The DOI matches its Crossref record; 39 of the 40 references it cites were found in a registry or an index.
Determination of reaction coordinates via locally scaled diffusion map
Abstract
We present a multiscale method for the determination of collective reaction coordinates for macromolecular dynamics based on two recently developed mathematical techniques: diffusion map and the determination of local intrinsic dimensionality of large datasets. Our method accounts for the local variation of molecular configuration space, and the resulting global coordinates are correlated with the time scales of the molecular motion. To illustrate the approach, we present results for two model systems: all-atom alanine dipeptide and coarse-grained src homology 3 protein domain. We provide clear physical interpretation for the emerging coordinates and use them to calculate transition rates. The technique is general enough to be applied to any system for which a Boltzmann-sampled set of molecular configurations is available.
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 construction of diffusion maps—which aim to approximate these eigenfunctions for overdamped Langevin dynamics—have been extended to model biomolecular dynamics, despite being originally introduced as a general data analysis tool [10].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [10]
In the citing paper
“methods such as diffusion maps 9,77-79 try to link geometric data to the characteristic time scale of the system's motion.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [79]
Citations
Cites
GROMACS: Fast, flexible, and free
van der Spoel, D., Lindahl, E. R., Hess, B., Groenhof, G., Mark, A. E., & Berendsen, H. J. C. (2005) · Journal of Computational Chemistry · doi:10.1002/jcc.20291 · Cited by 19,461
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
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
Brownian motion in a field of force and the diffusion model of chemical reactions
Kramers, H. A. (1940) · Physica · doi:10.1016/s0031-8914(40)90098-2 · Cited by 8,561
Dunteman, G. H. (1989) · Sage eBooks · doi:10.4135/9781412985475 · Cited by 2,713
Coifman, R. R., & Lafon, S. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.006 · Cited by 2,380
Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B., Warner, F., & Zucker, S. W. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0500334102 · Cited by 1,675
Self-citationClementi, C., Nymeyer, H., & Onuchic, J. N. (2000) · Journal of Molecular Biology · doi:10.1006/jmbi.2000.3693 · Cited by 1,228
Self-citationTransition path sampling and the calculation of rate constants
Dellago, C., Bolhuis, P. G., Csajka, F. S., & Chandler, D. (1998) · The Journal of Chemical Physics · doi:10.1063/1.475562 · Cited by 1,072
E, W., Ren, W.-Q., & Vanden-Eijnden, E. (2007) · Journal of Chemical Physics · doi:10.1063/1.2720838 · Cited by 728
Computing time scales from reaction coordinates by milestoning
Faradjian, A. K., & Elber, R. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1738640 · Cited by 635
Hummer, G. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/034 · Cited by 532
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
Coifman, R. R., & Maggioni, M. (2006) · Applied and Computational Harmonic Analysis · doi:10.1016/j.acha.2006.04.004 · Cited by 491
Self-citationOn 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
Energy landscape of a small peptide revealed by dihedral angle principal component analysis
Mu, Y., Nguyen, P. H., & Stock, G. (2004) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.20310 · Cited by 436
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
Das, P., Moll, M., Stamati, H., Kavraki, L. E., & Clementi, C. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0603553103 · Cited by 331
Self-citationDiffusion Maps, Reduction Coordinates, and Low Dimensional Representation of Stochastic Systems
Coifman, R., Kevrekidis, I., Lafon, S., Maggioni, M., & Nadler, B. (2008) · Multiscale Modeling & simulation · doi:10.1137/070696325 · Cited by 323
Self-citationGrantcharova, V., Riddle, D. S., Santiago, J. V., & Baker, D. A. (1998) · Nature Structural & Molecular Biology · doi:10.1038/1412 · Cited by 294
Coordinate-dependent diffusion in protein folding
Best, R. B., & Hummer, G. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0910390107 · Cited by 290
Mahadevan, S., & Maggioni, M. (2007) · doi:10.5555/1314498.1314570 · Cited by 287
Self-citationP 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
Coifman, R. R., Lafon, S., Lee, A. B., Maggioni, M., Nadler, B., Warner, F. J., & Zucker, S. W. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0500896102 · Cited by 217
Self-citationOne-dimensional reaction coordinates for diffusive activated rate processes in many dimensions
Berezhkovskii, A. M., & Szabó, A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1818091 · Cited by 185
On-the-fly string method for minimum free energy paths calculation
Maragliano, L., & Vanden‐Eijnden, E. (2007) · Chemical Physics Letters · doi:10.1016/j.cplett.2007.08.017 · Cited by 177
Kinetics, thermodynamics and evolution of non-native interactions in a protein folding nucleus.
Shakhnovich, E. I., Li, L., & Mirny, L. A. (2000) · Nature Structural Biology · doi:10.1038/74111 · Cited by 160
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-citationManifold parametrizations by eigenfunctions of the Laplacian and heat kernels
Jones, P. W., Maggioni, M., & Schul, R. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0710175104 · Cited by 147
Self-citationTopological methods for exploring low-density states in biomolecular folding pathways
Yao, Y., Sun, J. Z., Huang, X., Bowman, G. R., Singh, G., Lesnick, M., Guibas, L. J., Pande, V. S., & Carlsson, G. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3103496 · Cited by 129
Das, P., Matysiak, S., & Clementi, C. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0409471102 · Cited by 100
Self-citationEffective stochastic dynamics on a protein folding energy landscape
Yang, S., Onuchic, J. N., & Levine, H. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2229206 · Cited by 78
Unspecific hydrophobic stabilization of folding transition states
Viguera, A. R., Vega, C. G., & Serrano, L. G. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.072387799 · Cited by 69
Multiscale Estimation of Intrinsic Dimensionality of Data Sets
Little, A. V., Jung, Y.-M., & Maggioni, M. (2009) · National Conference on Artificial Intelligence · Cited by 54
Self-citationPlaku, E., Stamati, H., Clementi, C., & Kavraki, L. E. (2007) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21337 · Cited by 43
Self-citationThe rate constant of polymer reversal inside a pore
Huang, L., & Makarov, D. E. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2890006 · Cited by 35
Complexity of free energy landscapes of peptides revealed by nonlinear principal component analysis
Nguyen, P. H. (2006) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21185 · Cited by 32
Qi, B., Muff, S., Caflisch, A., & Dinner, A. R. (2010) · The Journal of Physical Chemistry B · doi:10.1021/jp101476g · Cited by 21
Szlam, F., Taketomi, T., Sheppard, C., Kempton, C. L., Levy, J. H., & Tanaka, K. A. (2008) · Anesthesia & Analgesia · doi:10.1213/ane.0b013e3181618702 · Cited by 18
Flagged first, then by citations
1 of the 40 references couldn’t be matched to a known paper.
Research works printed but not linked: 1
- 2007, J. Mach. Learn. Res., 8, 2169
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
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models
Scherer, M. K., Trendelkamp-Schroer, B., Paul, F., Pérez‐Hernández, G., Hoffmann, M., Plattner, N., Wehmeyer, C., Prinz, J.-H., & Noé, F. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00743 · Cited by 1,160
Identification of slow molecular order parameters for Markov model construction
Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G., & Noé, F. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4811489 · Cited by 990
“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundMarkov state models of biomolecular conformational dynamics
Chodera, J. D., & Noé, F. (2014) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2014.04.002 · Cited by 776
Using 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
Metadata
- Authors
- Rohrdanz, M. A., Zheng, W., Maggioni, M., & Clementi, C.
- Affiliations
- Rice University (US)
- Duke University (US)
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2011-03-28
- Volume
- 134
- Issue
- 12
- Pages
- 124116-124116
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1971725855
- Cited by
- 292
- References
- 40
- Citations by year
- 2026: 8 · 2025: 12 · 2024: 15 · 2023: 12 · 2022: 14 · 2021: 18 · 2020: 18 · 2019: 22 · 2018: 23 · 2017: 46 · 2016: 24 · 2015: 25 · 2014: 19 · 2013: 19 · 2012: 9
- FWCI
- 7.12
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation (0835712, 0835824, CHE-0349303, CNS-0421109, CNS-0821727, DMS-0650413, EIA-0216467)
- 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
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Keywords
- reaction coordinate, diffusion maps, collective variables, macromolecular dynamics, intrinsic dimension, multiscale methods, alanine dipeptide, SH3 domain, transition rates
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
