The DOI matches its Crossref record; 47 of the 48 references it cites were found in a registry or an index.
Using sketch-map coordinates to analyze and bias molecular dynamics simulations
Open accessAbstract
When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.
Overview
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
The claims and statistics of this paper haven’t been checked yet.
Run the check — free, no account needed. It reads the open-access text and checks the sources it cites.
Claims other papers make about this one
Each is checked against this paper’s own text: does it say what the citing paper says it does?
In the citing paper
“The challenge of identifying the most appropriate low-dimensional space to accelerate conformational sampling is reflected in the fact that most of early (and recent) applications of dimensionality reduction to atomistic modeling involved simulations of rare events or phase transitions 71,72,95-98 .”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [72]
Self-check
Percentages, sums and reported differences re-computed from the paper’s own numbers.
The self-check needs the paper’s full text.
Citations
Cites
GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation
Hess, B., Kutzner, C., van der Spoel, D., & Lindahl, E. R. (2008) · Journal of Chemical Theory and Computation · doi:10.1021/ct700301q · Cited by 15,830
A Global Geometric Framework for Nonlinear Dimensionality Reduction
Tenenbaum, J. B., Silva, V. D., & Langford, J. C. (2000) · Science · doi:10.1126/science.290.5500.2319 · Cited by 13,585
Numerical Recipes, The Art of Scientific Computing
Press, W. H., Flannery, B. P., Teukolsky, S. A., Vetterling, W. T., & Gould, H. (1987) · American Journal of Physics · doi:10.1119/1.14981 · Cited by 10,032
Nonlinear Component Analysis as a Kernel Eigenvalue Problem
Schölkopf, B., Smola, A. J., & Müller, K. (1998) · Neural Computation · doi:10.1162/089976698300017467 · Cited by 8,196
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,562
THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method
Kumar, S., Rosenberg, J. M., Bouzida, D., Swendsen, R. H., & Kollman, P. A. (1992) · Journal of Computational Chemistry · doi:10.1002/jcc.540130812 · Cited by 6,808
Numerical Recipes: The Art of Scientific Computing
Ziegel, E. R., Press, W. H., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1987) · Technometrics · doi:10.2307/1269484 · Cited by 6,704
Advances in kernel methods: support vector learning
Schölkopf, B., Burges, C. J. C., & Smola, A. J. (1999) · doi:10.5555/299094 · Cited by 5,809
Laio, A., & Parrinello, M. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.202427399 · Cited by 5,626
Self-citationUnderstanding Molecular Simulation
Frenkel, D., Smit, B., Tobochnik, J., McKay, S. R., & Christian, W. (1997) · Computers in Physics · doi:10.1063/1.4822570 · Cited by 5,395
Research works printed but not linked: 1
- DJ Wales Energy Landscapes (Cambridge Univ Press, Cambridge, UK, 2003).
Cited by
Sorted by citations
Computer Simulation of Liquids
Allen, M. P., & Tildesley, D. J. (2017) · doi:10.1093/oso/9780198803195.001.0001 · Cited by 20,945
Role of Molecular Dynamics and Related Methods in Drug Discovery
Vivo, M. D., Masetti, M., Bottegoni, G., & Cavalli, A. (2016) · Journal of Medicinal Chemistry · doi:10.1021/acs.jmedchem.5b01684 · Cited by 1,358
Comparing molecules and solids across structural and alchemical space
De, S., Bartók, A. P., Csányi, G., & Ceriotti, M. (2016) · Physical Chemistry Chemical Physics · doi:10.1039/c6cp00415f · Cited by 778
Self-citationUsing metadynamics to explore complex free-energy landscapes
Bussi, G., & Laio, A. (2020) · Nature Reviews Physics · doi:10.1038/s42254-020-0153-0 · Cited by 726
Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint
Valsson, Ó., Tiwary, P., & Parrinello, M. (2016) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-040215-112229 · Cited by 646
Self-citation
Metadata
- Authors
- Tribello, G. A., Ceriotti, M., & Parrinello, M.
- Affiliations
- ETH Zurich (CH)
- University of Oxford (GB)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2012-03-16
- Volume
- 109
- Issue
- 14
- Pages
- 5196-5201
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC3325650
- OpenAlex
- W2038458884
- Cited by
- 202
- References
- 48
- Citations by year
- 2026: 8 · 2025: 9 · 2024: 5 · 2023: 9 · 2022: 19 · 2021: 20 · 2020: 18 · 2019: 16 · 2018: 12 · 2017: 40 · 2016: 15 · 2015: 13 · 2014: 10 · 2013: 5 · 2012: 3
- FWCI
- 3.99
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- Research Portal (Queen's University Belfast) (submittedVersion, other-oa)
- Funders
- FP7 Ideas: European Research Council (247075)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Pharmacology, Toxicology and Pharmaceutics › Drug Discovery › Computational Drug Discovery Methods
- Keywords
- sketch maps, dimensionality reduction, collective variables, free energy landscape, biasing potential, metadynamics, phase space exploration, protein folding, coarse-grained models, parallel tempering
- MeSH terms
- Probability, Protein Folding, Molecular Dynamics Simulation
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.
What counts as a claim ›How we measure confidence ›How we check this ›
Are you an author, or do you see a problem with this page? Request a review
