Google Scholar 

  54. A. Savelyev, G.A. Papoian, J. Phys. Chem. B 113, 7785 (2009)

    Article  Google Scholar 

  55. A. Savelyev, G.A. Papoian, Biophys. J. 96, 4044 (2009)

    Article  ADS  Google Scholar 

  56. J.D. Honeycutt, D. Thirumalai, Proc. Natl. Acad. Sci. USA 87, 3526 (1990)

    Article  ADS  Google Scholar 

  57. J.D. Honeycutt, D. Thirumalai, Biopolymers 32, 695 (1992)

    Article  Google Scholar 

  58. J.W. Mullinax, W.G. Noid, J. Chem. Phys. 131, 104110 (2009)

    Article  ADS  Google Scholar 

  59. W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, J. Am. Chem. Soc. 118, 11225 (1996)

    Article  Google Scholar 

  60. K. Lu, J.F. Rudzinski, W.G. Noid, S.T. Milner, J.K. Maranas, Soft Matter 10, 978 (2014)

    Article  ADS  Google Scholar 

  61. S. Dou, S. Zhang, R.J. Klein, J. Runt, R.H. Colby, Chem. Mater. 18(18), 4288 (2006)

    Article  Google Scholar 

  62. K.J. Lin, J.K. Maranas, Macromolecules 45, 6230 (2012)

    Article  ADS  Google Scholar 

  63. L.Y. Lu, S. Izvekov, A. Das, H.C. Andersen, G.A. Voth, J. Chem. Theor. Comp. 6(3), 954 (2010)

    Article  Google Scholar 

  64. V. Ruhle, C. Junghans, A. Lukyanov, K. Kremer, D. Andrienko, J. Chem. Theor. Comp. 5(12), 3211 (2009)

    Article  Google Scholar 

  65. A. Das, L. Lu, H.C. Andersen, G.A. Voth, J. Chem. Phys. 136, 194115 (2012)

    Article  ADS  Google Scholar 

  66. V.A. Harmandaris, D. Reith, N.F.A. Van der Vegt, K. Kremer, Macromol. Chem. Phys. 208, 2109 (2007)

    Article  Google Scholar 

  67. H.M. Cho, J.W. Chu, J. Chem. Phys. 131, 134107 (2009)

    Article  ADS  Google Scholar 

  68. L. Lu, J.F. Dama, G.A. Voth, J. Chem. Phys. 139, 121906 (2013)

    Article  ADS  Google Scholar 

  69. J.F. Rudzinski, W.G. Noid, J. Chem. Theor. Comp. 11, 1278 (2015)

    Article  Google Scholar 

  70. S. Jain, S. Garde, S.K. Kumar, Ind. Eng. Chem. Res. 45, 5614 (2006)

    Article  Google Scholar 

  71. G. Megariotis, A. Vyrkou, A. Leygue, D.N. Theodorou, Ind. Eng. Chem. Res. 50, 546 (2011)

    Article  Google Scholar 

  72. S.P. Carmichael, M.S. Shell, J. Phys. Chem. B 116, 8383 (2012)

    Article  Google Scholar 

  73. A. Naômé, A. Laaksonen, D.P. Vercauteren, J. Chem. Theor. Comp. 10(8), 3541 (2014)

    Article  Google Scholar 

  74. A. Das, H.C. Andersen, J. Chem. Phys. 131, 034102 (2009)

    Article  ADS  Google Scholar 

  75. A. Das, H.C. Andersen, J. Chem. Phys. 136, 194114 (2012)

    Article  ADS  Google Scholar 

  76. A. Das, H.C. Andersen, J. Chem. Phys. 136, 194113 (2012)

    Article  ADS  Google Scholar 

  77. M. Enciso, C. Schutte, L. Delle Site, Soft Matter 9, 6118 (2013)

    Article  ADS  Google Scholar 

  78. J. McCarty, A.J. Clark, J. Copperman, M.G. Guenza, J. Chem. Phys. 140, 204913 (2014)

    Article  ADS  Google Scholar 

  79. B. Mukherjee, L. Delle Site, K. Kremer, C. Peter, J. Phys. Chem. B 116(29), 8474 (2012)

    Article  Google Scholar 

  80. I. Vorobyov, L. Li, T.W. Allen, J. Phys. Chem. B 112, 9588 (2008)

    Article  Google Scholar 

  81. W.D. Bennett, D.P. Tieleman, J. Chem. Theor. Comp. 7, 2981 (2011)

    Article  Google Scholar 

  82. S.Y. Mashayak, N.R. Aluru, J. Chem. Theor. Comp. 8(5), 1828 (2012)

    Article  Google Scholar 

  83. M. Jochum, D. Andrienko, K. Kremer, C. Peter, J. Chem. Phys. 137, 064102 (2012)

    Article  ADS  Google Scholar 

  84. T. Vettorel, H. Meyer, J. Chem. Theor. Comp. 2, 616 (2006)

    Article  Google Scholar 

  85. J. Ghosh, R. Faller, Mol. Sim. 33, 759 (2007)

    Article  Google Scholar 

  86. M.E. Johnson, T. Head-Gordon, A.A. Louis, J. Chem. Phys. 126, 144509 (2007)

    Article  ADS  Google Scholar 

  87. A. Liwo, M. Khalili, C. Czaplewski, S. Kalinowski, S. Ołdziej, K. Wachucik, H.A. Scheraga, J. Phys. Chem. B 111, 260 (2007)

    Article  Google Scholar 

  88. H.J. Qian, P. Carbone, X. Chen, H.A. Karimi-Varzaneh, C.C. Liew, F. Müller-Plathe, Macromolecules 41, 9919 (2008)

    Article  ADS  Google Scholar 

  89. E. Sobolewski, M. Makowski, S. Oldziej, C. Czaplewski, A. Liwo, H.A. Scheraga, Protein Eng. Des. Sel. 22, 547 (2009)

    Article  Google Scholar 

  90. K. Farah, A.C. Fogarty, M.C. Böhm, F. Müller-Plathe, Phys. Chem. Chem. Phys. 13, 2894 (2011)

    Article  Google Scholar 

  91. L. Lu, G.A. Voth, J. Chem. Phys. 134, 224107 (2011)

    Article  ADS  Google Scholar 

  92. S. Izvekov, J. Chem. Phys. 134, 034104 (2011)

    Article  ADS  Google Scholar 

  93. O. Engin, A. Villa, C. Peter, M. Sayar, Macromol. Theory Sim. 20, 451 (2011)

    Article  Google Scholar 

  94. E. Brini, V. Marcon, N.F.A. van der Vegt, Phys. Chem. Chem. Phys. 13, 10468 (2011)

    Article  Google Scholar 

  95. E. Brini, N.F.A. van der Vegt, J. Chem. Phys. 137, 154113 (2012)

    Article  ADS  Google Scholar 

  96. E. Brini, C.R. Herbers, G. Deichmann, N.F.A. van der Vegt, Phys. Chem. Chem. Phys. 14, 11896 (2012)

    Article  Google Scholar 

  97. T.C. Moore, C.R. Iacovella, C. McCabe, J. Chem. Phys. 140(22), 224104 (2014)

    Article  ADS  Google Scholar 

  98. V. Krishna, W.G. Noid, G.A. Voth, J. Chem. Phys. 131, 024103 (2009)

    Article  ADS  Google Scholar 

  99. A.A. Louis, J. Phys.: Condens. Matter 14, 9187 (2002)

    ADS  Google Scholar 

  100. G. D’Adamo, A. Pelissetto, C. Pierleoni, J. Chem. Phys. 138, 234107 (2013)

    Article  ADS  Google Scholar 

  101. T. Murtola, E. Falck, M. Karttunen, I. Vattulainen, J. Chem. Phys. 126, 075101 (2007)

    Article  ADS  Google Scholar 

  102. C.C. Fu, P.M. Kulkarni, M.S. Shell, L.G. Leal, J. Chem. Phys. 137, 164106 (2012)

    Article  ADS  Google Scholar 

  103. A. Das, H.C. Andersen, J. Chem. Phys. 132, 164106 (2010)

    Article  ADS  Google Scholar 

  104. R. Evans, Mol. Sim. 4, 409 (1990)

    Article  Google Scholar 

  105. A.P. Lyubartsev, A. Laaksonen, Phys. Rev. E 55, 5689 (1997)

    Article  ADS  Google Scholar 

  106. T.R. Lezon, I. Bahar, PLoS Comput. Biol. 6, e1000816 (2010)

    Article  MathSciNet  ADS  Google Scholar 

  107. A. Savelyev, G.A. Papoian, Proc. Natl. Acad. Sci. USA 107, 20340 (2010)

    Article  ADS  Google Scholar 

  108. L. Larini, L.Y. Lu, G.A. Voth, J. Chem. Phys. 132, 164107 (2010)

    Article  ADS  Google Scholar 

  109. J. Lu, Y. Qiu, R. Baron, V. Molinero, J. Chem. Theor. Comp. 10, 4104 (2014)

    Article  Google Scholar 

  110. G. van Anders, D. Klotsa, N.K. Ahmed, M. Engel, S.C. Glotzer, Proc. Natl. Acad. Sci. USA 111, E4812 (2014)

    Article  ADS  Google Scholar 

  111. A. Morriss-Andrews, J. Rottler, S.S. Plotkin, J. Chem. Phys. 132, 035105 (2010)

    Article  ADS  Google Scholar 

  112. J. Zhou, I.F. Thorpe, S. Izvekov, G.A. Voth, Biophys. J. 92, 4289 (2007)

    Article  ADS  Google Scholar 

  113. W. Schommers, Phys. Rev. A 28, 3599 (1983)

    Article  ADS  Google Scholar 

  114. L. Reatto, D. Levesque, J.J. Weis, Phys. Rev. A 33, 3451 (1986)

    Article  ADS  Google Scholar 

  115. R.L. McGreevy, L. Pusztai, Mol. Sim. 1, 359 (1988)

    Article  Google Scholar 

  116. D.A. Keen, R.L. McGreevy, Nature 344, 423 (1990)

    Article  ADS  Google Scholar 

  117. A.K. Soper, Chem. Phys. 202, 295 (1996)

    Article  ADS  Google Scholar 

  118. M.C. Rechtsman, F.H. Stillinger, S. Torquato, Phys. Rev. Lett. 95, 228301 (2005)

    Article  ADS  Google Scholar 

  119. S.C. Glotzer, M.J. Solomon, Nat. Mater. 6, 557 (2007)

    Article  Google Scholar 

  120. S. Sacanna, D.J. Pine, G.R. Yi, Soft Matter 9, 8096 (2013)

    Article  ADS  Google Scholar 

  121. M.A. Bevan, S.L. Eichmann, Curr. Opin. Colloid Interface Sci. 16, 149 (2011)

    Article  Google Scholar 

  122. S. Torquato, Soft Matter 5, 1157 (2009)

    Article  ADS  Google Scholar 

  123. Z. Li, Y. Yang, J. Zhan, L. Dai, Y. Zhou, Annu. Rev. Biophys. 42, 315 (2013)

    Article  Google Scholar 

  124. S. Tanaka, H.A. Scheraga, Macromolecules 9, 945 (1976)

    Article  ADS  Google Scholar 

  125. S. Miyazawa, R.L. Jernigan, Macromolecules 18, 534 (1985)

    Article  ADS  Google Scholar 

  126. M.J. Sippl, J. Mol. Biol. 213, 859 (1990)

    Article  Google Scholar 

  127. P.D. Thomas, K.A. Dill, J. Mol. Biol. 257, 457 (1996)

    Article  Google Scholar 

  128. A. Ben-Naim, J. Chem. Phys. 107, 3698 (1997)

    Article  ADS  Google Scholar 

  129. M.R. Betancourt, Proteins 76, 72 (2009)

    Article  Google Scholar 

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  1. J. F. Rudzinski

    Present address: Max-Planck-Institute for Polymer Research, Mainz, Germany

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  1. Department of Chemistry, The Pennsylvania State University, University Park, PA, 16802, USA

    J. F. Rudzinski & W. G. Noid

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Rudzinski, J.F., Noid, W.G. A generalized-Yvon-Born-Green method for coarse-grained modeling. Eur. Phys. J. Spec. Top. 224, 2193–2216 (2015). https://doi.org/10.1140/epjst/e2015-02408-9

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