Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science
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Metadynamics is a powerful algorithm that can be used both for reconstructing the free energy and for accelerating rare events in systems described by complex Hamiltonians, at the classical or at the quantum level. In the algorithm the normal evolution of the system is biased by a history-dependent potential constructed as a sum of Gaussians centered along the trajectory followed by a suitably chosen set of collective variables. The sum of Gaussians is exploited for reconstructing iteratively an estimator of the free energy and forcing the system to escape from local minima. This review is intended to provide a comprehensive description of the algorithm, with a focus on the practical aspects that need to be addressed when one attempts to apply metadynamics to a new system: (i) the choice of the appropriate set of collective variables; (ii) the optimal choice of the metadynamics parameters and (iii) how to control the error and ensure convergence of the algorithm.
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In metadynamics, the volume of a free energy minimum grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the free-energy basin.
“Take for instance the case of metadynamics, in which a repulsive bias is accumulated in locations that have already been visited during the trajectory, forcing the system out of free energy minima 93,94 . The volume of one of these minima grows exponentially with the dimensionality d of collective variable space, and so does the time to accumulate sufficient bias to escape the freeenergy basin.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [94]
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Deprotonation of Solvated Formic Acid: Car−Parrinello and Metadynamics Simulations
Lee, J.-G., Asciutto, E. K., Babin, V., Sagui, C., Darden, T. A., & Roland, C. (2006) · The Journal of Physical Chemistry B · doi:10.1021/jp055809i · Cited by 54 · see citing works
From four- to six-coordinated silica: Transformation pathways from metadynamics
Martoňák, R., Donadio, D., Оганов, А. Р., et al. (2007) · Physical Review B · doi:10.1103/physrevb.76.014120 · Cited by 52 · see citing works
β-Lactone Synthesis from Epoxide and CO: Reaction Mechanism Revisited
Stirling, A., Iannuzzi, M., Parrinello, M., Molnar, F., Bernhart, V., & Luinstra, G. A. (2005) · Organometallics · doi:10.1021/om0502234 · Cited by 50 · see citing works
Molecular dynamics investigation of oxygen vacancy diffusion in rutile
Jug, K., Nair, N. N., & Bredow, T. (2005) · Physical Chemistry Chemical Physics · doi:10.1039/b502507a · Cited by 50 · see citing works
Piana, S., Laio, A., Marinelli, F., Van Troys, M., Bourry, D., Ampe, C., & Martins, J. C. (2008) · Journal of Molecular Biology · doi:10.1016/j.jmb.2007.10.020 · Cited by 48 · see citing works
Self-citationBoero, M., Tateno, M., Terakura, K., & Oshiyama, A. (2005) · Journal of Chemical Theory and Computation · doi:10.1021/ct050066q · Cited by 46 · see citing works
Using Metadynamics to Understand the Mechanism of Calmodulin/Target Recognition at Atomic Detail
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Role of Layering Oscillations at Liquid Metal Surfaces in Bulk Recrystallization and Surface Melting
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Insight into the Folding Inhibition of the HIV-1 Protease by a Small Peptide
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Self-citationDetermining the Structure of Phosphorus in Phase IV
Ishikawa, T., Nagara, H., Kusakabe, K., et al. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.095502 · Cited by 39 · see citing works
Michel, C., Laio, A., Mohamed, F., et al. (2007) · Organometallics · doi:10.1021/om060980h · Cited by 36 · see citing works
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Zipoli, F., Bernasconi, M., & Martoňák, R. (2004) · The European Physical Journal B · doi:10.1140/epjb/e2004-00168-y · Cited by 32 · see citing works
Molecular dynamics simulation of reconstructive phase transitions on an anhydrous zeolite
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Self-citationAtomistic Simulation of the DNA Helix−Coil Transition
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Diffusion and desorption of SiH3 on hydrogenated H:Si(100)−(2×1) from first principles
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Rodríguez‐Fortea, A., Iannuzzi, M., & Parrinello, M. (2007) · The Journal of Physical Chemistry C · doi:10.1021/jp066581h · Cited by 23 · see citing works
Mapping potential energy surfaces
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Ab initiosimulation of photoinduced transformation of small rings in amorphous silica
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Lithium Hydroxide Phase Transition under High Pressure: An Ab Initio Molecular Dynamics Study
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Ab Initio Simulations of Lewis‐Acid‐Catalyzed Hydrosilylation of Alkynes
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Self-citationAsciutto, E. K., & Sagui, C. (2005) · The Journal of Physical Chemistry A · doi:10.1021/jp053428z · Cited by 16 · see citing works
Ab Initio Molecular Dynamics Simulation of NO Reactivity on the CaO(001) Surface
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The role of Li+, Na+, and K+ in the ligand binding inside the human acetylcholinesterase gorge
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Migration of positively charged defects in α -quartz
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Zipoli, F., & Bernasconi, M. (2006) · The Journal of Physical Chemistry B · doi:10.1021/jp064518m · Cited by 13 · see citing works
Solid-State Phase Transition Induced by Pressure in LiOH·H2O
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First-principles molecular dynamics study of proton transfer mechanism in bovine cytochromecoxidase
Kamiya, K., Boero, M., Tateno, M., et al. (2007) · Journal of Physics Condensed Matter · doi:10.1088/0953-8984/19/36/365220 · Cited by 9 · see citing works
Michel, C., & Milet, A. (2007) · Journal of Molecular Structure THEOCHEM · doi:10.1016/j.theochem.2007.12.012 · Cited by 9 · see citing works
Liquid-solid coexistence via the metadynamics approach
Prestipino, S., & Giaquinta, P. V. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2841081 · Cited by 7 · see citing works
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Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945 · see citing works
Wei, G., Xi, W., Nussinov, R., & Ma, B. (2016) · Chemical Reviews · doi:10.1021/acs.chemrev.5b00562 · Cited by 436 · see citing works
Döntgen, M., Przybylski-Freund, M.-D., Kröger, L. C., Kopp, W. A., Ismail, A. E., & Leonhard, K. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00201 · Cited by 308 · see citing works
Using sketch-map coordinates to analyze and bias molecular dynamics simulations
Tribello, G. A., Ceriotti, M., & Parrinello, M. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201152109 · Cited by 202 · see citing works
Unsupervised machine learning in atomistic simulations, between predictions and understanding
Ceriotti, M. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5091842 · Cited by 173 · see citing works
Huggins, D. J., Biggin, P. C., Dämgen, M. A., Essex, J. W., Harris, S. A., Henchman, R. H., Khalid, S., Kuzmanic, A., Laughton, C. A., Michel, J., et al. (2019) · WIREs Computational Molecular Science · doi:10.1002/wcms.1393 · Cited by 169 · see citing works
Characterization of the free-energy landscapes of proteins by NMR-guided metadynamics
Granata, D., Camilloni, C., Vendruscolo, M., & Laio, A. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1218350110 · Cited by 143 · see citing works
Self-citationHistone acetylation regulates chromatin accessibility: Role of H4K16 in inter-nucleosome interaction
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Choreographing an enzyme's dance
Villali, J., & Kern, D. (2010) · Current Opinion in Chemical Biology · doi:10.1016/j.cbpa.2010.08.007 · Cited by 98 · see citing works
Mei, Y., Sherman, D. M., Liu, W., & Brugger, J. (2013) · Geochimica et Cosmochimica Acta · doi:10.1016/j.gca.2012.10.027 · Cited by 96 · see citing works
Exploration, Sampling, And Reconstruction of Free Energy Surfaces with Gaussian Process Regression
Mones, L., Bernstein, N., & Csányi, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00553 · Cited by 91 · see citing works
Metadynamics in the conformational space nonlinearly dimensionally reduced by Isomap
Spiwok, V., & Králová, B. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3660208 · Cited by 70 · see citing works
- Authors
- Laio, A., & Gervasio, F. L.
- Affiliations
- Scuola Internazionale Superiore di Studi Avanzati (IT)
- ETH Zurich (CH)
- Venue
- Reports on Progress in Physics
- Publisher
- IOP Publishing
- Published
- 2008-11-26
- Volume
- 71
- Issue
- 12
- Pages
- 126601
- ISSN
- 0034-4885 (ISSN-L)
- 1361-6633
- OpenAlex
- W2066951434
- Cited by
- 1,619
- References
- 144
- Citations by year
- 2026: 49 · 2025: 65 · 2024: 94 · 2023: 108 · 2022: 102 · 2021: 93 · 2020: 128 · 2019: 94 · 2018: 138 · 2017: 157 · 2016: 123 · 2015: 91 · 2014: 94 · 2013: 83 · 2012: 74
- FWCI
- 25.54
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- Reports on Progress in Physics (publishedVersion)
- UCL Discovery (University College London) (submittedVersion)
- SDL (submittedVersion)
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- metadynamics, rare events, collective variables, sampling acceleration, algorithm convergence, error control
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
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