Molecular Modeling of Proteins pp 151-171

Part of the Methods in Molecular Biology book series (MIMB, volume 1215)

Tackling Sampling Challenges in Biomolecular Simulations

  • Alessandro Barducci
  • Jim Pfaendtner
  • Massimiliano Bonomi
Protocol

Abstract

Molecular dynamics (MD) simulations are a powerful tool to give an atomistic insight into the structure and dynamics of proteins. However, the time scales accessible in standard simulations, which often do not match those in which interesting biological processes occur, limit their predictive capabilities. Many advanced sampling techniques have been proposed over the years to overcome this limitation. This chapter focuses on metadynamics, a method based on the introduction of a time-dependent bias potential to accelerate sampling and recover equilibrium properties of a few descriptors that are able to capture the complexity of a process at a coarse-grained level. The theory of metadynamics and its combination with other popular sampling techniques such as the replica exchange method is briefly presented. Practical applications of these techniques to the study of the Trp-Cage miniprotein folding are also illustrated. The examples contain a guide for performing these calculations with PLUMED, a plugin to perform enhanced sampling simulations in combination with many popular MD codes.

Key words

Enhanced sampling Metadynamics PLUMED Replica exchange methods Molecular dynamics Collective variables Free energy 

References

  1. 1.
    Shaw DE, Maragakis P, Lindorff-Larsen K et al (2010) Atomic-level characterization of the structural dynamics of proteins. Science 330:341–346PubMedCrossRefGoogle Scholar
  2. 2.
    Beberg AL, Ensign DL, Jayachandran G, Khaliq S, Pande VS (2009) Folding@home: lessons from eight years of volunteer distributed computing, IEEE International Symposium on, Parallel & Distributed Processing, 2009. IPDPS 2009, 23-29 May 2009, Rome, pp. 1624–1631Google Scholar
  3. 3.
    Chipot C, Pohorille A (2007) Free energy calculations: theory and applications in chemistry and biology. Springer, BerlinCrossRefGoogle Scholar
  4. 4.
    Dellago C, Bolhuis PG (2009) Transition path sampling and other advanced simulation techniques for rare events. Adv Polym Sci 221:167–233Google Scholar
  5. 5.
    Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci U S A 99:12562–12566PubMedCrossRefPubMedCentralGoogle Scholar
  6. 6.
    Barducci A, Bonomi M, Parrinello M (2011) Metadynamics. Wir Comput Mol Sci 1:826–843CrossRefGoogle Scholar
  7. 7.
    Sugita Y, Okamoto Y (1999) Replica-exchange molecular dynamics method for protein folding. Chem Phys Lett 314:141–151CrossRefGoogle Scholar
  8. 8.
    Hansmann UHE (1997) Parallel tempering algorithm for conformational studies of biological molecules. Chem Phys Lett 281: 140–150CrossRefGoogle Scholar
  9. 9.
    Neidigh JW, Fesinmeyer RM, Andersen NH (2002) Designing a 20-residue protein. Nat Struct Biol 9:425–430PubMedCrossRefGoogle Scholar
  10. 10.
    Bonomi M, Branduardi D, Bussi G et al (2009) PLUMED: a portable plugin for free-energy calculations with molecular dynamics. Comput Phys Commun 180:1961–1972CrossRefGoogle Scholar
  11. 11.
    Barducci A, Bussi G, Parrinello M (2008) Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys Rev Lett 100:020603PubMedCrossRefGoogle Scholar
  12. 12.
    Bonomi M, Parrinello M (2010) Enhanced sampling in the well-tempered ensemble. Phys Rev Lett 104:190601PubMedCrossRefGoogle Scholar
  13. 13.
    Bonomi M, Barducci A, Parrinello M (2009) Reconstructing the equilibrium Boltzmann distribution from well-tempered metadynamics. J Comput Chem 30:1615–1621PubMedCrossRefGoogle Scholar
  14. 14.
    Barducci A, Bonomi M, Parrinello M (2010) Linking well-tempered metadynamics simulations with experiments. Biophys J 98:L44–L46PubMedCrossRefPubMedCentralGoogle Scholar
  15. 15.
    Earl DJ, Deem MW (2005) Parallel tempering: theory, applications, and new perspectives. Phys Chem Chem Phys 7:3910–3916PubMedCrossRefGoogle Scholar
  16. 16.
    Bussi G, Gervasio FL, Laio A, Parrinello M (2006) Free-energy landscape for beta hairpin folding from combined parallel tempering and metadynamics. J Am Chem Soc 128:13435–13441PubMedCrossRefGoogle Scholar
  17. 17.
    Deighan M, Bonomi M, Pfaendtner J (2012) Efficient simulation of explicitly solvated proteins in the well-tempered ensemble. J Chem Theory Comput 8:2189–2192CrossRefGoogle Scholar
  18. 18.
    Hess B, Kutzner C, van der Spoel D, Lindahl E (2008) GROMACS 4: algorithms for highly efficient, load-balanced, and scalable molecular simulation. J Chem Theory Comput 4:435–447CrossRefGoogle Scholar
  19. 19.
    Tribello GA, Bonomi M, Branduardi D, Camilloni C, Bussi G (2014) PLUMED 2: new feathers for an old bird, Comput Phys Commun 185:604–613Google Scholar
  20. 20.
    Pettersen EF, Goddard TD, Huang CC et al (2004) UCSF chimera - A visualization system for exploratory research and analysis. J Comput Chem 25:1605–1612PubMedCrossRefGoogle Scholar
  21. 21.
    Hunter JD (2007) Matplotlib: a 2D graphics environment. Comput Sci Eng 9:90–95CrossRefGoogle Scholar
  22. 22.
    Qiu LL, Pabit SA, Roitberg AE, Hagen SJ (2002) Smaller and faster: the 20-residue Trp-cage protein folds in 4 mu s. J Am Chem Soc 124:12952–12953PubMedCrossRefGoogle Scholar
  23. 23.
    Streicher WW, Makhatadze GI (2007) Unfolding thermodynamics of Trp-cage, a 20 residue miniprotein, studied by differential scanning calorimetry and circular dichroism spectroscopy. Biochemistry US 46:2876–2880CrossRefGoogle Scholar
  24. 24.
    Neuweiler H, Doose S, Sauer M (2005) A microscopic view of miniprotein folding: enhanced folding efficiency through formation of an intermediate. Proc Natl Acad Sci U S A 102:16650–16655PubMedCrossRefPubMedCentralGoogle Scholar
  25. 25.
    Ahmed Z, Beta IA, Mikhonin AV, Asher SA (2005) UV-resonance Raman thermal unfolding study of Trp-cage shows that it is not a simple two-state miniprotein. J Am Chem Soc 127:10943–10950PubMedCrossRefGoogle Scholar
  26. 26.
    Zhou RH (2003) Trp-cage: folding free energy landscape in explicit water. Proc Natl Acad Sci U S A 100:13280–13285PubMedCrossRefPubMedCentralGoogle Scholar
  27. 27.
    Ota M, Ikeguchi M, Kidera A (2004) Phylogeny of protein-folding trajectories reveals a unique pathway to native structure. Proc Natl Acad Sci U S A 101:17658–17663PubMedCrossRefPubMedCentralGoogle Scholar
  28. 28.
    Juraszek J, Bolhuis PG (2006) Sampling the multiple folding mechanisms of Trp-cage in explicit solvent. Proc Natl Acad Sci U S A 103:15859–15864PubMedCrossRefPubMedCentralGoogle Scholar
  29. 29.
    Paschek D, Nymeyer H, Garcia AE (2007) Replica exchange simulation of reversible folding/unfolding of the Trp-cage miniprotein in explicit solvent: on the structure and possible role of internal water. J Struct Biol 157:524–533PubMedCrossRefGoogle Scholar
  30. 30.
    Marinelli F, Pietrucci F, Laio A, Piana S (2009) A kinetic model of trp-cage folding from multiple biased molecular dynamics simulations. PLoS Comput Biol 5:e1000452PubMedCrossRefPubMedCentralGoogle Scholar
  31. 31.
    Lindorff-Larsen K, Piana S, Dror RO, Shaw DE (2011) How fast-folding proteins fold. Science 334:517–520PubMedCrossRefGoogle Scholar
  32. 32.
    Hornak V, Abel R, Okur A et al (2006) Comparison of multiple amber force fields and development of improved protein backbone parameters. Proteins 65:712–725PubMedCrossRefGoogle Scholar
  33. 33.
    Jorgensen WL, Chandrasekhar J, Madura JD, Impey RW, Klein ML (1983) Comparison of simple potential functions for simulating liquid water. J Chem Phys 79:926–935CrossRefGoogle Scholar
  34. 34.
    Branduardi D, Gervasio FL, Parrinello M (2007) From A to B in free energy space. J Chem Phys 126:054103PubMedCrossRefGoogle Scholar
  35. 35.
    Ceriotti M, Tribello GA, Parrinello M (2011) Simplifying the representation of complex free-energy landscapes using sketch-map. Proc Natl Acad Sci U S A 108:13023–13028PubMedCrossRefPubMedCentralGoogle Scholar
  36. 36.
    Spiwok V, Kralova B (2011) Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap. J Chem Phys 135:224504PubMedCrossRefGoogle Scholar
  37. 37.
    Piana S, Laio A (2007) A bias-exchange approach to protein folding. J Phys Chem B 111:4553–4559PubMedCrossRefGoogle Scholar
  38. 38.
    Sindhikara DJ, Emerson DJ, Roitberg AE (2010) Exchange often and properly in replica exchange molecular dynamics. J Chem Theory Comput 6:2804–2808CrossRefGoogle Scholar
  39. 39.
    Torrie GM, Valleau JP (1977) Non-physical sampling distributions in monte-carlo free-energy estimation - umbrella sampling. J Comput Phys 23:187–199CrossRefGoogle Scholar
  40. 40.
    Branduardi D, Bussi G, Parrinello M (2012) Metadynamics with adaptive gaussians. J Chem Theory Comput 8:2247–2254CrossRefGoogle Scholar
  41. 41.
    Prakash MK, Barducci A, Parrinello M (2011) Replica temperatures for uniform exchange and efficient roundtrip times in explicit solvent parallel tempering simulations. J Chem Theory Comput 7:2025–2027CrossRefGoogle Scholar
  42. 42.
    Nose S (1984) A unified formulation of the constant temperature molecular-dynamics methods. J Chem Phys 81:511–519CrossRefGoogle Scholar
  43. 43.
    Bussi G, Donadio D, Parrinello M (2007) Canonical sampling through velocity rescaling. J Chem Phys 126:014101PubMedCrossRefGoogle Scholar
  44. 44.
    Rosta E, Buchete NV, Hummer G (2009) Thermostat artifacts in replica exchange molecular dynamics simulations. J Chem Theory Comput 5:1393–1399PubMedCrossRefPubMedCentralGoogle Scholar
  45. 45.
    Ceriotti M, Brain GAR, Riordan O, Manolopoulos DE (2012) The inefficiency of re-weighted sampling and the curse of system size in high-order path integration. P Roy Soc a-Math Phys 468:2–17CrossRefGoogle Scholar
  46. 46.
    Angioletti-Uberti S, Ceriotti M, Lee PD, Finnis MW (2010) Solid-liquid interface free energy through metadynamics simulations. Phys Rev B 81:125416CrossRefGoogle Scholar
  47. 47.
    Berteotti A, Barducci A, Parrinello M (2011) Effect of urea on the beta-hairpin conformational ensemble and protein denaturation mechanism. J Am Chem Soc 133: 17200–17206PubMedCrossRefGoogle Scholar
  48. 48.
    Sutto L, D’Abramo M, Gervasio FL (2010) Comparing the efficiency of biased and unbiased molecular dynamics in reconstructing the free energy landscape of met-enkephalin. J Chem Theory Comput 6:3640–3646CrossRefGoogle Scholar
  49. 49.
    Kullback S, Leibler RA (1951) On Information and Sufficiency. Ann Math Stat 22:142–143CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Alessandro Barducci
    • 1
  • Jim Pfaendtner
    • 2
  • Massimiliano Bonomi
    • 3
  1. 1.Laboratory of Statistical Biophysics, School of Basic SciencesEcole Polytechnique Fédérale de LausanneLausanneSwitzerland
  2. 2.Department of Chemical EngineeringUniversity of WashingtonSeattleUSA
  3. 3.Department of ChemistryUniversity of CambridgeCambridgeUK

Personalised recommendations