Skip to main content
SpringerLink
Log in

Enhanced Sampling for Biomolecular Simulations

  • Chapter
  • First Online:
Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 8))

Abstract

The use of computer simulations as “virtual microscopes” is limited by sampling difficulties that arise from the large dimensionality and the complex energy landscapes of biological systems leading to poor convergences already in folding simulations of single proteins. In this chapter we discuss a few strategies to enhance sampling in biomolecular simulations, and present some recent applications.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 219.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Hardcover Book
USD 279.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

References

  1. Lindorff-Larsen, K., Piana, S., Dror, R.O., Shaw, D.E.: How fast-folding proteins fold. Science 334, 517–520 (2011)

    Article  Google Scholar 

  2. Chen, Y., Ding, F., Nie, H., Serohjos, A.W., Sharma, S., Wilocx, K.C., Yin, S., Dokholyan, N.V.: Protein folding: then and now. Arch. Biochem. Biophys. 469, 4–19 (2007)

    Article  Google Scholar 

  3. Daggett, V., Fersht, A.: Is there a unifying mechanism for protein folding? Trends Biochem. Sci. 28, 18–25 (2003)

    Article  Google Scholar 

  4. Daggett, V.: Molecular dynamics simulations of the protein unfolding/folding reaction. Acc. Chem. Res. 35, 422–429 (2002)

    Article  Google Scholar 

  5. Duane, S., Kennedy, A.D., Pendleton, B.J., Roweth, D.: Hybrid Monte Carlo. Phys. Lett. B195, 216–221 (1987)

    Article  Google Scholar 

  6. Brass, A., Pendleton, B.J., Chen, Y., Robson, B.: Hybrid Monte Carlo simulation theory and initial comparison with molecular dynamics. Biopolymers 33, 1307–1315 (1993)

    Article  Google Scholar 

  7. Berg, B.A.: Metropolis importance sampling for rugged dynamical variables. Phys. Rev. Lett 90, 180601 (2003)

    Article  Google Scholar 

  8. Hansmann, U.H.E., Wille, L.: Global optimization by energy landscape paving. Phys. Rev. Lett. 88, 068105 (2002)

    Article  Google Scholar 

  9. Schug, A., Wenzel, W., Hansmann, U.H.E.: Energy landscape paving simulations of the trp-cage protein. J. Chem. Phys. 122, 194711 (2005)

    Article  Google Scholar 

  10. Hansmann, U.H.E., Okamoto, Y.: The generalized-ensemble approach for protein folding simulations. In: Stauffer, D. (ed.) Annual Reviews in Computational Physics, pp. 129–157. World Scientific, Singapore (1998)

    Google Scholar 

  11. Kumar, S., Payne, P., Vásquez, M.: Method for free-energy calculations using iterative techniques. J. Comp. Chem. 17, 1269–1275 (1996)

    Article  Google Scholar 

  12. Torrie, G.M., Valleau, J.P.: Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comp. Phys. 23, 187–199 (1977)

    Article  Google Scholar 

  13. Berg, B.A., Neuhaus, T.: Multicanonical algorithms for first order phase transitions. Phys. Lett. B 267, 249–253 (1991)

    Article  Google Scholar 

  14. Hansmann, U.H.E., Okamoto, Y.: Prediction of peptide conformation by multicanonical algorithm: a new approach to the multiple-minima problem. J. Comp. Chem. 14, 1333–1338 (1993)

    Article  Google Scholar 

  15. Hansmann, U.H.E., Okamoto, Y., Eisenmenger, F.: Molecular dynamics, Langevin and hybrid Monte Carlo simulations in a multicanonical ensemble. Chem. Phys. Lett. 259, 321–330 (1996)

    Article  Google Scholar 

  16. Ferrenberg, A.M., Swendsen, R.H.: New Monte Carlo technique for studying phase transitions. Phys. Rev. Lett. 61, 2635–2638 (1988). Optimized Monte Carlo data analysis. Phys. Rev. Lett. 63, 1195–1198 (1989)

    Article  Google Scholar 

  17. Berg, B.A.: Markov chain Monte Carlo simulations and their statistical analysis. World Scientific, Singapore (2004)

    Book  MATH  Google Scholar 

  18. Hansmann, U.H.E., Okamoto, Y.: Comparative study of multicanonical and simulated annealing algorithms in the protein folding problem. Physica A 212, 415–437 (1994)

    Article  Google Scholar 

  19. Wang, F.G., Landau, D.P.: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86, 2050–2053 (2001)

    Article  Google Scholar 

  20. Hansmann, U.H.E., Okamoto, Y.: Finite-size scaling of helix-coil transitions in poly-alanine studied by multicanonical simulations. J. Chem. Phys. 110, 1267–1276 (1999)

    Article  Google Scholar 

  21. Hansmann, U.H.E., Okamoto, Y.: New Monte Carlo algorithms for protein folding. Curr. Opin. Struct. Biol. 9, 177–184 (1999)

    Article  Google Scholar 

  22. Curado, E.M.F., Tsallis, C.: Possible generalization of Boltzmann-Gibbs statistics. J. Phys. A: Math. Gen. 27, 3663 (1994)

    Article  Google Scholar 

  23. Wenzel, W., Hamacher, K.: Stochastic tunneling approach for global minimization of complex potential energy landscapes. Phys. Rev. Lett. 82, 3003 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  24. Hansmann, U.H.E.: Protein folding simulations in a deformed energy landscape. Eur. Phy. J. B 12, 607–612 (1999)

    Article  Google Scholar 

  25. Laio, A., Parrinello, M.: Escaping free-energy minima. Proc. Natl. Acad. Sci. USA 99, 12562–12566 (2002)

    Article  Google Scholar 

  26. Lyubartsev, A.P., Martinovski,  A.A., Shevkunov, S.V., Vorontsov-Velyaminov, P.N.: New approach to Monte Carlo calculations of the free energy: method of expanded ensembles. J. Chem. Phys. 96, 1776–1783 (1992). Marinari, E., Parisi, G.: Simulated tempering: a new Monte Carlo Scheme. Europhys. Lett. 19, 451–458 (1992)

    Google Scholar 

  27. Hukushima, K., Nemoto, K.: Exchange Monte Carlo method and applications to spin glass simulations. J. Phys. Soc. (Japan) 65, 1604–1608 (1996); Geyer, G.J., Thompson, E.A.: Annealing Markov chain Monte Carlo with applications to ancestral inference. J. Am. Stat. Assn. 90, 909–920 (1995)

    Article  Google Scholar 

  28. Hansmann, U.H.E.: Parallel tempering algorithm for conformational studies of biological molecules. Chem. Phys. Lett. 281, 140–150 (1997)

    Article  Google Scholar 

  29. Periole, X., Mark, A.E.: Convergence and sampling efficiency of replica-exchange molecular dynamic simulations of peptide folding in explicit solvent. J. Chem. Phys. 126, 014903 (2007)

    Article  Google Scholar 

  30. Abraham, M.J., Gready, J.E.: Ensuring mixing efficiency of replica-exchange molecular dynamics simulations. J. Chem. Theor. Comput. 4, 1119–1128 (2008)

    Article  Google Scholar 

  31. Sindhikara, D.J., Emerson, D.J., Roitberg, A.E.: Exchange often and properly in replica exchange molecular dynamics. J. Chem. Theor. Comput. 6, 2804–2808 (2010)

    Article  Google Scholar 

  32. Sindhikara, D.J., Emerson, D.J., Roitberg, A.E.: Exchange frequency in replica exchange molecular dynamics. J. Chem. Phys. 128, 10 (2008)

    Article  Google Scholar 

  33. Rhee, Y.M., Pande, V.S.: Multiplexed-replica exchange molecular dynamics method for protein folding simulation. Biophys. J. 84, 755–786 (2003)

    Article  Google Scholar 

  34. Wallace, J.A., Shen, J.K.: Continuous constant pH molecular dynamics in explicit solvent with pH-based replica exchange. J. Chem. Theor. Comput. 7, 2617–2629 (2011)

    Article  Google Scholar 

  35. Kwak, W., Hansmann, U.H.E.: Efficient sampling of protein structures by model hopping. Phys. Rev. Lett. 95, 138102 (2005)

    Article  Google Scholar 

  36. Fukunishi, H., Watanabe, O., Takada, S.: On the Hamiltonian replica exchange method for efficient sampling, of biomolecular systems: application to protein structure prediction. J. Chem. Phys. 116, 9058–9067 (2002)

    Article  Google Scholar 

  37. Sugita, Y., Kitao, A., Okamoto, Y.: Multidimensional replica-exchange method for free-energy calculations. J. Chem. Phys. 113, 6042–6051 (2000)

    Article  Google Scholar 

  38. Gront, D., Kolinski, A., Hansmann, U.H.E.: Exploring protein energy landscape with hierarchical clustering. Int. J. Quant. Chem. 105, 826 (2005)

    Article  Google Scholar 

  39. Williamson, T.E., Vitalis, A., Crick, S.L., Pappu, R.V.: Modulation of polyglutamine conformations and dimer formation by the N-terminus of huntingtin. J. Mol. Biol. 396, 1295–1309 (2010)

    Article  Google Scholar 

  40. Vitalis, A., Pappu, R.V.: Assessing the contribution of heterogeneous distributions of oligomers to aggregation mechanisms of polyglutamine peptides. Biophys. Chem. 159, 14–33 (2011)

    Article  Google Scholar 

  41. Nadler, W., Hansmann, U.H.E.: Generalized ensemble and tempering simulations: a unified view. Phys. Rev. E 75, 026109 (2007)

    Article  Google Scholar 

  42. Nadler, W., Hansmann, U.H.E.: Optimized explicit-solvent replica-exchange molecular dynamics from scratch. J. Phys. Chem. B 112, 10386 (2008)

    Article  Google Scholar 

  43. Trebst, S., Troyer, M., Hansmann, U.H.E.: Optimized parallel tempering simulations of proteins. J. Chem. Phys. 124, 174903 (2006)

    Article  Google Scholar 

  44. Nadler, W., Meinke, J.A., Hansmann, U.H.E.: Folding proteins by first-passage-times optimized replica exchange. Phys. Rev. E 78, 061905 (2008)

    Article  Google Scholar 

  45. Gallicchio, E., Levy, R.M., Parashar, M.: Asynchronous replica exchange for molecular simulations. J. Comput. Chem. 29, 788–794 (2008)

    Article  Google Scholar 

  46. Sugita, Y., Okamoto, Y.: Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 314, 141–151 (1999)

    Article  Google Scholar 

  47. Nadler, W., Hansmann, U.H.E.: Optimizing replica exchange moves for molecular dynamics. Phys. Rev. E 76, 057102 (2007)

    Article  Google Scholar 

  48. Kar, P., Nadler, W., Hansmann, U.H.E.: Microcanonical replica exchange molecular dynamics simulation of proteins. Phys. Rev. E 80, 056703 (2009)

    Article  Google Scholar 

  49. Kim, B., Hagen, M., Liu, P., Friesner, R.A., Berne, B.J.: Serial replica exchange. J. Phys. Chem. B. 111, 1416–1423 (2007)

    Article  Google Scholar 

  50. Lee, M., Olson, M.: Comparison of two adaptive temperature-based replica exchange methods applied to a sharp phase transition of protein unfolding-folding. J. Chem. Phys. 134, 244111 (2011)

    Article  Google Scholar 

  51. Okur, A., Wickstrom, L., Layten, M., Geney, R., Song, K., Hornak, V., Simmerling, C.: Improved efficiency of replica exchange simulations through use of a hybrid explicit/implicit solvation model. J. Chem. Theor. Comput. 2, 420–433 (2006)

    Article  Google Scholar 

  52. Huang, X., Hagen, M., Kim, B., Friesner, R.A., Zhou, R., Berne, B.J.: Replica exchange with solute tempering: efficiency in large scale systems. J. Phys. Chem. B 111, 5405–5410 (2007)

    Article  Google Scholar 

  53. Wang, J., Zhu, W., Li, G., Hansmann, U.H.E.: Velocity-scaling for replica exchange simulations of proteins in explicit solvent. J. Chem. Phys. 135, 084115 (2011)

    Article  Google Scholar 

  54. Yaşar, F., Bernhardt, N.A., Hansmann, U.H.E.: Replica-exchange-with-tunneling for fast exploration of protein landscapes. J. Chem. Phys. 143, 224102 (2015)

    Article  Google Scholar 

  55. Lyman, E., Ytreberg, F.M., Zuckerman, D.M.: Resolution exchange simulation. Phys. Rev. Lett. 96, 028105 (2006)

    Article  Google Scholar 

  56. Lyman, E., Zuckerman, D.M.: Resolution exchange simulation with incremental coarsening. J. Chem. Theor. Comput. 2, 656–666 (2006)

    Article  Google Scholar 

  57. Liu, P., Shi, Q., Lyman, E., Both, G.A.: Reconstructing atomistic detail for coarse-grained models with resolution exchange. J. Chem. Phys. 129, 114103 (2008)

    Article  Google Scholar 

  58. Moritsugu, K., Terada, T., Kidera, A.: Scalable free energy calculation of proteins via multiscale essential sampling. J. Chem. Phys. 133, 224105 (2010)

    Article  Google Scholar 

  59. Bernhardt, N.A., Xi, W., Wang, W., Hansmann, U.H.E.: Simulating protein fold switching by replica-exchange-with-tunneling. J. Chem. Theor. Comput. 12, 5656–5666 (2016); 13 393 (2017)

    Article  Google Scholar 

  60. Zhang, H., Xi, W., Hansmann, U.H.E., Wei, Y.: Fibril-barrel transitions in cylindrin amyloids. J. Chem. Theor. Comput. 13, 3936–3944 (2017)

    Article  Google Scholar 

  61. Mohanty, S., Meinke, J.H., Zimmermann, O., Hansmann, U.H.E.: Simulation of top7-CFr: a transient helix extension guides folding. Proc. Natl. Acad. Sci. U.S.A. 105, 8004–8007 (2008)

    Article  Google Scholar 

  62. Mohanty, S., Hansmann, U.H.E.: Caching of a chameleon segment facilitates folding of a protein with end-to-end \(\beta \) -sheet. J. Phys. Chem. B 112, 15134 (2008)

    Article  Google Scholar 

  63. Kuhlman, B., Dantas, G., Ireton, G.C., Varani, G., Stoddard, B.L., Baker, D.: Design of a novel globular protein fold with atomic level accuracy. Science 302, 1364–1368 (2003)

    Article  Google Scholar 

  64. Dantas, G., Watters, A.L., Lunde, B.M., Eletr, Z.M., Isern, N.G., Roseman, T., Lipfert, J., Doniach, S., Tompa, M., Kuhlman, B., Stoddard, B.L., Varani, G., Baker, D.: Mis-translation of a computationally designed protein yields an exceptionally stable homodimer: implications for protein engineering and evolution. J. Mol. Biol. 362, 1004–1024 (2006)

    Article  Google Scholar 

  65. Gaye, M.L., Hardwick, C., Kouza, M., Hansmann, U.H.E.: Chamelonicity and folding of the C-fragment of TOP7. Eur. Phys. Let. 97, 68003 (2012)

    Article  Google Scholar 

  66. Kouza, M., Gowtham, S., Seel, M., Hansmann, U.H.E.: A numerical investigation into possible mechanisms by that the A629P mutant of ATP7A causes Menkes Disease. Phys. Chem. Chem. Phys. 12, 11390–11397 (2010)

    Article  Google Scholar 

  67. Jiang, P., Hansmann, U.H.E.: Modeling structural flexibility of proteins with Go-models. J. Chem. Theor. Comput. 8, 2127–2133 (2012)

    Article  Google Scholar 

  68. Alexander, P., He, Y., Chen, Y., Orban, J., Bryan, P.: A minimal sequence code for switching protein structure and function. Proc. Natl. Acad. Sci U.S.A. 106, 21149–21154 (2009)

    Article  Google Scholar 

  69. Kouza, M., Hansmann, U.H.E.: Folding simulations of the A and B domains of protein G. J. Phys. Chem. B. 116, 6645–6653 (2012)

    Article  Google Scholar 

Download references

Acknowledgements

This article is an updated version of a review published in the first edition of this book, adding new algorithmic developments and applications. We thank Nathan Bernhardt, Yanjie Wei, Huilin Zang, Wei Wang, Wenhui Xi and Fatih Yasar for their contributions to work now also reviewed here. Support by the National Science Foundation (research grants CHE-998174, 0313618, 0809002, 1266256) and the National Institutes of Health (GM62838) are acknowledged.

Author information

Authors and Affiliations

  1. Department of Chemistry and Biochemistry, University of Oklahoma, Norman, 73019-5251, USA

    Workalemahu Berhanu & Ulrich H. E. Hansmann

  2. Tiandao, Education, Shanghai, People’s Republic of China

    Ping Jiang

Authors
  1. Workalemahu Berhanu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ping Jiang
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Ulrich H. E. Hansmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ping Jiang .

Editor information

Editors and Affiliations

  1. Faculty of Chemistry, University of Gdańsk, Gdańsk, Poland

    Adam Liwo

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Berhanu, W., Jiang, P., Hansmann, U.H.E. (2019). Enhanced Sampling for Biomolecular Simulations. In: Liwo, A. (eds) Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes. Springer Series on Bio- and Neurosystems, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-95843-9_8

Download citation

Publish with us

Policies and ethics

Search

Navigation