Simplifying the representation of complex free-energy landscapes using sketch-map
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A new scheme, sketch-map, for obtaining a low-dimensional representation of the region of phase space explored during an enhanced dynamics simulation is proposed. We show evidence, from an examination of the distribution of pairwise distances between frames, that some features of the free-energy surface are inherently high-dimensional. This makes dimensionality reduction problematic because the data does not satisfy the assumptions made in conventional manifold learning algorithms We therefore propose that when dimensionality reduction is performed on trajectory data one should think of the resultant embedding as a quickly sketched set of directions rather than a road map. In other words, the embedding tells one about the connectivity between states but does not provide the vectors that correspond to the slow degrees of freedom. This realization informs the development of sketch-map, which endeavors to reproduce the proximity information from the high-dimensionality description in a space of lower dimensionality even when a faithful embedding is not possible.
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The challenge of identifying the most appropriate low-dimensional space to accelerate conformational sampling is reflected in the fact that most early (and recent) applications of dimensionality reduction to atomistic modeling involved simulations of rare events or phase transitions.
“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 [71]
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Self-citation
- Authors
- Ceriotti, M., Tribello, G. A., & Parrinello, M.
- Affiliations
- University of Oxford (GB)
- ETH Zurich (CH)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2011-07-05
- Volume
- 108
- Issue
- 32
- Pages
- 13023-13028
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC3156203
- OpenAlex
- W1980782498
- Cited by
- 340
- References
- 40
- Citations by year
- 2026: 14 · 2025: 17 · 2024: 18 · 2023: 22 · 2022: 26 · 2021: 36 · 2020: 40 · 2019: 34 · 2018: 26 · 2017: 45 · 2016: 18 · 2015: 20 · 2014: 5 · 2013: 9 · 2012: 8
- FWCI
- 3.11
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (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
- National Science Foundation
- Royal Society
- European Commission (ERC-2009-AdG-247075)
- Schweizerischer Nationalfonds zur Förderung der Wissenschaftlichen Forschung (ERC-2009-AdG)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- sketch maps, free energy landscape, dimensionality reduction, manifold learning, enhanced sampling, phase space exploration, molecular dynamics trajectories
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