The DOI matches its Crossref record; 60 of the 60 references it cites were found in a registry or an index.
Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction
Open accessAbstract
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.
Overview
Integrity signals
Registry
Cites
Statistics
Verification
Claims the paper makes
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 [95]
Citations
Cites
Adhi Harmoko, S., M.Komp, Jacquard, J. M., Zuse, K., & Eniac (2005) · Cited by 18,035
Nonlinear Dimensionality Reduction by Locally Linear Embedding
Roweis, S. T., & Saul, L. K. (2000) · Science · doi:10.1126/science.290.5500.2323 · Cited by 14,965
Iterative Methods for Sparse Linear Systems
Saad, Y. E.-M. (2003) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898718003 · Cited by 13,931
Turk, M., & Pentland, A. (1991) · Journal of Cognitive Neuroscience · doi:10.1162/jocn.1991.3.1.71 · Cited by 13,733
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
Advances in Neural Information Processing Systems 14
(2002) · The MIT Press eBooks · doi:10.7551/mitpress/1120.001.0001 · Cited by 9,187
Jolliffe, I. T. (1986) · Springer series in statistics · doi:10.1007/978-1-4757-1904-8 · Cited by 8,481
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,562
Face recognition using eigenfaces
Turk, M., & Pentland, A. (2002) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr.1991.139758 · Cited by 5,262
Lehoucq, R. B., Sorensen, D. C., & Yang, C. (1998) · Society for Industrial and Applied Mathematics eBooks · doi:10.1137/1.9780898719628 · Cited by 2,938
Dunteman, G. H. (1989) · Sage eBooks · doi:10.4135/9781412985475 · Cited by 2,713
New Monte Carlo technique for studying phase transitions
Ferrenberg, A. M., & Swendsen, R. H. (1988) · Physical Review Letters · doi:10.1103/physrevlett.61.2635 · Cited by 2,655
Optimized Monte Carlo data analysis
Ferrenberg, A. M., & Swendsen, R. H. (1989) · Physical Review Letters · doi:10.1103/physrevlett.63.1195 · Cited by 2,613
Application of the Karhunen-Loeve procedure for the characterization of human faces
Kirby, M. J. L., & Sirovich, L. (1990) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/34.41390 · Cited by 2,459
THEORY OF PROTEIN FOLDING: The Energy Landscape Perspective
Onuchic, J. N., Luthey-Schulten, Z., & Wolynes, P. G. (1997) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.48.1.545 · Cited by 2,210
The principle of minimized iterations in the solution of the matrix eigenvalue problem
Arnoldi, W. E. (1951) · Quarterly of Applied Mathematics · doi:10.1090/qam/42792 · Cited by 1,835
The calculation of the potential of mean force using computer simulations
Roux, B. (1995) · Computer Physics Communications · doi:10.1016/0010-4655(95)00053-i · Cited by 1,755
Clementi, C., Nymeyer, H., & Onuchic, J. N. (2000) · Journal of Molecular Biology · doi:10.1006/jmbi.2000.3693 · Cited by 1,228
Self-citationGlobal Versus Local Methods in Nonlinear Dimensionality Reduction
de Silva, V., & Tenenbaum, J. B. (2002) · Cited by 794
Large-amplitude nonlinear motions in proteins
Garcı́a, A. E. (1992) · Physical Review Letters · doi:10.1103/physrevlett.68.2696 · Cited by 788
Intermediates and barrier crossing in a random energy model (with applications to protein folding)
Bryngelson, J. D., & Wolynes, P. G. (1989) · The Journal of Physical Chemistry · doi:10.1021/j100356a007 · Cited by 746
Near Neighbor Search in Large Metric Spaces
Brin, S. (1995) · Cited by 556
Reaction coordinates and rates from transition paths
Best, R. B., & Hummer, G. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0408098102 · Cited by 514
Shea, J.-E., & Brooks III, C. L. (2001) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.52.1.499 · Cited by 481
On the transition coordinate for protein folding
Du, R., Pande, V., Grosberg, A., Tanaka, T., & Shakhnovich, E. (1998) · The Journal of Chemical Physics · doi:10.1063/1.475393 · Cited by 479
From transition paths to transition states and rate coefficients
Hummer, G. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1630572 · Cited by 419
Automatic Method for Identifying Reaction Coordinates in Complex Systems
Ma, A., & Dinner, A. R. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp045546c · Cited by 400
Seventy-five percent accuracy in protein secondary structure prediction
Frishman, D., & Argos, P. (1997) · Proteins Structure Function and Bioinformatics · doi:10.1002/(sici)1097-0134(199703)27:3 · Cited by 367
Φ-Value analysis and the nature of protein-folding transition states
Fersht, A. R., & Sato, S. (2004) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0402684101 · Cited by 351
Folding funnels and frustration in off-lattice minimalist protein landscapes
Nymeyer, H., Garcı́a, A. E., & Onuchic, J. N. (1998) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.95.11.5921 · Cited by 324
Topological determinants of protein folding
Dokholyan, N. V., Li, L., Ding, F., & Shakhnovich, E. I. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.122076099 · Cited by 287
Collective Variable Description of Native Protein Dynamics
Hayward, S., & Gō, N. (1995) · Annual Review of Physical Chemistry · doi:10.1146/annurev.pc.46.100195.001255 · Cited by 277
P versus Q : Structural reaction coordinates capture protein folding on smooth landscapes
Cho, S. S., Levy, Y., & Wolynes, P. G. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0509768103 · Cited by 220
Chavez, L. L., Onuchic, J. N., & Clementi, C. (2004) · Journal of the American Chemical Society · doi:10.1021/ja049510+ · Cited by 217
Self-citationFolding Dynamics of the src SH3 Domain
Grantcharova, V., & Baker, D. A. (1997) · Biochemistry · doi:10.1021/bi971786p · Cited by 189
The effects of nonnative interactions on protein folding rates: Theory and simulation
Clementi, C., & Plotkin, S. S. (2004) · Protein Science · doi:10.1110/ps.03580104 · Cited by 158
Self-citationHayward, S., Kitao, A., & Gō, N. (1994) · Protein Science · doi:10.1002/pro.5560030608 · Cited by 129
Maschhoff, K., & Sorensen, D. C. (1996) · Lecture notes in computer science · doi:10.1007/3-540-62095-8_51 · Cited by 123
Fersht, A. R., Leatherbarrow, R. J., & Wells, T. N. C. (1986) · Nature · doi:10.1038/322284a0 · Cited by 104
Understanding Protein Flexibility through Dimensionality Reduction
Teodoro, M. L., Phillips, G. N., & Kavraki, L. E. (2003) · Journal of Computational Biology · doi:10.1089/10665270360688228 · Cited by 100
Self-citationDas, P., Matysiak, S., & Clementi, C. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0409471102 · Cited by 100
Self-citationPrediction of folding mechanism for circular-permuted proteins.
Clementi, C., Jennings, P., & Onuchic, J. (2001) · Journal of Molecular Biology · doi:10.1006/jmbi.2001.4871 · Cited by 96
Self-citationDynamic Stark effect of exciton and continuum states in CdS
Peyghambarian, N. N., Koch, S. W., Lindberg, M., Fluegel, B., & Joffre, M. (1989) · Physical Review Letters · doi:10.1103/physrevlett.62.1185 · Cited by 91
Rhee, Y. M., & Pande, V. S. (2005) · The Journal of Physical Chemistry B · doi:10.1021/jp045544s · Cited by 78
Multiple protein folding nuclei and the transition state ensemble in two‐state proteins
Klimov, D. K., & Thirumalai, D. (2001) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.1058 · Cited by 78
Ding, F., Guo, W., Dokholyan, N. V., Shakhnovich, E. I., & Shea, J. (2005) · Journal of Molecular Biology · doi:10.1016/j.jmb.2005.05.017 · Cited by 73
Continuous nonlinear dimensionality reduction by kernel eigenmaps
Brand, M. (2003) · Cited by 60
Nonlinear dimensionality reduction in climate data
Gamez, A. J., Zhou, C., Timmermann, A., & Kurths, J. (2004) · Nonlinear processes in geophysics · doi:10.5194/npg-11-393-2004 · Cited by 53
Gutin, A. M., Abkevich, V. I., & Shakhnovich, E. I. (1998) · Folding and Design · doi:10.1016/s1359-0278(98)00026-1 · Cited by 48
Das, P., Wilson, C. J., Fossati, G., Wittung-Stafshede, P. E., Matthews, K. S., & Clementi, C. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0505844102 · Cited by 47
Self-citationFlexibility of Monomeric and Dimeric HIV-1 Protease
Levy, Y., & Caflisch, A. (2003) · The Journal of Physical Chemistry B · doi:10.1021/jp0219956 · Cited by 43
Essential domain motions in barnase revealed by MD simulations
Nolde, S. B., Arseniev, A. S., Orekhov, V., & Billeter, M. (2002) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.10030 · Cited by 28
On the role of chemical detail in simulating protein folding kinetics
Rhee, Y. M., & Pande, V. S. (2005) · Chemical Physics · doi:10.1016/j.chemphys.2005.08.060 · Cited by 22
Real-time interactive frequency filtering of molecular dynamics trajectories
Levitt, M. (1991) · Journal of Molecular Biology · doi:10.1016/0022-2836(91)90373-e · Cited by 19
Progressing from folding trajectories to transition state ensemble in proteins
Klimov, D. K., & Thirumalai, D. (2004) · Chemical Physics · doi:10.1016/j.chemphys.2004.06.071 · Cited by 14
Approximation of protein structure for fast similarity measures
Schwarzer, F., & Lotan, I. (2003) · doi:10.1145/640075.640110 · Cited by 11
Baumketner, A., Shea, J., & Hiwatari, Y. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1760744 · Cited by 8
Posed Face Image Synthesis Using Nonlinear Manifold Learning
Cho, E., Kim, D., & Lee, S. (2003) · Lecture notes in computer science · doi:10.1007/3-540-44887-x_110 · Cited by 4
Dimensionality Reduction with Image Data
Benito, M., & Peña, D. (2004) · Lecture notes in computer science · doi:10.1007/978-3-540-28651-6_48 · Cited by 4
Mutai, C. (2000) · doi:10.1175/1520-0442(2000)013
Research works printed but not linked: 7
- A. Ma, A. Dinner J. Phys. B.. 109, 6769–6779 (2005).
- Y. Rhee, V. Pande J. Phys. B.. 109, 6780–6786 (2005).
- 10.1021/ja049510 · DOI
- Y. Levy, A. Caflisch J. Phys. B.. 107, 3068–3079 (2003).
- K. Q. Weinberger L. K. Saul (IEEE Washington DC) pp. 988–995 (2004).
- V. de Silva, J. Tenenbaum Sparse Multidimensional Scaling Using Landmark Points. (Stanford Univ., Stanford, CA, 2004).
- A. Ferrenberg, R. Swendsen Phys. Rev. Lett.. 63, 1185–1198 (1989).
Cited by
Sorted by citations
Big-Data Science in Porous Materials: Materials Genomics and Machine Learning
Jablonka, K. M., Ongari, D., Moosavi, S. M., & Smit, B. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00004 · Cited by 656
Schwantes, C. R., & Pande, V. S. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300878a · Cited by 597
Physics-Inspired Structural Representations for Molecules and Materials
Musil, F., Grisafi, A., Bartók, A. P., Ortner, C., Cśanyi, G., & Ceriotti, M. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00021 · Cited by 594
Abrams, C. F., & Bussi, G. (2013) · Entropy · doi:10.3390/e16010163 · Cited by 441
Physics-Inspired Structural Representations for Molecules and Materials
Musil, F., Grisafi, A., Bartók, A., Ortner, C., Cśanyi, G., Ceriotti, M., et al. (2021) · Cambridge University Engineering Department Publications Database · Cited by 440
Metadata
- 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
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
