1932
0
  1. Home
  2. A-Z Publications
  3. Annual Review of Physical Chemistry
  4. Volume 67, 2016
  5. Article

Annual Review of Physical Chemistry

Volume 67, 2016

Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint

Abstract

Atomistic simulations play a central role in many fields of science. However, their usefulness is often limited by the fact that many systems are characterized by several metastable states separated by high barriers, leading to kinetic bottlenecks. Transitions between metastable states are thus rare events that occur on significantly longer timescales than one can simulate in practice. Numerous enhanced sampling methods have been introduced to alleviate this timescale problem, including methods based on identifying a few crucial order parameters or collective variables and enhancing the sampling of these variables. Metadynamics is one such method that has proven successful in a great variety of fields. Here we review the conceptual and theoretical foundations of metadynamics. As demonstrated, metadynamics is not just a practical tool but can also be considered an important development in the theory of statistical mechanics.

Keyword(s): atomistic simulations, collective variables, enhanced sampling, free energy calculations, kinetic bottlenecks, kinetic rate calculations
Loading

Article metrics loading...

/content/journals/10.1146/annurev-physchem-040215-112229
2016-05-27
2024-04-25
Loading full text...

Full text loading...

/deliver/fulltext/physchem/67/1/annurev-physchem-040215-112229.html?itemId=/content/journals/10.1146/annurev-physchem-040215-112229&mimeType=html&fmt=ahah

Literature Cited

  1. Frenkel D Smit. 1.  2002. Understanding Molecular Simulation New York: Academic, 2nd. ed.
  2. Tuckerman ME. 2.  2012. Statistical Mechanics: Theory and Molecular Simulation New York: Oxford Univ. Press
  3. Phillips JC, Braun R, Wang W, Gumbart J, Tajkhorshid E. 3.  et al. 2005. Scalable molecular dynamics with NAMD. J. Comput. Chem. 26:1781–802 [Google Scholar]
  4. Pronk S, Pall S, Schulz R, Larsson P, Bjelkmar P. 4.  et al. 2013. GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit. Bioinformatics 29:845–54 [Google Scholar]
  5. Páll S, Abraham MJ, Kutzner C, Hess B, Lindahl E. 5.  2015. Tackling exascale software challenges in molecular dynamics simulations with GROMACS. Lect. Notes Comput. Sci. 8759:3–27 [Google Scholar]
  6. Shaw DE, Chao JC, Eastwood MP, Gagliardo J, Grossman JP. 6.  et al. 2008. Anton, a special-purpose machine for molecular dynamics simulation. Commun. ACM 51:91–97 [Google Scholar]
  7. Lindorff-Larsen K, Piana S, Dror RO, Shaw DE. 7.  2011. How fast-folding proteins fold. Science 334:517–20 [Google Scholar]
  8. Shan Y, Kim ET, Eastwood MP, Dror RO, Seeliger MA, Shaw DE. 8.  2011. How does a drug molecule find its target binding site?. J. Am. Chem. Soc. 133:9181–83 [Google Scholar]
  9. Pan AC, Borhani DW, Dror RO, Shaw DE. 9.  2013. Molecular determinants of drug–receptor binding kinetics. Drug Discov. Today 18:667–73 [Google Scholar]
  10. Earl DJ, Deem MW. 10.  2005. Parallel tempering: theory, applications, and new perspectives. Phys. Chem. Chem. Phys. 7:3910–16 [Google Scholar]
  11. Bolhuis PG, Chandler D, Dellago C, Geissler PL. 11.  2002. Transition path sampling: throwing ropes over rough mountain passes, in the dark. Annu. Rev. Phys. Chem. 53:291–318 [Google Scholar]
  12. Voter AF, Montalenti F, Germann TC. 12.  2002. Extending the time scale in atomistic simulation of materials. Annu. Rev. Mater. Res. 32:321–46 [Google Scholar]
  13. Perez D, Uberuaga BP, Shim Y, Amar JG, Voter AF. 13.  2009. Accelerated molecular dynamics methods: introduction and recent developments. Annu. Rep. Comput. Chem. 5:79–98 [Google Scholar]
  14. Chipot C, Pohorille A. 14.  2007. Free Energy Calculations: Theory and Applications in Chemistry and Biology Berlin: Springer-Verlag
  15. Allen RJ, Valeriani C, Rein ten Wolde P. 15.  2009. Forward flux sampling for rare event simulations. J. Phys. Condens. Matter 21:463102 [Google Scholar]
  16. E W, Vanden-Eijnden E. 16.  2010. Transition-path theory and path-finding algorithms for the study of rare events. Annu. Rev. Phys. Chem. 61:391–420 [Google Scholar]
  17. Singh S, Chopra M, de Pablo JJ. 17.  2012. Density of states–based molecular simulations. Annu. Rev. Chem. Biomol. Eng. 3:369–94 [Google Scholar]
  18. Abrams C, Bussi G. 18.  2013. Enhanced sampling in molecular dynamics using metadynamics, replica-exchange, and temperature-acceleration. Entropy 16:163–99 [Google Scholar]
  19. Doshi U, Hamelberg D. 19.  2015. Towards fast, rigorous and efficient conformational sampling of biomolecules: advances in accelerated molecular dynamics. Biochim. Biophys. Acta 1850:878–88 [Google Scholar]
  20. Torrie G, Valleau J. 20.  1977. Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J. Comput. Phys. 23:187–99 [Google Scholar]
  21. Huber T, Torda AE, Gunsteren WF. 21.  1994. Local elevation: a method for improving the searching properties of molecular dynamics simulation. J. Comput.-Aided Mol. Des. 8:695–708 [Google Scholar]
  22. Darve E, Pohorille A. 22.  2001. Calculating free energies using average force. J. Chem. Phys. 115:9169–83 [Google Scholar]
  23. Wang F, Landau D. 23.  2001. Efficient, multiple-range random walk algorithm to calculate the density of states. Phys. Rev. Lett. 86:2050–53 [Google Scholar]
  24. Hansmann U, Wille L. 24.  2002. Global optimization by energy landscape paving. Phys. Rev. Lett. 88:068105 [Google Scholar]
  25. Maragakis P, van der Vaart A, Karplus M. 25.  2009. Gaussian-mixture umbrella sampling. J. Phys. Chem. B 113:4664–73 [Google Scholar]
  26. Laio A, Parrinello M. 26.  2002. Escaping free-energy minima. PNAS 99:12562–66 [Google Scholar]
  27. Ensing B, De Vivo M, Liu Z, Moore P, Klein ML. 27.  2006. Metadynamics as a tool for exploring free energy landscapes of chemical reactions. Acc. Chem. Res. 39:73–81 [Google Scholar]
  28. Laio A, Gervasio FL. 28.  2008. Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science. Rep. Prog. Phys. 71:126601 [Google Scholar]
  29. Barducci A, Bonomi M, Parrinello M. 29.  2011. Metadynamics. WIREs Comput. Mol. Sci. 1:826–43 [Google Scholar]
  30. Sutto L, Marsili S, Gervasio FL. 30.  2012. New advances in metadynamics. WIREs Comput. Mol. Sci. 2:771–79 [Google Scholar]
  31. Zheng S, Pfaendtner J. 31.  2014. Enhanced sampling of chemical and biochemical reactions with metadynamics. Mol. Simul. 41:55–72 [Google Scholar]
  32. Giberti F, Salvalaglio M, Parrinello M. 32.  2015. Metadynamics studies of crystal nucleation. IUCrJ 2:256–66 [Google Scholar]
  33. Cavalli A, Spitaleri A, Saladino G, Gervasio FL. 33.  2015. Investigating drug–target association and dissociation mechanisms using metadynamics-based algorithms. Acc. Chem. Res. 48:277–85 [Google Scholar]
  34. Bussi G, Branduardi D. 34.  2015. Free-energy calculations with metadynamics: theory and practice. Rev. Comput. Chem. 28:1–49 [Google Scholar]
  35. Leone V, Marinelli F, Carloni P, Parrinello M. 35.  2010. Targeting biomolecular flexibility with metadynamics. Curr. Opin. Struct. Biol. 20:148–54 [Google Scholar]
  36. Biarnés X, Bongarzone S, Vargiu AV, Carloni P, Ruggerone P. 36.  2011. Molecular motions in drug design: the coming age of the metadynamics method. J. Comput.-Aided Mol. Des. 25:395–402 [Google Scholar]
  37. Branduardi D, Gervasio FL, Cavalli A, Recanatini M, Parrinello M. 37.  2005. The role of the peripheral anionic site and cation–π interactions in the ligand penetration of the human AChE gorge. J. Am. Chem. Soc. 1279147–55
  38. Blumberger J, Ensing B, Klein ML. 38.  2006. Formamide hydrolysis in alkaline aqueous solution: insight from ab initio metadynamics calculations. Angew. Chem. Int. Ed. 45:2893–97 [Google Scholar]
  39. Lau D, Broderick K, Buehler MJ, Büyüköztürk O. 39.  2014. A robust nanoscale experimental quantification of fracture energy in a bilayer material system. PNAS 111:11990–95 [Google Scholar]
  40. Zhu Q, Zeng Q, Oganov AR. 40.  2012. Systematic search for low-enthalpy sp3carbon allotropes using evolutionary metadynamics. Phys. Rev. B 85201407
  41. Dopieralski P, Ribas-Arino J, Anjukandi P, Krupicka M, Kiss J, Marx D. 41.  2013. The janus-faced role of external forces in mechanochemical disulfide bond cleavage. Nat. Chem. 5:685–91 [Google Scholar]
  42. Jug K, Nair NN, Bredow T. 42.  2005. Molecular dynamics investigation of oxygen vacancy diffusion in rutile. Phys. Chem. Chem. Phys. 7:2616–21 [Google Scholar]
  43. Granata D, Camilloni C, Vendruscolo M, Laio A. 43.  2013. Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics. PNAS 110:6817–22 [Google Scholar]
  44. Tiwary P, Limongelli V, Salvalaglio M, Parrinello M. 44.  2015. Kinetics of protein–ligand unbinding: predicting pathways, rates, and rate-limiting steps. PNAS 112:E386–91 [Google Scholar]
  45. Limongelli V, Bonomi M, Marinelli L, Gervasio FL, Cavalli A. 45.  et al. 2010. Molecular basis of cyclooxygenase enzymes (COXs) selective inhibition. PNAS 107:5411–16 [Google Scholar]
  46. Saladino G, Gauthier L, Bianciotto M, Gervasio FL. 46.  2012. Assessing the performance of metadynamics and path variables in predicting the binding free energies of p38 inhibitors. J. Am. Chem. Soc. 8:1165–70 [Google Scholar]
  47. Provasi D, Bortolato A, Filizola M. 47.  2009. Exploring molecular mechanisms of ligand recognition by opioid receptors with metadynamics. Biochemistry 48:10020–29 [Google Scholar]
  48. Delemotte L, Kasimova MA, Klein ML, Tarek M, Carnevale V. 48.  2014. Free-energy landscape of ion-channel voltage-sensor–domain activation. PNAS 112:124–29 [Google Scholar]
  49. McCullagh M, Saunders MG, Voth GA. 49.  2014. Unraveling the mystery of ATP hydrolysis in actin filaments. J. Am. Chem. Soc. 136:13053–58 [Google Scholar]
  50. Angioletti-Uberti S, Ceriotti M, Lee PD, Finnis MW. 50.  2010. Solid-liquid interface free energy through metadynamics simulations. Phys. Rev. B 81:125416 [Google Scholar]
  51. Salvalaglio M, Vetter T, Giberti F, Mazzotti M, Parrinello M. 51.  2012. Uncovering molecular details of urea crystal growth in the presence of additives. J. Am. Chem. Soc. 134:17221–33 [Google Scholar]
  52. De Wispelaere K, Ensing B, Ghysels A, Meijer EJ, Van Speybroeck V. 52.  2015. Complex reaction environments and competing reaction mechanisms in zeolite catalysis: insights from advanced molecular dynamics. Chem. Eur. J. 21:9385–96 [Google Scholar]
  53. Polino D, Parrinello M. 53.  2015. Combustion chemistry via metadynamics: benzyl decomposition revisited. J. Phys. Chem. A 119:978–89 [Google Scholar]
  54. Doro F, Saladino G, Belvisi L, Civera M, Gervasio FL. 54.  2015. New insights into the molecular mechanism of E-cadherin-mediated cell adhesion by free energy calculations. J. Chem. Theory Comput. 11:1354–59 [Google Scholar]
  55. Iglesias-Fernández J, Raich L, Ardèvol A, Rovira C. 55.  2015. The complete conformational free energy landscape of β-xylose reveals a two-fold catalytic itinerary for β-xylanases. Chem. Sci. 6:1167–77 [Google Scholar]
  56. Ma C, Pietrucci F, Andreoni W. 56.  2015. Capture and release of CO2 in monoethanolamine aqueous solutions: new insights from first-principles reaction dynamics. J. Chem. Theory Comput. 11:3189–98 [Google Scholar]
  57. Palazzesi F, Barducci A, Tollinger M, Parrinello M. 57.  2013. The allosteric communication pathways in KIX domain of CBP. PNAS 110:14237–42 [Google Scholar]
  58. Burney PR, White N, Pfaendtner J. 58.  2014. Structural effects of methionine oxidation on isolated subdomains of human fibrin D and αC regions. PLOS ONE 9:e86981 [Google Scholar]
  59. Zhang Z, Schindler CEM, Lange OF, Zacharias M. 59.  2015. Application of enhanced sampling Monte Carlo methods for high-resolution protein-protein docking in Rosetta. PLOS ONE 10:e0125941 [Google Scholar]
  60. Loerbroks C, Boulanger E, Thiel W. 60.  2015. Solvent influence on cellulose 1,4–glycosidic bond cleavage: a molecular dynamics and metadynamics study. Chem. Eur. J. 21:5477–87 [Google Scholar]
  61. Landau L, Lifshitz E. 61.  1980. Statistical Physics Oxford, UK: Butterworth-Heinemann, 3rd ed..
  62. Marcus RA. 62.  1993. Electron transfer reactions in chemistry: theory and experiment. Rev. Mod. Phys. 65:599–610 [Google Scholar]
  63. Zwanzig R. 63.  2003. Nonequilibrium Statistical Mechanics New York: Oxford Univ. Press
  64. Barducci A, Bussi G, Parrinello M. 64.  2008. Well-tempered metadynamics: a smoothly converging and tunable free-energy method. Phys. Rev. Lett. 100:020603 [Google Scholar]
  65. Dama JF, Parrinello M, Voth GA. 65.  2014. Well-tempered metadynamics converges asymptotically. Phys. Rev. Lett. 112:240602 [Google Scholar]
  66. VandeVondele J, Rothlisberger U. 66.  2002. Canonical adiabatic free energy sampling (CAFES): a novel method for the exploration of free energy surfaces. J. Phys. Chem. B 106:203–8 [Google Scholar]
  67. Rosso L, Mináry P, Zhu Z, Tuckerman ME. 67.  2002. On the use of the adiabatic molecular dynamics technique in the calculation of free energy profiles. J. Chem. Phys. 116:4389–402 [Google Scholar]
  68. Maragliano L, Vanden-Eijnden E. 68.  2006. A temperature accelerated method for sampling free energy and determining reaction pathways in rare events simulations. Chem. Phys. Lett. 426:168–75 [Google Scholar]
  69. Bonomi M, Barducci A, Parrinello M. 69.  2009. Reconstructing the equilibrium Boltzmann distribution from well-tempered metadynamics. J. Comput. Chem. 30:1615–21 [Google Scholar]
  70. Tiwary P, Parrinello M. 70.  2015. A time-independent free energy estimator for metadynamics. J. Phys. Chem. B 119:736–42 [Google Scholar]
  71. Tiwary P, Parrinello M. 71.  2013. From metadynamics to dynamics. Phys. Rev. Lett. 111:230602 [Google Scholar]
  72. Iannuzzi M, Laio A, Parrinello M. 72.  2003. Efficient exploration of reactive potential energy surfaces using Car-Parrinello molecular dynamics. Phys. Rev. Lett. 90:238302 [Google Scholar]
  73. Laio A, Rodriguez-Fortea A, Gervasio FL, Ceccarelli M, Parrinello M. 73.  2005. Assessing the accuracy of metadynamics. J. Phys. Chem. B 109:6714–21 [Google Scholar]
  74. Branduardi D, Bussi G, Parrinello M. 74.  2012. Metadynamics with adaptive Gaussians. J. Chem. Theory Comput. 8:2247–54 [Google Scholar]
  75. Micheletti C, Laio A, Parrinello M. 75.  2004. Reconstructing the density of states by history-dependent metadynamics. Phys. Rev. Lett. 92:170601 [Google Scholar]
  76. Tiwary P, Dama JF, Parrinello M. 76.  2015. A perturbative solution to metadynamics ordinary differential equation. J. Chem. Phys. 116:4389–402 [Google Scholar]
  77. Kushner HJ, Yin GG. 77.  2003. Stochastic Approximation and Recursive Algorithms and Applications Berlin: Springer-Verlag, 2nd ed..
  78. Bonomi M, Branduardi D, Bussi G, Camilloni C, Provasi D. 78.  et al. 2009. PLUMED: a portable plugin for free-energy calculations with molecular dynamics. Comput. Phys. Commun. 180:1961–72 [Google Scholar]
  79. Tribello GA, Bonomi M, Branduardi D, Camilloni C, Bussi G. 79.  2014. PLUMED 2: new feathers for an old bird. Comput. Phys. Commun. 185:604–13 [Google Scholar]
  80. Branduardi D, Gervasio FL, Parrinello M. 80.  2007. From A to B in free energy space. J. Chem. Phys. 126:054103 [Google Scholar]
  81. Bonomi M, Parrinello M. 81.  2010. Enhanced sampling in the well-tempered ensemble. Phys. Rev. Lett. 104:190601 [Google Scholar]
  82. Pietrucci F, Andreoni W. 82.  2011. Graph theory meets ab initio molecular dynamics: atomic structures and transformations at the nanoscale. Phys. Rev. Lett. 107:085504 [Google Scholar]
  83. Limongelli V, Bonomi M, Parrinello M. 83.  2013. Funnel metadynamics as accurate binding free-energy method. PNAS 110:6358–63 [Google Scholar]
  84. Quhe R, Nava M, Tiwary P, Parrinello M. 84.  2015. Path integral metadynamics. J. Chem. Theory Comput. 11:1383–88 [Google Scholar]
  85. Bussi G, Gervasio FL, Laio A, Parrinello M. 85.  2006. Free-energy landscape for β hairpin folding from combined parallel tempering and metadynamics. J. Am. Chem. Soc. 128:13435–41 [Google Scholar]
  86. Henkelman G, Uberuaga BP, Jónsson H. 86.  2000. A climbing image nudged elastic band method for finding saddle points and minimum energy paths. J. Chem. Phys. 113:9901–4 [Google Scholar]
  87. Ren W, Vanden-Eijnden E. 87.  2005. Finite temperature string method for the study of rare events. J. Phys. Chem. B 109:6688–93 [Google Scholar]
  88. Tribello GA, Ceriotti M, Parrinello M. 88.  2010. A self-learning algorithm for biased molecular dynamics. PNAS 107:17509–14 [Google Scholar]
  89. Ceriotti M, Tribello GA, Parrinello M. 89.  2011. Simplifying the representation of complex free-energy landscapes using sketch-map. PNAS 108:13023–28 [Google Scholar]
  90. Ceriotti M, Tribello GA, Parrinello M. 90.  2013. Demonstrating the transferability and the descriptive power of sketch-map. J. Chem. Theory Comput. 9:1521–32 [Google Scholar]
  91. Ardevol A, Tribello GA, Ceriotti M, Parrinello M. 91.  2015. Probing the unfolded configurations of a β-hairpin using sketch-map. J. Chem. Theory Comput. 11:1086–93 [Google Scholar]
  92. Tribello GA, Ceriotti M, Parrinello M. 92.  2012. Using sketch-map coordinates to analyze and bias molecular dynamics simulations. PNAS 109:5196–201 [Google Scholar]
  93. Coifman RR, Kevrekidis IG, Lafon S, Maggioni M, Nadler B. 93.  2008. Diffusion maps, reduction coordinates, and low dimensional representation of stochastic systems. Multiscale Model. Simul. 7:842–64 [Google Scholar]
  94. Rohrdanz MA, Zheng W, Maggioni M, Clementi C. 94.  2011. Determination of reaction coordinates via locally scaled diffusion map. J. Chem. Phys. 134:124116 [Google Scholar]
  95. Rohrdanz MA, Zheng W, Clementi C. 95.  2013. Discovering mountain passes via torchlight: methods for the definition of reaction coordinates and pathways in complex macromolecular reactions. Annu. Rev. Phys. Chem. 64:295–316 [Google Scholar]
  96. Hashemian B, Millán D, Arroyo M. 96.  2013. Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables. J. Chem. Phys. 139:214101 [Google Scholar]
  97. Gasparotto P, Ceriotti M. 97.  2014. Recognizing molecular patterns by machine learning: an agnostic structural definition of the hydrogen bond. J. Chem. Phys. 141:174110 [Google Scholar]
  98. Chen M, Yu TQ, Tuckerman ME. 98.  2015. Locating landmarks on high-dimensional free energy surfaces. PNAS 112:3235–40 [Google Scholar]
  99. Wales D. 99.  2003. Energy Landscapes: Applications to Clusters, Biomolecules and Glasses Cambridge, UK: Cambridge Univ. Press
  100. Valsson O, Parrinello M. 100.  2013. Thermodynamical description of a quasi-first-order phase transition from the well-tempered ensemble. J. Chem. Theory Comput. 9:5267–76 [Google Scholar]
  101. Berg B, Neuhaus T. 101.  1992. Multicanonical ensemble: a new approach to simulate first-order phase transitions. Phys. Rev. Lett. 68:9–12 [Google Scholar]
  102. Hansmann UH. 102.  1997. Parallel tempering algorithm for conformational studies of biological molecules. Chem. Phys. Lett. 281:140–50 [Google Scholar]
  103. Sugita Y, Okamoto Y. 103.  1999. Replica-exchange molecular dynamics method for protein folding. Chem. Phys. Lett. 314:141–51 [Google Scholar]
  104. Fukunishi H, Watanabe O, Takada S. 104.  2002. On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: application to protein structure prediction. J. Chem. Phys. 116:9058–67 [Google Scholar]
  105. Liu P, Kim B, Friesner RA, Berne BJ. 105.  2005. Replica exchange with solute tempering: a method for sampling biological systems in explicit water. PNAS 102:13749–54 [Google Scholar]
  106. Wang L, Friesner RA, Berne BJ. 106.  2011. Replica exchange with solute scaling: a more efficient version of replica exchange with solute tempering (REST2). J. Phys. Chem. B 115:9431–38 [Google Scholar]
  107. Bussi G. 107.  2013. Hamiltonian replica exchange in GROMACS: a flexible implementation. Mol. Phys. 112:379–84 [Google Scholar]
  108. Deighan M, Bonomi M, Pfaendtner J. 108.  2012. Efficient simulation of explicitly solvated proteins in the well-tempered ensemble. J. Chem. Theory Comput. 8:2189–92 [Google Scholar]
  109. Gil-Ley A, Bussi G. 109.  2015. Enhanced conformational sampling using replica exchange with collective-variable tempering. J. Chem. Theory Comput. 11:1077–85 [Google Scholar]
  110. Camilloni C, Provasi D, Tiana G, Broglia RA. 110.  2007. Exploring the protein G helix free-energy surface by solute tempering metadynamics. Proteins 71:1647–54 [Google Scholar]
  111. Piana S, Laio A. 111.  2007. A bias-exchange approach to protein folding. J. Phys. Chem. B 111:4553–59 [Google Scholar]
  112. Baftizadeh F, Cossio P, Pietrucci F, Laio A. 112.  2012. Protein folding and ligand-enzyme binding from bias-exchange metadynamics simulations. Curr. Phys. Chem. 2:79–91 [Google Scholar]
  113. Marinelli F, Pietrucci F, Laio A, Piana S. 113.  2009. A kinetic model of Trp-cage folding from multiple biased molecular dynamics simulations. PLOS Comput. Biol. 5:e1000452 [Google Scholar]
  114. Raiteri P, Laio A, Gervasio FL, Micheletti C, Parrinello M. 114.  2006. Efficient reconstruction of complex free energy landscapes by multiple walkers metadynamics. J. Phys. Chem. B 110:3533–39 [Google Scholar]
  115. Singh S, Chiu CC, de Pablo JJ. 115.  2011. Flux tempered metadynamics. J. Stat. Phys. 145:932–45 [Google Scholar]
  116. Singh S, Chiu CC, de Pablo JJ. 116.  2012. Efficient free energy calculation of biomolecules from diffusion-biased molecular dynamics. J. Chem. Theory Comput. 8:4657–62 [Google Scholar]
  117. Trebst S, Huse D, Troyer M. 117.  2004. Optimizing the ensemble for equilibration in broad-histogram Monte Carlo simulations. Phys. Rev. E 70:046701 [Google Scholar]
  118. Dama JF, Rotskoff G, Parrinello M, Voth GA. 118.  2014. Transition-tempered metadynamics: robust, convergent metadynamics via on-the-fly transition barrier estimation. J. Chem. Theory Comput. 10:3626–33 [Google Scholar]
  119. McGovern M, de Pablo J. 119.  2013. A boundary correction algorithm for metadynamics in multiple dimensions. J. Chem. Phys. 139:084102 [Google Scholar]
  120. Bussi G, Laio A, Parrinello M. 120.  2006. Equilibrium free energies from nonequilibrium metadynamics. Phys. Rev. Lett. 96:090601 [Google Scholar]
  121. Crespo Y, Marinelli F, Pietrucci F, Laio A. 121.  2010. Metadynamics convergence law in a multidimensional system. Phys. Rev. E 81:055701 [Google Scholar]
  122. Carter E, Ciccotti G, Hynes JT, Kapral R. 122.  1989. Constrained reaction coordinate dynamics for the simulation of rare events. Chem. Phys. Lett. 156:472–77 [Google Scholar]
  123. Faradjian AK, Elber R. 123.  2004. Computing time scales from reaction coordinates by milestoning. J. Chem. Phys. 120:10880–89 [Google Scholar]
  124. Voter AF. 124.  1997. A method for accelerating the molecular dynamics simulation of infrequent events. J. Chem. Phys. 106:4665–77 [Google Scholar]
  125. Voter AF. 125.  1997. Hyperdynamics: accelerated molecular dynamics of infrequent events. Phys. Rev. Lett. 78:3908–11 [Google Scholar]
  126. Voter AF. 126.  1998. Parallel replica method for dynamics of infrequent events. Phys. Rev. B 57:R13985 [Google Scholar]
  127. Grubmüller H. 127.  1995. Predicting slow structural transitions in macromolecular systems: conformational flooding. Phys. Rev. E 52:2893–906 [Google Scholar]
  128. Tiwary P, van de Walle A. 128.  2011. Hybrid deterministic and stochastic approach for efficient atomistic simulations at long time scales. Phys. Rev. B 84:100301 [Google Scholar]
  129. Tiwary P, van de Walle A. 129.  2013. Accelerated molecular dynamics through stochastic iterations and collective variable based basin identification. Phys. Rev. B 87:094304 [Google Scholar]
  130. Henkelman G, Jónsson H. 130.  2001. Long time scale kinetic Monte Carlo simulations without lattice approximation and predefined event table. J. Chem. Phys. 115:9657–66 [Google Scholar]
  131. Prinz JH, Wu H, Sarich M, Keller B, Senne M. 131.  et al. 2011. Markov models of molecular kinetics: generation and validation. J. Chem. Phys. 134:174105 [Google Scholar]
  132. Juraszek J, Saladino G, van Erp T, Gervasio F. 132.  2013. Efficient numerical reconstruction of protein folding kinetics with partial path sampling and pathlike variables. Phys. Rev. Lett. 110:108106 [Google Scholar]
  133. Salvalaglio M, Tiwary P, Parrinello M. 133.  2014. Assessing the reliability of the dynamics reconstructed from metadynamics. J. Chem. Theory Comput. 10:1420–25 [Google Scholar]
  134. Berne BJ, Borkovec M, Straub JE. 134.  1988. Classical and modern methods in reaction rate theory. J. Chem. Phys. 92:3711–25 [Google Scholar]
  135. Grote RF, Hynes JT. 135.  1980. The stable states picture of chemical reactions. II. Rate constants for condensed and gas phase reaction models. J. Chem. Phys. 73:2715–32 [Google Scholar]
  136. Hänggi P, Talkner P, Borkovec M. 136.  1990. Reaction-rate theory: fifty years after Kramers. Rev. Mod. Phys. 62:251–341 [Google Scholar]
  137. Bolhuis PG, Dellago C, Chandler D. 137.  2000. Reaction coordinates of biomolecular isomerization. PNAS 97:5877–82 [Google Scholar]
  138. Best RB, Hummer G. 138.  2005. Reaction coordinates and rates from transition paths. PNAS 102:6732–37 [Google Scholar]
  139. Straub JE, Berne BJ. 139.  1985. A rapid method for determining rate constants by molecular dynamics. J. Chem. Phys. 83:1138–39 [Google Scholar]
  140. Mullen RG, Shea JE, Peters B. 140.  2014. Transmission coefficients, committors, and solvent coordinates in ion-pair dissociation. J. Chem. Theory Comput. 10:659–67 [Google Scholar]
  141. Bohner MU, Zeman J, Smiatek J, Arnold A, Kästner J. 141.  2014. Nudged-elastic band used to find reaction coordinates based on the free energy. J. Chem. Phys. 140:074109 [Google Scholar]
  142. Sicard F, Destainville N, Manghi M. 142.  2015. DNA denaturation bubbles: free-energy landscape and nucleation/closure rates. J. Chem. Phys. 142:034903 [Google Scholar]
  143. Tiwary P, Mondal J, Morrone JA, Berne BJ. 143.  2015. Role of water and steric constraints in the kinetics of cavity-ligand unbinding. PNAS 112:12015–19 [Google Scholar]
  144. Valsson O, Parrinello M. 144.  2014. Variational approach to enhanced sampling and free energy calculations. Phys. Rev. Lett. 113:090601 [Google Scholar]
  145. Chaimovich A, Shell MS. 145.  2011. Coarse-graining errors and numerical optimization using a relative entropy framework. J. Chem. Phys. 134:094112 [Google Scholar]
  146. de Boer PT, Kroese DP, Mannor S, Rubinstein RY. 146.  2005. A tutorial on the cross-entropy method. Ann. Oper. Res. 134:19–67 [Google Scholar]
  147. Bilionis I, Koutsourelakis P. 147.  2012. Free energy computations by minimization of Kullback–Leibler divergence: an efficient adaptive biasing potential method for sparse representations. J. Comput. Phys. 231:3849–70 [Google Scholar]
  148. Bach F, Moulines E. 148.  2013. Non-strongly-convex smooth stochastic approximation with convergence rate O(1/n). Advances in Neural Information Processing Systems 26 C Burges, L Bottou, M Welling, Z Ghahramani, K Weinberger 773–81 Red Hook, NY: Curran Assoc.
  149. Boyd JP. 149.  2001. Chebyshev and Fourier Spectral Methods New York: Dover, 2nd ed..
  150. Valsson O, Parrinello M. 150.  2015. Well-tempered variational approach to enhanced sampling. J. Chem. Theory Comput. 11:1996–2002 [Google Scholar]
  151. Rychlewski J, Komasa J. 151.  2003. Explicitly correlated functions in variational calculations. Explicitly Correlated Wave Functions in Chemistry and Physics J Rychlewski 91–147 New York: Springer [Google Scholar]
  152. Needs RJ, Towler MD, Drummond ND, López Ríos P. 152.  2009. Continuum variational and diffusion quantum Monte Carlo calculations. J. Phys. Condens. Matter 22:023201 [Google Scholar]
  153. Shaffer P, Valsson O, Parrinello M. 153.  2016. Enhanced, targeted sampling of high-dimensional free-energy landscapes using variationally enhanced sampling, with an application to chignolin. PNAS 113:1150–55 [Google Scholar]
  154. McCarty J, Valsson O, Tiwary P, Parrinello M. 154.  2015. Variationally optimized free-energy flooding for rate calculation. Phys. Rev. Lett. 115:070601 [Google Scholar]
/content/journals/10.1146/annurev-physchem-040215-112229
Loading
Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
Annual Review of Physical Chemistry 67, 159 (2016); https://doi.org/10.1146/annurev-physchem-040215-112229
/content/journals/10.1146/annurev-physchem-040215-112229
/content/journals/10.1146/annurev-physchem-040215-112229
Loading

Data & Media loading...

  • Article Type: Review Article

Most Cited Most Cited RSS feed

This is a required field
Please enter a valid email address
Approval was a Success
Invalid data
An Error Occurred
Approval was partially successful, following selected items could not be processed due to error