Skip to main content
SpringerLink
Log in

Parametrizing coarse grained models for molecular systems at equilibrium

  • Regular Article
  • Methodological Aspects of Coarse Graining
  • Published:
The European Physical Journal Special Topics Aims and scope Submit manuscript

Abstract

Hierarchical coarse graining of atomistic molecular systems at equilibrium has been an intensive research topic over the last few decades. In this work we (a) review theoretical and numerical aspects of different parametrization methods (structural-based, force matching and relative entropy) to derive the effective interaction potential between coarse-grained particles. All methods approximate the many body potential of mean force; resulting, however, in different optimization problems. (b) We also use a reformulation of the force matching method by introducing a generalized force matching condition for the local mean force in the sense that allows the approximation of the potential of mean force under both linear and non-linear coarse graining mappings (E. Kalligiannaki, et al., J. Chem. Phys. 2015). We apply and compare these methods to: (a) a benchmark system of two isolated methane molecules; (b) methane liquid; (c) water; and (d) an alkane fluid. Differences between the effective interactions, derived from the various methods, are found that depend on the actual system under study. The results further reveal the relation of the various methods and the sensitivities that may arise in the implementation of numerical methods used in each case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. D. Frenkel, B. Smit, Understanding Molecular Simulation: From Algorithms to Applications, 2nd edn. (Academic Press, 2001)

  2. M. Kotelyanskii, D.N. Theodorou, Simulation Methods for Polymers (Taylor & Francis, 2004)

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

  4. V. Harmandaris, V.G. Mavrantzas, D. Theodorou, M. Kröger, J. Ramirez, H.C. Öttinger, D. Vlassopoulos, Macromolecules 36, 1376 (2003)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  6. W. Tschöp, K. Kremer, O. Hahn, J. Batoulis, T. Bürger, Acta Polym. 49, 61 (1998)

    Article  Google Scholar 

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

    Google Scholar 

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

  9. W.J. Briels, R.L.C. Akkermans, J. Chem. Phys. 115, 6210 (2001)

    Article  ADS  Google Scholar 

  10. V.A. Harmandaris, N.P. Adhikari, N.F.A. van der Vegt, K. Kremer, Macromolecules 39, 6708 (2006)

    Article  ADS  Google Scholar 

  11. V. Harmandaris, K. Kremer, Macromolecules 42, 791 (2009)

    Article  Google Scholar 

  12. V. Harmandaris, K. Kremer, Soft Matter 5, 3920 (2009)

    Article  ADS  Google Scholar 

  13. K. Johnston, V. Harmandaris, Soft Matter 9, 6696 (2013)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  15. L. Lu, S. Izvekov, A. Das, H.C. Andersen, G.A. Voth, J. Chem. Theory Comput. 6, 954 (2010)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  18. A. Chaimovich, M.S. Shell, Phys. Chem. Chem. Phys. 11, 1901 (2009)

    Article  Google Scholar 

  19. I. Bilionis, N. Zabaras, J. Chem. Phys. 138, (2013)

  20. R.R. Coifman, I.G. Kevrekidis, S. Lafon, M. Maggioni, B. Nadler, Multiscale Model. Simul. 7, 842 (2008)

    Article  MathSciNet  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  23. A.P. Lyubartsev, A. Laaksonen, On the Reduction of Molecular Degrees of Freedom in Computer Simulations, edited by M. Karttunen, A. Lukkarinen, and I. Vattulainen, Novel Methods in Soft Matter Simulations, Vol. 640 of Lecture Notes in Physics (Berlin Springer Verlag, 2004), p. 219

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

  25. M.A. Katsoulakis, A.J. Majda, D.G. Vlachos, Proc. Nat. Acad. Sci. 100, 782 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  26. P. Plecháč, M.A. Katsoulakis, L. Rey-Bellet, J. Sci. Comput. 37, 43 (2008)

    Article  MathSciNet  Google Scholar 

  27. J. Trashorras, D.K. Tsagkarogiannis, SIAM J. Num. Anal. 48, 1647 (2010)

    Article  MathSciNet  Google Scholar 

  28. V. Harmandaris, E. Kalligiannaki, M.A. Katsoulakis, P. Plecháč, J. Comp. Phys. 314, 355 (2016)

    Article  ADS  Google Scholar 

  29. E. Kalligiannaki, M.A. Katsoulakis, P. Plechac, D.G. Vlachos, J. Comp. Phys. 231, 2599 (2012)

    Article  ADS  MathSciNet  Google Scholar 

  30. V. Harmandaris, Korea-Australia Rheol. J. 26, 15 (2014)

    Article  Google Scholar 

  31. P. Espanol, I. Zuniga, Phys. Chem. Chem. Phys. 13, 10538 (2011)

    Article  Google Scholar 

  32. E. Brini, E.A. Algaer, P. Ganguly, C. Li, F.R. Ropero, N.F.A. van der Vegt, Soft Matter 9, 2108 (2013)

    Article  ADS  Google Scholar 

  33. C. Peter, K. Kremer, Soft Matter 5, 4357 (2009)

    Article  ADS  Google Scholar 

  34. P. Carbone, H. Ali Karimi Varzaneh, X. Chen, F. Müller-Plathe, J. Chem. Phys. 128, 064904 (2008)

    Article  ADS  Google Scholar 

  35. Y.N. Pandey, A. Brayton, C. Burkhart, G.J. Papakonstantopoulos, M.J. Doxastakis, J. Chem. Phys. 140, 054908 (2014)

    Article  ADS  Google Scholar 

  36. J.T. Padding, W.J. Briels, J. Chem. Phys. 115, 2846 (2001)

    Article  ADS  Google Scholar 

  37. C. Hijon, P. Español, E. Vanden-Eijnden, R. Delgado-Buscalioni, Faraday Discuss. 144, 301 (2010)

    Article  ADS  Google Scholar 

  38. A.J. Clark, J. McCarty, M.G. Guenza, J. Chem. Phys. 139, 124906 (2013)

    Article  ADS  Google Scholar 

  39. G.A. Pavliotis, A.M. Stuart, Multiscale Methods, Vol. 53, Texts in Applied Mathematics (Springer, New York, 2008)

  40. A. Papavasiliou, G.A. Pavliotis, A.M. Stuart, Stochastic Proc. Appl. 119, 3173 (2009)

    Article  MathSciNet  Google Scholar 

  41. S. Izvekov, G.A. Voth, J. Phys. Chem. B 109, 6573 (2005)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

  43. M.A. Katsoulakis, P. Plechac, J. Chem. Phys. 139, 4852 (2013)

    Article  Google Scholar 

  44. T. Cover, J. Thomas, Elements of Information Theory (John Wiley & Sons, 1991)

  45. P. Dupuis, M.A. Katsoulakis, Y. Pantazis, P. Plecháč, SIAM J. Uncert. Quant. 4, 80 (2016)

    Article  Google Scholar 

  46. D. Fritz, V. Harmandaris, K. Kremer, N. van der Vegt, Macromolecules 42, 7579 (2009)

    Article  Google Scholar 

  47. D. Reith, M. Pütz, F. Müller Plathe, J. Comp. Chem. 24, 1624 (2003)

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  54. Z. Li, X. Bian, X. Li, G.E. Karniadakis, J. Chem. Phys. 143, 243128 (2015)

    Article  ADS  Google Scholar 

  55. V. Ruhle, C. Junghans, A. Lukyanov, K. Kremer, D. Andrienko, J. Chem. Theory Comput. 5, 3211 (2009)

    Article  Google Scholar 

  56. E. Kalligiannaki, V. Harmandaris, M.A. Katsoulakis, P. Plechac, J. Chem. Phys. 143, (2015)

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

    Article  Google Scholar 

  58. R. Potestio, C. Peter, K. Kremer, Entropy 16, 4199 (2014)

    Article  ADS  Google Scholar 

  59. W.H. Press, S.A. Teukolsky, W.T. Vetterling, B.P. Flannery, Numerical Recipes (Cambridge University Press, 2007)

  60. M. Maiolo, A. Vancheri, R. Krause, A. Danani, J. Comp. Phys. 300, 592 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  61. A.P. Bartok, M.C. Payen, R. Kondor, G. Csanyi, Phys. Rev. Lett. 104, 136403 (2010)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  64. J.F. Rudzinski, W.G. Noid, J. Phys. Chem. B. 116, 8621 (2012) PMID: 22564079

    Article  Google Scholar 

  65. P. Plecháč, S. Are, M.A. Katsoulakis, L. Rey-Bellet, SIAM J. Scientific Computing 31, 987 (2009)

    Article  Google Scholar 

  66. M.A. Katsoulakis, P. Plecháč, L. Rey-Bellet, D.K. Tsagkarogiannis, ESAIM: M2AN 41, 627 (2007)

    Article  Google Scholar 

  67. A. Tsourtis, V. Harmandaris, D. Tsagarogiannis, Parameterization of CG models through numerical simulations and cluster expansions (submitted) (2016)

  68. D. Reith, M. Pütz, F. Müller Plathe, J. Comp. Chem. 24, 1624 (2003)

    Article  Google Scholar 

  69. D.A. McQuarrie, Statistical Mechanics (University Science Books, 2000)

  70. J.D. McCoy, J.G. Curro, Macromolecules 31, 9352 (1998)

    Article  ADS  Google Scholar 

  71. N.F.A. van der Vegt, V.R. Ardham, G. Deichmann, F. Leroy, J. Chem. Phys. 143, 243135 (2015)

    Article  ADS  Google Scholar 

  72. G. Deichmann, V. Marcon, N.F.A. van der Vegt, J. Chem. Phys. 141, 224109 (2014)

    Article  ADS  Google Scholar 

  73. K. Johnston, V. Harmandaris, Macromolecules 46, 5741 (2013)

    Article  ADS  Google Scholar 

  74. C.M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics) (Springer-Verlag New York, Inc., Secaucus, NJ, USA, 2006)

  75. A.P. Lyubartsev, A. Mirzoev, L. Chen, A. Laaksonen, Faraday Discussion 144, 43 (2010)

    Article  ADS  Google Scholar 

  76. T. Murtola, A. Bunker, I. Vattulainen, M. Deserno, M. Karttunen, Phys. Chem. Chem. Phys. 11, 1869 (2009)

    Article  Google Scholar 

  77. R.L. Henderson, Phys. Lett. A 49, 197 (1974)

    Article  ADS  Google Scholar 

  78. A.J. Chorin, O.H. Hald, R. Kupferman, PNAS 97, 2968 (2000)

    Article  ADS  MathSciNet  Google Scholar 

  79. T. Lelièvre, M. Rousset, G. Stoltz, Free Energy Computations: A Mathematical Perspective (Imperial College Press, 2010)

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

    Google Scholar 

  81. W.K. den Otter, W.J. Briels, J. Chem. Phys. 109, 4139 (1998)

    Article  ADS  Google Scholar 

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

    Article  ADS  Google Scholar 

  83. A. Tsourtis, Y. Pantazis, M. Katsoulakis, V. Harmandaris, J. Chem. Phys. 143, 014116 (2015)

    Article  ADS  Google Scholar 

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

    Article  Google Scholar 

  85. J.C. Spall, Introduction to Stochastic Search and Optimization, 1st edn. (John Wiley & Sons, Inc., New York, NY, USA, 2003)

  86. L. Bottou, Stochastic learning. In Olivier Bousquet and Ulrike von Luxburg, editors, Advanced Lectures on Machine Learning, Lecture Notes in Artificial Intelligence, LNAI 3176, 146 (Springer Verlag, Berlin, 2004)

  87. D.M. Blei, M.D. Hoffman, C. Wang, J. Paisley, J. Mach. Learn. Res. 14, 1303 (2013)

    MathSciNet  Google Scholar 

  88. S. Mayo, B. Olafson, W. Goddard, J. Phys. Chem. 94, 8897 (1990)

    Article  Google Scholar 

  89. H. Wang, C. Junghans, K. Kremer, Eur. Phys. J. E 28, 221 (2009)

    Article  Google Scholar 

  90. J.R. Straatsma, T.P. Berendsen, H.J.C. Grigera, J. Phys. Chem. 91, 6269 (1987)

    Article  Google Scholar 

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

    Article  Google Scholar 

  92. S. Izvekov, G.A. Voth, J. Chem. Phys. 125, (2006)

  93. C. Baig, V. Harmandaris, Macromolecules 43, 3156 (2010)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Applied Mathematics University of Crete, Heraklion, Greece

    A. Chazirakis, A. Tsourtis & V. Harmandaris

  2. Mathematical and Computer Sciences and Engineering Division, King Abdullah University of Science and Technology (KAUST), Thuwal, Saudi Arabia

    E. Kalligiannaki

  3. Department of Mathematics and Statistics, University of Massachusetts at Amherst, Amherst, USA

    M.A. Katsoulakis

  4. Mathematical Sciences, University of Delaware, Newark, Delaware, USA

    P. Plecháč

  5. Institute of Applied and Computational Mathematics, Foundation for Research and Technology Hellas, IACM/FORTH, G71110, Heraklion, Greece

    V. Harmandaris

Authors
  1. E. Kalligiannaki
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. A. Chazirakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. A. Tsourtis
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. M.A. Katsoulakis
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. P. Plecháč
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. V. Harmandaris
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to E. Kalligiannaki or V. Harmandaris.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kalligiannaki, E., Chazirakis, A., Tsourtis, A. et al. Parametrizing coarse grained models for molecular systems at equilibrium. Eur. Phys. J. Spec. Top. 225, 1347–1372 (2016). https://doi.org/10.1140/epjst/e2016-60145-x

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjst/e2016-60145-x

Search

Navigation