The European Physical Journal Special Topics

, Volume 227, Issue 14, pp 1547–1558 | Cite as

Studying equilibria of polymers in solution by direct molecular dynamics simulations: poly(N-isopropylacrylamide) in water as a test case

  • Edder J. GarcíaEmail author
  • Hans Hasse
Regular Article
Part of the following topical collections:
  1. Particle Methods in Natural Science and Engineering


It is well known that studying equilibria of polymers in solution by atomistic simulations is computationally demanding as a large phase space has to be adequately sampled. Nevertheless, direct molecular dynamics (MD) simulations are often used for this purpose in the literature. To assess whether such approach is adequate, we have conducted a case study for a polymer + solvent system that has been commonly studied with direct MD simulations by many authors: poly(N-isopropylacrylamide) (PNIPAM) in water. The total simulation time of the present study is much longer than that typically used in MD simulations of that system. A NIPAM chain of 30 monomers was studied in explicit water at 295 K. Three initial configurations were used. For each configuration, five replicas were run for 1000 ns. The statistical analysis of our data shows that the equilibration time is of the order of 600–700 ns and that the remaining time for the production run is not sufficient to sample the equilibrium state adequately. These results underpin the well-known difficulty of sampling equilibrium states of polymers in solution with direct MD simulations and the need for a careful interpretation of results of such studies. The problem with the unsatisfactory sampling persists despite the increasing available computing power. Therefore, enhanced sampling techniques and workarounds, such as simplified scenarios or coarse-graining, remain important.


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  1. 1.
    A. Grosberg, A. Khokhlov, Statistical physics of macromolecules (AIP Press, New York, NY, 1994)Google Scholar
  2. 2.
    S.M. Mel’nikov, V.G. Sergeyev, K. Yoshikawa, J. Am. Chem. Soc. 117, 2401 (1995)CrossRefGoogle Scholar
  3. 3.
    D. Ito, K. Kubota, Macromolecules 30, 7828 (1997)ADSCrossRefGoogle Scholar
  4. 4.
    M. Alaghemandi, S. Eckhard, Macromol. Theory Simul. 21, 106 (2011)CrossRefGoogle Scholar
  5. 5.
    S.A. Deshmukh, S.K.R.S. Sankaranarayanan, K. Suthar, D.C. Mancini, J. Phys. Chem. B 116, 2651 (2012)CrossRefGoogle Scholar
  6. 6.
    S.A. Deshmukh, Z. Li, G. Kamath, K.J. Suthar, S.K.R.S. Sankaranarayanan, D.C. Mancini, Polymer 54, 210 (2013)CrossRefGoogle Scholar
  7. 7.
    V. Botan, V. Ustach, R. Faller, K. Leonhard, J. Phys. Chem. B 120, 3434 (2016)CrossRefGoogle Scholar
  8. 8.
    G. Longhi, F. Lebon, S. Abbate, S.L. Fornili, Chem. Phys. Lett. 386, 123 (2004)ADSCrossRefGoogle Scholar
  9. 9.
    F. Gangemi, G. Longhi, S. Abbate, F. Lebon, R. Cordone, G.P. Ghilardi, S.L. Fornili, J. Phys. Chem. B 112, 11896 (2008)CrossRefGoogle Scholar
  10. 10.
    J. Walter, V. Ermatchkov, J. Vrabec, H. Hasse, Fluid Phase Equilib. 296, 164 (2010)CrossRefGoogle Scholar
  11. 11.
    H. Du, R. Wickramasinghe, X. Qian, J. Phys. Chem. B 114, 16594 (2010)CrossRefGoogle Scholar
  12. 12.
    E. Chiessi, A. Lonardi, G. Paradossi, J. Phys. Chem. B 114, 8301 (2010)CrossRefGoogle Scholar
  13. 13.
    Y. Kang, H. Joo, J.S. Kim, J. Phys. Chem. B 120, 13184 (2016)CrossRefGoogle Scholar
  14. 14.
    T.E. de Oliveira, D. Mukherji, K. Kremer, P.A. Netz, J. Chem. Phys. 146, 034904 (2017)ADSCrossRefGoogle Scholar
  15. 15.
    T.E. de Oliveira, C.M. Marques, P.A. Netz, Phys. Chem. Chem. Phys. 20, 10100 (2018)CrossRefGoogle Scholar
  16. 16.
    F. Afroze, E. Nies, H. Berghmans, J. Mol. Struct. 554, 55 (2000)ADSCrossRefGoogle Scholar
  17. 17.
    R. Gomesde Azevedo, L.P.N. Rebelo, A.M. Ramos, J. Szydlowski, H.C. de Sousa, J. Klein, Fluid Phase Equilib. 185, 189 (2001)CrossRefGoogle Scholar
  18. 18.
    A. Milewska, J. Szydlowski, L.P.N. Rebelo, J. Polymer Sci. Part B Polym. Phys. 41, 1219 (2003)ADSCrossRefGoogle Scholar
  19. 19.
    R. Singh, S.A. Deshmukh, G. Kamath, S.K.R.S. Sankaranarayanan, G. Balasubramanian, Comput. Mater. Sci. 126, 191 (2017)CrossRefGoogle Scholar
  20. 20.
    J.B. Clarage, T. Romo, B.K. Andrews, B.M. Pettitt, G.N. Phillips, Proc. Natl. Acad. Sci. 92, 3288 (1995)ADSCrossRefGoogle Scholar
  21. 21.
    S. Genheden, U. Ryde, Phys. Chem. Chem. Phys. 14, 8662 (2012)CrossRefGoogle Scholar
  22. 22.
    L. Sawle, K. Ghosh, J. Chem. Theory Comput. 12, 861 (2016)CrossRefGoogle Scholar
  23. 23.
    K. Lindorff-Larsen, S. Piana, R.O. Dror, D.E. Shaw, Science 334, 517 (2011)ADSCrossRefGoogle Scholar
  24. 24.
    C. Andrea, F. Philippe, C. Amedeo, Proteins Struct. Funct. Bioinf. 47, 305 (2002)CrossRefGoogle Scholar
  25. 25.
    E.J. García, D. Bhandary, M.T. Horsch, H. Hasse, J. Mol. Liq. 268, 294 (2018)CrossRefGoogle Scholar
  26. 26.
    C. Dalgicdir, F. Rodriguez-Ropero, N.F. van der Vegt, J. Phys. Chem. B 121, 7741 (2017)CrossRefGoogle Scholar
  27. 27.
    R.C. Bernardi, M.C. Melo, K. Schulten, Biochim. Biophys. Acta BBA-Gen. Subj. 1850, 872 (2015)CrossRefGoogle Scholar
  28. 28.
    M. Saunders, K.N. Houk, Y.D. Wu, W.C. Still, M. Lipton, G. Chang, W.C. Guida, J. Am. Chem. Soc. 112, 1419 (1990)CrossRefGoogle Scholar
  29. 29.
    T. Kawai, N. Tomioka, T. Ichinose, M. Takeda, A. Itai, Chem. Pharm. Bull. 42, 1315 (1994)CrossRefGoogle Scholar
  30. 30.
    I.T. Jørgensen, J. Comput. Aided Mol. Des. 11, 385 (1997)ADSCrossRefGoogle Scholar
  31. 31.
    S.K. Schiferl, D.C. Wallace, J. Chem. Phys. 83, 5203 (1985)ADSCrossRefGoogle Scholar
  32. 32.
    S.P. Brooks, A. Gelman, J. Comput. Graph. Stat. 7, 434 (1998)Google Scholar
  33. 33.
    W. Yang, R. Bitetti-Putzer, M. Karplus, J. Chem. Phys. 120, 2618 (2004)ADSCrossRefGoogle Scholar
  34. 34.
    A. Grossfield, D.M. Zuckerman, Annu. Rep. Comput. Chem. 5, 23 (2009)CrossRefGoogle Scholar
  35. 35.
    T.D. Romo, A. Grossfield, J. Chem. Theory Comput. 7, 2464 (2011)CrossRefGoogle Scholar
  36. 36.
    H.B. Mann, Econometrica 13, 245 (1945)MathSciNetCrossRefGoogle Scholar
  37. 37.
    M.G. Kendall, Rank correlation methods (C. Griffin, London, UK, 1975)Google Scholar
  38. 38.
    J. Kstner, W. Thiel, J. Chem. Phys. 124, 234106 (2006)ADSCrossRefGoogle Scholar
  39. 39.
    L.S. Caves, J.D. Evanseck, M. Karplus, Protein Sci. 7, 649 (1998)CrossRefGoogle Scholar
  40. 40.
    E. Chiessi, G. Paradossi, J. Phys. Chem. B 120, 3765 (2016)CrossRefGoogle Scholar
  41. 41.
    S.W.I. Siu, K. Pluhackova, R.A. Böckmann, J. Chem. Theory Comput. 8, 1459 (2012)CrossRefGoogle Scholar
  42. 42.
    G. Bussi, D. Donadio, M. Parrinello, J. Chem. Phys. 126, 014101 (2007)ADSCrossRefGoogle Scholar
  43. 43.
    H.J.C. Berendsen, J.P.M. Postma, V.W.F. Gunsteren, A. DiNola, J.R. Haak, J. Chem. Phys. 81, 3684 (1984)ADSCrossRefGoogle Scholar
  44. 44.
    M. Parrinello, A. Rahman, J. Appl. Phys. 52, 7182 (1981)ADSCrossRefGoogle Scholar
  45. 45.
    T. Darden, D. York, L. Pedersen, J. Chem. Phys. 98, 10089 (1993)ADSCrossRefGoogle Scholar
  46. 46.
    W.L. Jorgensen, D.S. Maxwell, J. Tirado-Rives, J. Am. Chem. Soc. 118, 11225 (1996)CrossRefGoogle Scholar
  47. 47.
    H.J.C. Berendsen, J.R. Grigera, T.P. Straatsma, J. Phys. Chem. 91, 6269 (1987)CrossRefGoogle Scholar
  48. 48.
    B. Hess, H. Bekker, H.J.C. Berendsen, J.G.E.M. Fraaije, J. Comput. Chem. 18, 1463 (1997)CrossRefGoogle Scholar
  49. 49.
    F.K. Anton, H. Berk, H.J.C. Berendsen, J. Comput. Chem. 20, 786 (1999)CrossRefGoogle Scholar
  50. 50.
    B. Loubet, W. Kopec, H. Khandelia, J. Chem. Theory Comput. 10, 5690 (2014)CrossRefGoogle Scholar
  51. 51.
    K. Olesen, N. Awasthi, D.S. Bruhn, W. Pezeshkian, H. Khandelia, J. Chem. Theory Comput. 14, 3342 (2018)CrossRefGoogle Scholar
  52. 52.
    D. Van Der Spoel, E. Lindahl, B. Hess, G. Groenhof, A.E. Mark, H.J.C. Berendsen, J. Comput. Chem. 26, 1701 (2005)CrossRefGoogle Scholar
  53. 53.
    M.J. Abraham, T. Murtola, R. Schulz, S. Páll, J.C. Smith, B. Hess, E. Lindahl, SoftwareX 1–2, 19 (2015)ADSCrossRefGoogle Scholar
  54. 54.
    V. Palivec, D. Zadrazil, J. Heyda, arXiv:1806.05592, (2018)
  55. 55.
    D. Mukherji, K. Kremer, Macromolecules 46, 9158 (2013)ADSCrossRefGoogle Scholar

Copyright information

© EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Laboratory of Engineering Thermodynamics (LTD), University of KaiserslauternKaiserslauternGermany

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