Metadynamics

Metadynamics

Metadynamics is a technique in computational physics and chemistry, used to improve sampling of a system (or different systems) where ergodicity is hindered by the form of the system's energy landscape. It was first suggested by Laio and Parrinello in 2002[1] and is usually applied within molecular dynamics simulations. It closely resembles a number of recent methods such as adaptively biased molecular dynamics[2], adaptive reaction coordinate forces[3] and local elevation umbrella sampling[4].


Contents

Algorithm

The technique builds on a large number of related methods including (in a chronological order) the deflation[5], tunneling[6], tabu search[7], local elevation[8], conformational flooding[9], Engkvist-Karlström[10] and adaptive biasing force methods[11].

Metadynamics has been informally described as "filling the free energy wells with computational sand"[12]. The algorithm assumes that the system can be described by a few collective variables. During the simulation, the location of the system in the space determined by the collective variables is calculated and a positive Gaussian potential is added to the real energy landscape of the system. In this way the system is discouraged to come back to the previous point. During the evolution of the simulation, more and more Gaussians sum up, thus discouraging more and more the system to go back to its previous steps, until the system explores the full energy landscape -at this point the free energy becomes a constant as a function of the collective variables. At this point the energy landscape can be recovered as the opposite of the sum of all Gaussians.

The time interval between the addition of two Gaussian functions, as well as the Gaussian height and Gaussian width, are tuned to optimize the ratio between accuracy and computational cost. By simply changing the size of the Gaussian, metadynamics can be fitted to yield very quickly a rough map of the energy landscape by using large Gaussians, or can be used for a finer grained description by using smaller Gaussians[1].

Metadynamics has the advantage, upon methods like adaptive umbrella sampling, of not requiring an initial estimate of the energy landscape to explore[1].

Variants

Further refinements of the algorithm have been developed, like well-tempered metadynamics[13] or bias-exchange metadynamics[14]. Regarding the choice of collective variables, using essential coordinates has been proposed[15].

Applications

Metadynamics has been used to study, among other things, protein folding[14], chemical reactions[16], molecular docking[17][18] and phase transitions[19].

Implementations

A public implementation of the metadynamics algorithm is PLUMED. It is released as a plugin for several molecular dynamics software packages[20]

External links

See also

References

  1. ^ a b c Laio, A.; Parrinello, M. (2002). "Escaping free-energy minima". Proceedings of the National Academy of Sciences of the United States of America 99 (20): 12562–12566. arXiv:cond-mat/0208352. Bibcode 2002PNAS...9912562L. doi:10.1073/pnas.202427399. PMC 130499. PMID 12271136. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=130499.  edit
  2. ^ Babin, V.; Roland, C.; Sagui, C. (2008). "Stabilization of resonance states by an asymptotic Coulomb potential". J. Chem. Phys. 128 (2): 134101/1–134101/7. Bibcode 2008JChPh.128b4101A. doi:10.1063/1.2821102. 
  3. ^ Barnett, C.B.; Naidoo, K.J. (2009). "Free Energies from Adaptive Reaction Coordinate Forces (FEARCF): An application to ring puckering". Mol. Phys. 107 (8): 1243–1250. Bibcode 2009MolPh.107.1243B. doi:10.1080/00268970902852608. 
  4. ^ Hansen, H.S.; Hünenberger, P.H. (2010). "Using the local elevation method to construct optimized umbrella sampling potentials: Calculation of the relative free energies and interconversion barriers of glucopyranose ring conformers in water". J. Comput. Chem. 31 (1): 1–23. doi:10.1002/jcc.21253. PMID 19412904. 
  5. ^ Crippen, G.M.; Scheraga, H.A. (1969). Chemistry 64: 42–49. 
  6. ^ Levy, A.V.; Montalvo, A. (1985). "The Tunneling Algorithm for the Global Minimization of Functions". SIAM J. Sci. Stat. Comput. 6: 15–29. doi:10.1137/0906002. 
  7. ^ Glover, F. (1989). ORSA J. Comput. 1: 190–206. 
  8. ^ Huber, T.; Torda, A.E.; van Gunsteren, W.F. (1994). "Local elevation: A method for improving the searching properties of molecular dynamics simulation". J. Comput. -Aided. Mol. Des. 8 (6): 695–708. Bibcode 1994JCAMD...8..695H. doi:10.1007/BF00124016. PMID 7738605. 
  9. ^ Grubmüller, H. (1995). "Predicting slow structural transitions in macromolecular systems: Conformational flooding". Phys. Rev. E 52 (3): 2893–2906. Bibcode 1995PhRvE..52.2893G. doi:10.1103/PhysRevE.52.2893. 
  10. ^ Engkvist, O.; Karlström, G. (1996). "A method to calculate the probability distribution for systems with large energy barriers". Chem. Phys. 213: 63–76. Bibcode 1996CP....213...63E. doi:10.1016/S0301-0104(96)00247-9. 
  11. ^ Darve, E.; Pohorille, A. (2001). "Calculating free energies using average force". J. Chem. Phys. 115 (20): 9169. Bibcode 2001JChPh.115.9169D. doi:10.1063/1.1410978. 
  12. ^ http://www.grs-sim.de/cms/upload/Carloni/Presentations/Marinelli.ppt
  13. ^ Barducci, A.; Bussi, G.; Parrinello, M. (2008). "Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method". Physical Review Letters 100 (2): 020603. Bibcode 2008PhRvL.100b0603B. doi:10.1103/PhysRevLett.100.020603. PMID 18232845.  edit
  14. ^ a b Piana, S.; Laio, A. (2007). "A bias-exchange approach to protein folding". The journal of physical chemistry. B 111 (17): 4553–4559. doi:10.1021/jp067873l. PMID 17419610.  edit
  15. ^ Spiwok, V.; Lipovová, P.; Králová, B. (2007). "Metadynamics in essential coordinates: free energy simulation of conformational changes". The journal of physical chemistry. B 111 (12): 3073–3076. doi:10.1021/jp068587c. PMID 17388445.  edit
  16. ^ Ensing, B.; De Vivo, M.; Liu, Z.; Moore, P.; Klein, M. (2006). "Metadynamics as a tool for exploring free energy landscapes of chemical reactions". Accounts of chemical research 39 (2): 73–81. doi:10.1021/ar040198i. PMID 16489726.  edit
  17. ^ Gervasio, F.; Laio, A.; Parrinello, M. (2005). "Flexible docking in solution using metadynamics". Journal of the American Chemical Society 127 (8): 2600–2607. doi:10.1021/ja0445950. PMID 15725015.  edit
  18. ^ Vargiu, A. V.; Ruggerone, P.; Magistrato, A.; Carloni, P. (2008). "Dissociation of minor groove binders from DNA: insights from metadynamics simulations". Nucleic Acids Research 36 (18): 5910–5921. doi:10.1093/nar/gkn561. PMC 2566863. PMID 18801848. http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=2566863.  edit
  19. ^ Martoňák, R.; Laio, A.; Bernasconi, M.; Ceriani, C.; Raiteri, P.; Zipoli, F.; Parrinello, M. (2005). "Simulation of structural phase transitions by metadynamics". Zeitschrift für Kristallographie 220 (5-6-2005): 489. doi:10.1524/zkri.220.5.489.65078.  edit
  20. ^ Bonomi, M.; Branduardi, D.; Bussi, G.; Camilloni, C.; Provasi, D.; Raiteri, P.; Donadio, D.; Marinelli, F. et al. (2009). "PLUMED: A portable plugin for free-energy calculations with molecular dynamics☆". Computer Physics Communications 180: 1961. Bibcode 2009CoPhC.180.1961B. doi:10.1016/j.cpc.2009.05.011.  edit

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