Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction
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The definition of reaction coordinates for the characterization of a protein-folding reaction has long been a controversial issue, even for the “simple” case in which one single free-energy barrier separates the folded and unfolded ensemble. We propose a general approach to this problem to obtain a few collective coordinates by using nonlinear dimensionality reduction. We validate the usefulness of this method by characterizing the folding landscape associated with a coarse-grained protein model of src homology 3 as sampled by molecular dynamics simulations. The folding free-energy landscape projected on the few relevant coordinates emerging from the dimensionality reduction can correctly identify the transition-state ensemble of the reaction. The first embedding dimension efficiently captures the evolution of the folding process along the main folding route. These results clearly show that the proposed method can efficiently find a low-dimensional representation of a complex process such as protein folding.
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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 [95]
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- Authors
- Das, P., Moll, M., Stamati, H., Kavraki, L. E., & Clementi, C.
- Affiliations
- Departments of *Chemistry,
- Computer Science, and
- Baylor College of Medicine (US)
- Rice University (US)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2006-06-27
- Volume
- 103
- Issue
- 26
- Pages
- 9885-9890
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC1502548
- OpenAlex
- W2077412035
- Cited by
- 331
- References
- 60
- Citations by year
- 2026: 9 · 2025: 10 · 2024: 13 · 2023: 11 · 2022: 21 · 2021: 15 · 2020: 18 · 2019: 23 · 2018: 24 · 2017: 20 · 2016: 15 · 2015: 23 · 2014: 14 · 2013: 18 · 2012: 19
- FWCI
- 6.93
- Type
- journal article
- Language
- en
- Open access
- green
- europepmc.org
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- Europe PMC (PubMed Central) (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation (0523908, 0454333, 0349303, 0205671, 0216467)
- Alfred P. Sloan Foundation
- Division of Chemistry
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- protein folding, free energy landscape, reaction coordinate, nonlinear dimensionality reduction, collective coordinates, transition state ensemble, coarse-grained protein models, molecular dynamics sampling
- MeSH terms
- Algorithms, Models, Molecular, Protein Folding, src Homology Domains, Entropy
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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.
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