The European Physical Journal Special Topics

, Volume 224, Issue 12, pp 2269–2287 | Cite as

Adaptive resolution simulation in equilibrium and beyond

Regular Article A. Representation of Molecular Systems Across Scales
Part of the following topical collections:
  1. Discussion and Debate: Recurrent Problems in Scale Bridging Techniques in Molecular Simulation – What are the Current Options?

Abstract

In this paper, we investigate the equilibrium statistical properties of both the force and potential interpolations of adaptive resolution simulation (AdResS) under the theoretical framework of grand-canonical like AdResS (GC-AdResS). The thermodynamic relations between the higher and lower resolutions are derived by considering the absence of fundamental conservation laws in mechanics for both branches of AdResS. In order to investigate the applicability of AdResS method in studying the properties beyond the equilibrium, we demonstrate the accuracy of AdResS in computing the dynamical properties in two numerical examples: The velocity auto-correlation of pure water and the conformational relaxation of alanine dipeptide dissolved in water. Theoretical and technical open questions of the AdResS method are discussed in the end of the paper.

Keywords

European Physical Journal Special Topic Radial Distribution Function Thermodynamic Force Atomistic Region Hybrid Region 

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References

  1. 1.
    M. Praprotnik, L. Delle Site, K. Kremer, J. Chem. Phys. 123, 224106 (2005)CrossRefADSGoogle Scholar
  2. 2.
    M. Praprotnik, L. Delle Site, K. Kremer, Phys. Rev. E 73(6), 066701 (2006)CrossRefADSGoogle Scholar
  3. 3.
    M. Praprotnik, S. Matysiak, L. Delle Site, K. Kremer, C. Clementi, J. Phys: Condens. Matter 19, 292201 (2007)Google Scholar
  4. 4.
    M. Praprotnik, L. Delle Site, K. Kremer, Annu. Rev. Phys. Chem. 59, 545 (2008)CrossRefADSGoogle Scholar
  5. 5.
    A.B. Poma, L. Delle Site, Phys. Rev. Lett. 104(25), 250201 (2010)CrossRefADSGoogle Scholar
  6. 6.
    S. Poblete, M. Praprotnik, K. Kremer, L. Delle Site, J. Chem. Phys. 132, 114101 (2010)CrossRefADSGoogle Scholar
  7. 7.
    M. Praprotnik, S. Poblete, K. Kremer, J. Stat. Phys., 1 (2011)Google Scholar
  8. 8.
    S. Fritsch, S. Poblete, C. Junghans, G. Ciccotti, L. Delle Site, K. Kremer, Phys. Rev. Lett. 108, 170602 (2012)CrossRefADSGoogle Scholar
  9. 9.
    S. Bevc, C. Junghans, K. Kremer, M. Praprotnik, New J. Phys. 15, 105007 (2013)CrossRefADSGoogle Scholar
  10. 10.
    J. Zavadlav, M.M. Melo, S.J. Marrink, M. Praprotnik, J. Chem. Phys. 140(5), 054114 (2014)CrossRefADSGoogle Scholar
  11. 11.
    J. Zavadlav, M.N. Melo, A.V. Cunha, A.H. De Vries, S.J. Marrink, M. Praprotnik, J. Chem. Theor. Comput. 10(6), 2591 (2014)CrossRefGoogle Scholar
  12. 12.
    R. Delgado-Buscalioni, K. Kremer, M. Praprotnik, J. Chem. Phys. 131, 244107 (2009)CrossRefADSGoogle Scholar
  13. 13.
    B. Ensing, S.O. Nielsen, P.B. Moore, M.L. Klein, M. Parrinello, J. Chem. Theor. Comput. 3(3), 1100 (2007)CrossRefGoogle Scholar
  14. 14.
    D.M. Heyes, J. Chem. Phys. 132(6), 064504 (2010)CrossRefADSGoogle Scholar
  15. 15.
    Q. Shi, S. Izvekov, G.A. Voth, J. Phys. Chem. B 110(31), 15045 (2006)CrossRefGoogle Scholar
  16. 16.
    L. Shen, H. Hu, J. Chem. Theor. Comput. 10(6), 2528 (2014)CrossRefADSGoogle Scholar
  17. 17.
    S.O. Nielsen, P.B. Moore, B. Ensing, Phys. Rev. Lett. 105(23), 237802 (2010)CrossRefADSGoogle Scholar
  18. 18.
    M. Praprotnik, S. Poblete, L. Delle Site, K. Kremer, Phys. Rev. Lett. 107(9), 99801 (2011)CrossRefADSGoogle Scholar
  19. 19.
    L. Delle Site, Phys. Rev. E 76(4), 047701 (2007)CrossRefADSGoogle Scholar
  20. 20.
    H. Wang, C. Hartmann, C. Schütte, L. Delle Site, Phys. Rev. X 3(1), 011018 (2013)Google Scholar
  21. 21.
    R. Potestio, S. Fritsch, P. Espanol, R. Delgado-Buscalioni, K. Kremer, R. Everaers, D. Donadio, Phys. Rev. Lett. 110(10), 108301 (2013)CrossRefADSGoogle Scholar
  22. 22.
    A. Agarwal, H. Wang, C. Schütte, L. Delle Site, J. Chem. Phys. 141, 034102 (2014)CrossRefADSGoogle Scholar
  23. 23.
    L. Delle Site, Entropy 16(1), 23 (2013)CrossRefGoogle Scholar
  24. 24.
    L. Onsager, J. Amer. Chem. Soc. 58(8), 1486 (1936)CrossRefGoogle Scholar
  25. 25.
    I.G. Tironi, R. Sperb, P.E. Smith, W.F. van Gunsteren, J. Chem. Phys. 102, 5451 (1995)CrossRefADSGoogle Scholar
  26. 26.
    D. Frenkel,B. Smit. Understanding molecular simulation (Academic Press, Inc. Orlando, FL, USA, 2001)Google Scholar
  27. 27.
    H. Wang, J. Chem. Theor. Comput. 8(8), 2878 (2012)CrossRefADSGoogle Scholar
  28. 28.
    H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys. Chem. 91(24), 6269 (1987)CrossRefGoogle Scholar
  29. 29.
    H. Wang, C. Junghans, K. Kremer, Eur. Phys. J. E: Soft Matter Biol. Phys. 28(2), 221 (2009)CrossRefGoogle Scholar
  30. 30.
    J.D. Weeks, D. Chandler, H.C. Andersen, J. Chem. Phys. 54(12), 5237 (1971)CrossRefADSGoogle Scholar
  31. 31.
    H. Wang, C. Schütte, G. Ciccotti, L. Delle Site, J. Chem. Theor. Comput. 10(4), 1376 (2014)CrossRefGoogle Scholar
  32. 32.
    M.S. Green, J. Chem. Phys. 22, 398 (1954)MathSciNetCrossRefADSGoogle Scholar
  33. 33.
    R. Kubo, J. Phys. Soc. Jpn. 12(6), 570 (1957)MathSciNetCrossRefADSGoogle Scholar
  34. 34.
    W.L. Jorgensen, J. Chandrasekhar, J.D. Madura, R.W. Impey, M.L. Klein, J. Chem. Phys. 79(2), 926 (1983)CrossRefADSGoogle Scholar
  35. 35.
    S. Pronk, S. Páll, R. Schulz, P. Larsson, P. Bjelkmar, R. Apostolov, M.R. Shirts, J.C. Smith, P.M. Kasson, D. van der Spoel, H.B. Lindahl E., Bioinformatics, 1 (2013)Google Scholar
  36. 36.
    I. Fukuda, Y. Yonezawa, H. Nakamura, J. Chem. Phys. 134, 164107 (2011)CrossRefADSGoogle Scholar
  37. 37.
    I. Fukuda, J. Chem. Phys. 139, 174107 (2013)CrossRefADSGoogle Scholar
  38. 38.
    J. Apostolakis, P. Ferrara, A. Caflisch, J. Chem. Phys. 110(4), 2099 (1999)CrossRefADSGoogle Scholar
  39. 39.
    J.D. Chodera, N. Singhal, V.S. Pande, K.A. Dill, W.C. Swope, J. Chem. Phys. 126, 155101 (2007)CrossRefADSGoogle Scholar
  40. 40.
    J. Kaminskỳ, F. Jensen, J. Chem. Theor. Comput. 3(5), 1774 (2007)CrossRefGoogle Scholar
  41. 41.
    G. Feller, P. De Los Rios, A. Caflisch, F. Rao, Proc. Natl Acad. Sci. 104(6), 1817 (2007)CrossRefADSGoogle Scholar
  42. 42.
    N. Foloppe, A.D. MacKerell Jr., J. Comput. Chem. 21(2), 86 (2000)CrossRefGoogle Scholar
  43. 43.
    A.D. MacKerell, M. Feig, C.L. Brooks III, J. Comput. Chem. 25(11), 1400 (2004)CrossRefGoogle Scholar
  44. 44.
    J.-H. Prinz, B. Keller, F. Noé, Phys. Chem. Chem. Phys. 13(38), 16912 (2011)CrossRefGoogle Scholar
  45. 45.
    J.-H. Prinz, H. Wu, M. Sarich, B. Keller, M. Senne, M. Held, J.D. Chodera, C. Schütte, F. Noé, J. Chem. Phys. 134, 174105 (2011)CrossRefADSGoogle Scholar
  46. 46.
    C. Schütte, F. Noé, J. Lu, M. Sarich, E. Vanden-Eijnden, J. Chem. Phys. 134, 204105 (2011)CrossRefADSGoogle Scholar
  47. 47.
    M. Sarich, F. Noé, C. Schütte, Multiscale Model. Simul. 8(4), 1154 (2010)MathSciNetCrossRefGoogle Scholar
  48. 48.
    N. Djurdjevac, M. Sarich, C. Schütte, Multiscale Model. Simul. 10(1), 61 (2012)MathSciNetCrossRefGoogle Scholar
  49. 49.
    F. Noé, C. Schütte, E. Vanden-Eijnden, L. Reich, T.R. Weikl, Proc. Natl. Acad. Sci. 106(45), 19011 (2009)CrossRefADSGoogle Scholar
  50. 50.
    K.J. Kohlhoff, D. Shukla, M. Lawrenz, G.R. Bowman, D.E. Konerding, D. Belov, R.B. Altman, V.S. Pande, Nat. Chem. 6(1), 15 (2014)CrossRefGoogle Scholar
  51. 51.
    M. Senne, B. Trendelkamp-Schroer, A.S.J.S. Mey, C. Schütte, F. Noé, J. Chem. Theor. Comput. 8(7), 2223 (2012)CrossRefGoogle Scholar
  52. 52.
    B.W. Kernighan, D.M. Ritchie, P. Ejeklint, The C programming language, Vol. 2 (Prentice-Hall Englewood Cliffs, 1988)Google Scholar

Copyright information

© EDP Sciences and Springer 2015

Authors and Affiliations

  1. 1.CAEP Software Center for High Performance Numerical SimulationBeijingChina
  2. 2.Zuse Institute Berlin (ZIB)BerlinGermany
  3. 3.Institut für MathematikFreie Universität BerlinBerlinGermany

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