Variational approach to molecular kinetics
Abstract
The eigenvalues and eigenvectors of the molecular dynamics propagator (or transfer operator) contain the essential information about the molecular thermodynamics and kinetics. This includes the stationary distribution, the metastable states, and state-to-state transition rates. Here, we present a variational approach for computing these dominant eigenvalues and eigenvectors. This approach is analogous to the variational approach used for computing stationary states in quantum mechanics. A corresponding method of linear variation is formulated. It is shown that the matrices needed for the linear variation method are correlation matrices that can be estimated from simple MD simulations for a given basis set. The method proposed here is thus to first define a basis set able to capture the relevant conformational transitions, then compute the respective correlation matrices, and then to compute their dominant eigenvalues and eigenvectors, thus obtaining the key ingredients of the slow kinetics.
Integrity signals
Registry
Cites
Statistics
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?
The variational principle has been applied to the approximation of peptide dynamics via Gaussian basis sets.
“Ref. [15] discusses differences and similarities to quantum-mechanical approaches that may be exploited and applies the variational principle to the approximation of the peptide dynamics via Gaussian basis sets.”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [15]
Cites
Particle mesh Ewald: An N⋅log(N) method for Ewald sums in large systems
Darden, T., York, D., & Pedersen, L. (1993) · The Journal of Chemical Physics · doi:10.1063/1.464397 · Cited by 29,588 · see citing works
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 19,292 · see citing works
LINCS: A linear constraint solver for molecular simulations
Hess, B., Bekker, H., Berendsen, H. J. C., & Fraaije, J. G. E. M. (1997) · Journal of Computational Chemistry · doi:10.1002/(sici)1096-987x(199709)18:12 · Cited by 18,369 · see citing works
Canonical sampling through velocity rescaling
Bussi, G., Donadio, D., & Parrinello, M. (2007) · The Journal of Chemical Physics · doi:10.1063/1.2408420 · Cited by 18,024 · see citing works
Improved side-chain torsion potentials for the Amber ff99SB protein force field
Lindorff-Larsen, K., Piana, S., Palmo, K., Maragakis, P., Klepeis, J., Dror, R., & Shaw, D. (2010) · Proteins: Structure, Function, and Bioinformatics · doi:10.1002/prot.22711 · Cited by 6,037 · see citing works
How fast-folding proteins fold
Lindorff-Larsen, K., Piana, S., Dror, R. O., & Shaw, D. E. (2011) · Science · doi:10.1126/science.1208351 · Cited by 1,980 · see citing works
Atomic-level characterization of the structural dynamics of proteins
Shaw, D. E., Maragakis, P., Lindorff-Larsen, K., Piana, S., Dror, R. O., Eastwood, M. P., Bank, J. A., Jumper, J. M., Salmon, J. K., Shan, Y., et al. (2010) · Science · doi:10.1126/science.1187409 · Cited by 1,923 · see citing works
Markov models of molecular kinetics: Generation and validation
Prinz, J.-H., Wu, H., Sarich, M., Keller, B., Senne, M., Held, M., Chodera, J. D., Schütte, C., & Noé, F. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3565032 · Cited by 1,275 · see citing works
Self-citationIdentification 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 · see citing works
Self-citationConstructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations
Noé, F., Schütte, C., Vanden-Eijnden, E., Reich, L., & Weikl, T. R. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0905466106 · Cited by 820 · see citing works
Self-citationEverything you wanted to know about Markov State Models but were afraid to ask
Pande, V. S., Beauchamp, K., & Bowman, G. R. (2010) · Methods · doi:10.1016/j.ymeth.2010.06.002 · Cited by 698 · see citing works
Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations
Buch, I., Giorgino, T., & De Fabritiis, G. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1103547108 · Cited by 655 · see citing works
Chodera, J., Singhal, N., Pande, V., Dill, K., & Swope, W. (2007) · Journal of Chemical Physics · doi:10.1063/1.2714538 · Cited by 613 · see citing works
Identification of slow molecular order parameters for Markov model constructionPreprint
Perez-hern, G., Paul, F., Toni Giorgino, A., Fabritiis, G. D., Noé, F., & Contribution, E. (2013) · Cited by 613 · see citing works
Self-citationSchwantes, C. R., & Pande, V. S. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct300878a · Cited by 597 · see citing works
Robust Perron cluster analysis in conformation dynamics
Deuflhard, P., & Weber, M. (2005) · Linear Algebra and its Applications · doi:10.1016/j.laa.2004.10.026 · Cited by 506 · see citing works
Towards a Theory of Transition Paths
Weinan, E., & Vanden‐Eijnden, E. (2006) · Journal of Statistical Physics · doi:10.1007/s10955-005-9003-9 · Cited by 478 · see citing works
Coarse master equations for peptide folding dynamics
Buchete, N.-V., & Hummer, G. (2008) · The Journal of Physical Chemistry B · doi:10.1021/jp0761665 · Cited by 477 · see citing works
Transition networks for modeling the kinetics of conformational change in macromolecules.
Noé, F., & Fischer, S. (2008) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2008.01.008 · Cited by 450 · see citing works
Self-citationDescribing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory
Swope, W., Pitera, J., & Suits, F. (2004) · The Journal of Physical Chemistry B · doi:10.1021/jp037421y · Cited by 450 · see citing works
Bowman, G. R., Beauchamp, K. A., Boxer, G., & Pande, V. S. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3216567 · Cited by 396 · see citing works
A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo
Schütte, C., Fischer, A., Huisinga, W., & Deuflhard, P. (1999) · Journal of Computational Physics · doi:10.1006/jcph.1999.6231 · Cited by 393 · see citing works
Noé, F., Horenko, I., Schütte, C., & Smith, J. C. (2007) · Journal of Chemical Physics · doi:10.1063/1.2714539 · Cited by 377 · see citing works
Self-citationMSMBuilder2: Modeling Conformational Dynamics on the Picosecond to Millisecond Scale
Beauchamp, K. A., Bowman, G. R., Lane, T. J., Maibaum, L., Haque, I. S., & Pande, V. S. (2011) · Journal of Chemical Theory and Computation · doi:10.1021/ct200463m · Cited by 372 · see citing works
Rao, F. V., & Caflisch, A. (2004) · Journal of Molecular Biology · doi:10.1016/j.jmb.2004.06.063 · Cited by 358 · see citing works
Hidden complexity of free energy surfaces for peptide (protein) folding.
Krivov, S., & Karplus, M. (2004) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.0406234101 · Cited by 336 · see citing works
Dihedral angle principal component analysis of molecular dynamics simulations.
Altis, A., Nguyen, P., Hegger, R., & Stock, G. (2007) · Journal of Chemical Physics · doi:10.1063/1.2746330 · Cited by 327 · see citing works
A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems
Noé, F., & Nüske, F. (2013) · Multiscale Modeling & Simulation · doi:10.1137/110858616 · Cited by 327 · see citing works
Self-citationIdentification of almost invariant aggregates in reversible nearly uncoupled Markov chains
Deuflhard, P., Huisinga, W., Fischer, A., & Schütte, C. (2000) · Linear Algebra and its Applications · doi:10.1016/s0024-3795(00)00095-1 · Cited by 319 · see citing works
Kinesin Assembly and Movement in Cells
Verhey, K. J., Kaul, N., & Soppina, V. (2011) · Annual Review of Biophysics · doi:10.1146/annurev-biophys-042910-155310 · Cited by 231 · see citing works
Markov state models based on milestoning
Schütte, C., Noé, F., Lu, J., Sarich, M., & Vanden-Eijnden, E. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3590108 · Cited by 228 · see citing works
Self-citationProtein folded states are kinetic hubs
Bowman, G., & Pande, V. (2010) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1003962107 · Cited by 216 · see citing works
Karpen, M. E., Tobias, D., & Brooks, C. (1993) · Biochemistry · doi:10.1021/bi00053a005 · Cited by 211 · see citing works
The Many Proofs and Applications of Perron’s Theorem
MacCluer, C. R. (2000) · SIAM Review · doi:10.1137/s0036144599359449 · Cited by 203 · see citing works
Markovian milestoning with Voronoi tessellations.
Vanden-Eijnden, E., & Venturoli, M. (2009) · Journal of Chemical Physics · doi:10.1063/1.3129843 · Cited by 198 · see citing works
On the Approximation Quality of Markov State Models
Sarich, M., Noé, F., & Schütte, C. (2010) · Multiscale Modeling & Simulation · doi:10.1137/090764049 · Cited by 182 · see citing works
Self-citationError analysis and efficient sampling in Markovian state models for molecular dynamics.
Singhal, N., & Pande, V. (2005) · Journal of Chemical Physics · doi:10.1063/1.2116947 · Cited by 175 · see citing works
Markov State Model Reveals Folding and Functional Dynamics in Ultra-Long MD Trajectories
Lane, T., Bowman, G., Beauchamp, K., Voelz, V. A., & Pande, V. (2011) · Journal of the American Chemical Society · doi:10.1021/ja207470h · Cited by 171 · see citing works
Building Markov state models along pathways to determine free energies and rates of transitions.
Pan, A. C., & Roux, B. (2008) · Journal of Chemical Physics · doi:10.1063/1.2959573 · Cited by 163 · see citing works
Simple few-state models reveal hidden complexity in protein folding
Beauchamp, K. A., McGibbon, R., Lin, Y.-S., & Pande, V. S. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201810109 · Cited by 161 · see citing works
EMMA: A Software Package for Markov Model Building and Analysis
Senne, M., Trendelkamp-Schroer, B., Mey, A. S. J. S., Schütte, C., & Noé, F. (2012) · Journal of Chemical Theory and Computation · doi:10.1021/ct300274u · Cited by 148 · see citing works
Self-citationProbability distributions of molecular observables computed from Markov models
Noé, F. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2916718 · Cited by 135 · see citing works
Self-citationComparing geometric and kinetic cluster algorithms for molecular simulation data
Keller, B. G., Daura, X., & van Gunsteren, W. F. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3301140 · Cited by 131 · see citing works
Self-citationA coarse graining method for the identification of transition rates between molecular conformations.
Kube, S., & Weber, M. (2007) · Journal of Chemical Physics · doi:10.1063/1.2404953 · Cited by 123 · see citing works
de Groot, B. L., Daura, X., Mark, A., & Grubmüller, H. (2001) · Journal of Molecular Biology · doi:10.1006/jmbi.2001.4655 · Cited by 121 · see citing works
Noé, F., Doose, S., Daidone, I., Löllmann, M., Sauer, M., Chodera, J. D., & Smith, J. C. (2011) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1004646108 · Cited by 116 · see citing works
Self-citationKinetic characterization of the critical step in HIV-1 protease maturation
Sadiq, S. K., Noé, F., & De Fabritiis, G. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1210983109 · Cited by 102 · see citing works
Self-citationRibosome Structure and Dynamics During Translocation and Termination
Dunkle, J. A., & Cate, J. H. D. (2010) · Annual Review of Biophysics · doi:10.1146/annurev.biophys.37.032807.125954 · Cited by 101 · see citing works
Noé, F., Krachtus, D., Smith, J. C., & Fischer, S. (2006) · Journal of Chemical Theory and Computation · doi:10.1021/ct050162r · Cited by 93 · see citing works
Self-citationRelationship between Side Chain Structure and 14-Helix Stability of β3-Peptides in Water
Kritzer, J. A., Tirado‐Rives, J., Hart, S. A., Lear, J. D., Jorgensen, W. L., & Schepartz, A. (2004) · Journal of the American Chemical Society · doi:10.1021/ja0459375 · Cited by 93 · see citing works
Muff, S., & Caflisch, A. (2008) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21565 · Cited by 91 · see citing works
Understanding ensemble protein folding at atomic detail
Hubner, I. A., Deeds, E. J., & Shakhnovich, E. I. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0605580103 · Cited by 67 · see citing works
Markov models and dynamical fingerprints: Unraveling the complexity of molecular kinetics
Keller, B. G., Prinz, J.-H., & Noé, F. (2012) · Chemical Physics · doi:10.1016/j.chemphys.2011.08.021 · Cited by 59 · see citing works
Self-citationExtracting Markov Models of Peptide Conformational Dynamics from Simulation Data.
Schultheis, V., Hirschberger, T., Carstens, H., & Tavan, P. (2005) · Journal of Chemical Theory and Computation · doi:10.1021/ct050020x · Cited by 44 · see citing works
Chodera, J., & Noé, F. (2010) · Journal of Chemical Physics · doi:10.1063/1.3463406 · Cited by 43 · see citing works
Self-citationKelley, N. W., Vishal, V., Krafft, G. A., & Pande, V. S. (2008) · The Journal of Chemical Physics · doi:10.1063/1.3010881 · Cited by 41 · see citing works
Keller, B., Hünenberger, P., & van Gunsteren, W. V. (2011) · Journal of Chemical Theory and Computation · doi:10.1021/ct200069c · Cited by 29 · see citing works
Self-citationDynamic neutron scattering from conformational dynamics. I. Theory and Markov models
Lindner, B., Yi, Z., Prinz, J.-H., Smith, J. C., & Noé, F. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4824070 · Cited by 23 · see citing works
Self-citationNoé, F., Oswald, M., Reinelt, G., Fischer, S., & Smith, J. C. (2006) · Multiscale Modeling and Simulation · doi:10.1137/050641922 · Cited by 20 · see citing works
Self-citationStatistical error estimation and grid-free hierarchical refinement in conformation dynamics
Röblitz, S. (2009) · Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver · doi:10.17169/refubium-12330 · Cited by 19 · see citing works
Yi, Z., Lindner, B., Prinz, J.-H., Noé, F., & Smith, J. C. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4824071 · Cited by 14 · see citing works
Self-citationA Bayesian method for construction of Markov models to describe dynamics on various time-scales
Rains, E. K., & Andersen, H. C. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3496438 · Cited by 13 · see citing works
Identifying and correcting non-Markov states in peptide conformational dynamics
Nerukh, D., Jensen, C. H., & Glen, R. C. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3328781 · Cited by 13 · see citing works
Jensen, C. H., Nerukh, D., & Glen, R. C. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2838980 · Cited by 12 · see citing works
Adaptive Spectral Clustering for Conformation Analysis
Haack, F., Röblitz, S., Scharkoi, O., Schmidt, B., Weber, M., Simos, T. E., Psihoyios, G., & Tsitouras, C. (2010) · AIP conference proceedings · doi:10.1063/1.3498116 · Cited by 4 · see citing works
Identification of metastable states in peptide’s dynamics
Ruzhytska, S., Jacobi, M. N., Jensen, C. H., & Nerukh, D. (2010) · The Journal of Chemical Physics · doi:10.1063/1.3493333 · Cited by 4 · see citing works
Flagged first, then by citations
Cited by
Sorted by citations
Deep learning for universal linear embeddings of nonlinear dynamics
Lusch, B., Kutz, J., & Brunton, S. (2017) · Nature Communications · doi:10.1038/s41467-018-07210-0 · Cited by 1,834 · see citing works
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 1,135 · see citing works
Self-citationData-Driven Science and Engineering
Brunton, S. L., & Kutz, J. N. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108380690 · Cited by 1,177 · see citing works
Markov State Models: From an Art to a Science
Husic, B. E., & Pande, V. S. (2018) · Journal of the American Chemical Society · doi:10.1021/jacs.7b12191 · Cited by 866 · see citing works
Markov 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 · see citing works
Self-citationModern Koopman Theory for Dynamical Systems
Brunton, S. L., Budišić, M., Kaiser, E., & Kutz, J. N. (2022) · SIAM Review · doi:10.1137/21m1401243 · Cited by 635 · see citing works
VAMPnets for deep learning of molecular kinetics
Mardt, A., Pasquali, L., Wu, H., & Noé, F. (2017) · Nature Communications · doi:10.1038/s41467-017-02388-1 · Cited by 557 · see citing works
Self-citationVAMPnets for deep learning of molecular kinetics
Mardt, A., Pasquali, L., Wu, H., & Noé, F. (2018) · RePEc: Research Papers in Economics · doi:10.17169/refubium-964 · Cited by 464 · see citing works
Self-citationTime-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
Wehmeyer, C., & Noé, F. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5011399 · Cited by 401 · see citing works
Self-citationUnsupervised Learning Methods for Molecular Simulation Data
Glielmo, A., Husic, B. E., Rodríguez, Á., Clementi, C., Noé, F., & Laio, A. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c01195 · Cited by 408 · see citing works
Self-citationVariational Approach for Learning Markov Processes from Time Series Data
Wu, H., & No'e, F. (2017) · Journal of nonlinear science · doi:10.1007/s00332-019-09567-y · Cited by 354 · see citing works
Self-citationBottom-up Coarse-Graining: Principles and Perspectives
Jin, J., Pak, A. J., Durumeric, A. E. P., Loose, T. D., & Voth, G. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00643 · Cited by 296 · see citing works
Machine learning approaches for analyzing and enhancing molecular dynamics simulations
Wang, Y., Lamim Ribeiro, J. M., & Tiwary, P. (2020) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2019.12.016 · Cited by 303 · see citing works
Data-Driven Model Reduction and Transfer Operator Approximation
Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., & Noé, F. (2018) · Journal of nonlinear science · doi:10.1007/s00332-017-9437-7
Self-citationMSMBuilder: Statistical Models for Biomolecular Dynamics
Harrigan, M. P., Sultan, M. M., Hernández, C. X., Husic, B. E., Eastman, P., Schwantes, C. R., Beauchamp, K. A., McGibbon, R. T., & Pande, V. S. (2017) · Biophysical Journal · doi:10.1016/j.bpj.2016.10.042 · Cited by 277 · see citing works
Klus, S., Nüske, F., Peitz, S., Niemann, J.-H., Clementi, C., & Schütte, C. (2020) · Physica D Nonlinear Phenomena · doi:10.1016/j.physd.2020.132416 · Cited by 269 · see citing works
Self-citationOn the numerical approximation of the Perron-Frobenius and Koopman operator
Klus, S., Koltai, P., & Schütte, C. (2015) · Journal of Computational Dynamics · doi:10.3934/jcd.2016003 · Cited by 346 · see citing works
Data-driven science and engineering : machine learning, dynamical systems, and control
Brunton, S. L., & Kutz, J. N. (2019) · doi:10.1017/978-1-009-08951-7 · Cited by 270 · see citing works
Kinetic distance and kinetic maps from molecular dynamics simulation.
Noé, F., & Clementi, C. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00553 · Cited by 211 · see citing works
Self-citationGkeka, P., Stoltz, G., Farimani, A. B., Belkacemi, Z., Ceriotti, M., Chodera, J. D., Dinner, A. R., Ferguson, A. L., Maillet, J., Minoux, H., et al. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00355 · Cited by 211 · see citing works
Variational cross-validation of slow dynamical modes in molecular kinetics
McGibbon, R. T., & Pande, V. S. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4916292 · Cited by 191 · see citing works
Machine learning and data science in soft materials engineering
Ferguson, A. L. (2018) · Journal of Physics: Condensed Matter · doi:10.1088/1361-648x/aa98bd · Cited by 137 · see citing works
Role of conformational dynamics in the evolution of novel enzyme function
Maria-Solano, M. A., Serrano-Hervás, E., Romero-Rivera, A., Iglesias-Fernández, J., & Osuna, S. (2018) · Chemical Communications · doi:10.1039/c8cc02426j · Cited by 112 · see citing works
Machine learning for protein folding and dynamics
Noé, F., Fabritiis, G. D., & Clementi, C. (2019) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2019.12.005 · Cited by 172 · see citing works
Self-citationtICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables
Sultan, M. M., & Pande, V. S. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00182 · Cited by 167 · see citing works
Discovery of nonlinear multiscale systems: Sampling strategies and embeddings
Champion, K. P., Brunton, S. L., & Kutz, J. N. (2019) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/18m1188227 · Cited by 171 · see citing works
Noé, F., & Clementi, C. (2017) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2017.02.006 · Cited by 161 · see citing works
Self-citationTime-Delay Observables for Koopman: Theory and Applications
Kamb, M., Kaiser, E., Brunton, S., & Kutz, J. (2018) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/18m1216572 · Cited by 168 · see citing works
Modeling Molecular Kinetics with tICA and the Kernel Trick
Schwantes, C. R., & Pande, V. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/ct5007357 · Cited by 157 · see citing works
Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders
Chen, W., Sidky, H., & Ferguson, A. L. (2019) · Journal of Chemical Physics · doi:10.1063/1.5092521 · Cited by 124 · see citing works
Deeptime: a Python library for machine learning dynamical models from time series data
Hoffmann, M., Scherer, M. K., Hempel, T., Mardt, A., de Silva, B. M., Husic, B., Klus, S., Wu, H., Kutz, N., Brunton, S., et al. (2021) · Machine Learning: Science and Technology · doi:10.1088/2632-2153/ac3de0 · Cited by 193 · see citing works
Self-citationChen, W., Tan, A. R., & Ferguson, A. L. (2018) · Journal of Chemical Physics · doi:10.1063/1.5023804 · Cited by 133 · see citing works
Ryckbosch, S., Wender, P., & Pande, V. (2017) · Nature Communications · doi:10.1038/s41467-016-0015-8 · Cited by 125 · see citing works
Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation
Sidky, H., Chen, W., & Ferguson, A. L. (2020) · Molecular Physics · doi:10.1080/00268976.2020.1737742 · Cited by 147 · see citing works
Wang, W., Cao, S.-Q., Zhu, L.-Z., & Huang, X.-H. (2018) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1343 · Cited by 137 · see citing works
Wu, H., Nüske, F., Paul, F., Klus, S., Koltai, P., & Noé, F. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4979344 · Cited by 140 · see citing works
Self-citationPromising directions of machine learning for partial differential equations
Brunton, S., & Kutz, J. (2024) · Nature Computational Science · doi:10.1038/s43588-024-00643-2 · Cited by 196 · see citing works
Enhanced Sampling with Machine Learning
Mehdi, S., Smith, Z., Herron, L., Zou, Z., & Tiwary, P. (2024) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-083122-125941 · Cited by 136 · see citing works
Estimation and uncertainty of reversible Markov models
Trendelkamp-Schroer, B., Wu, H., Paul, F., & Noé, F. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4934536 · Cited by 137 · see citing works
Self-citationDiscovering causal relations and equations from data
Camps‐Valls, G., Gerhardus, A., Ninad, U., Varando, G., Martius, G., Balaguer‐Ballester, E., Vinuesa, R., Díaz, E., Zanna, L., & Runge, J. (2023) · Physics Reports · doi:10.1016/j.physrep.2023.10.005 · Cited by 136 · see citing works
McCarty, J. J., & Parrinello, M. (2017) · Journal of Chemical Physics · doi:10.1063/1.4998598 · Cited by 120 · see citing works
Bello‐Rivas, J. M., & Elber, R. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4913399 · Cited by 118 · see citing works
Transferable Neural Networks for Enhanced Sampling of Protein Dynamics.
Sultan, M. M., Wayment-Steele, H. K., & Pande, V. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00025 · Cited by 110 · see citing works
Eigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
Klus, S., Schuster, I., & Muandet, K. (2017) · Journal of nonlinear science · doi:10.1007/s00332-019-09574-z · Cited by 153 · see citing works
Optimal Dimensionality Reduction of Multistate Kinetic and Markov-State Models
Hummer, G., & Szabó, A. (2014) · The Journal of Physical Chemistry B · doi:10.1021/jp508375q · Cited by 101 · see citing works
Neural Networks and Deep Learning
Brunton, S. L., & Kutz, J. N. (2019) · Cambridge University Press eBooks · doi:10.1017/9781108380690.007 · Cited by 104 · see citing works
Identification of simple reaction coordinates from complex dynamics
McGibbon, R. T., Husic, B. E., & Pande, V. S. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4974306 · Cited by 90 · see citing works
DeepGreen: deep learning of Green’s functions for nonlinear boundary value problems
Gin, C., Shea, D., Brunton, S., & Kutz, J. (2020) · Scientific Reports · doi:10.1038/s41598-021-00773-x · Cited by 129 · see citing works
Galerkin approximation of dynamical quantities using trajectory data
Thiede, E. H., Giannakis, D., Dinner, A. R., & Weare, J. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5063730 · Cited by 90 · see citing works
Perspective: Markov models for long-timescale biomolecular dynamics.
Schwantes, C. R., McGibbon, R., & Pande, V. (2014) · Journal of Chemical Physics · doi:10.1063/1.4895044 · Cited by 88 · see citing works
Coarse-grained modelling out of equilibrium
Schilling, T. (2021) · Physics reports · doi:10.1016/j.physrep.2022.04.006 · Cited by 92 · see citing works
Chasing Collective Variables Using Autoencoders and Biased Trajectories
Belkacemi, Z., Gkeka, P., Tony Lelièvre, A., & Stoltz, G. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c00415 · Cited by 85 · see citing works
Kutz, J., Proctor, J. L., & Brunton, S. (2018) · Complex · doi:10.1155/2018/6010634 · Cited by 98 · see citing works
Markov Models of Molecular Kinetics.
No'e, F., & Rosta, E. (2019) · Journal of Chemical Physics · doi:10.1063/1.5134029 · Cited by 77 · see citing works
Self-citationRigorous data‐driven computation of spectral properties of Koopman operators for dynamical systems
Colbrook, M. J., & Townsend, A. (2023) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.22125 · Cited by 88 · see citing works
Methods for data-driven multiscale model discovery for materials
Brunton, S., & Kutz, J. (2019) · Journal of Physics Materials · doi:10.1088/2515-7639/ab291e · Cited by 78 · see citing works
Pérez‐Hernández, G., & Noé, F. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00738 · Cited by 76 · see citing works
Self-citationRudzinski, J. F. (2019) · De Computis · doi:10.3390/computation7030042 · Cited by 73 · see citing works
Density-based cluster algorithms for the identification of core sets.
Lemke, O., & Keller, B. (2016) · Journal of Chemical Physics · doi:10.1063/1.4965440 · Cited by 71 · see citing works
Self-citationCollective variable-based enhanced sampling and machine learning
Chen, M. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00220-w · Cited by 72 · see citing works
Machine Learning for Molecular Dynamics on Long Timescales
Noé, F. (2020) · Lecture notes in physics · doi:10.1007/978-3-030-40245-7_16 · Cited by 71 · see citing works
Self-citationVariational selection of features for molecular kinetics.
Scherer, M. K., Husic, B., Hoffmann, M., Paul, F., Wu, H., & Noé, F. (2018) · Journal of Chemical Physics · doi:10.1063/1.5083040 · Cited by 63 · see citing works
Self-citationVariational tensor approach for approximating the rare-event kinetics of macromolecular systems
Nüske, F., Schneider, R., Vitalini, F., & Noé, F. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4940774 · Cited by 67 · see citing works
Self-citationSidky, H., Chen, W., & Ferguson, A. L. (2019) · Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.9b05578 · Cited by 67 · see citing works
Challenges in dynamic mode decomposition
Wu, Z.-Y., Brunton, S., & Revzen, S. (2021) · Journal of the Royal Society Interface · doi:10.1098/rsif.2021.0686 · Cited by 71 · see citing works
Discovering Reaction Pathways, Slow Variables, and Committor Probabilities with Machine Learning
Chen, H., Roux, B., & Chipot, C. J. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00028 · Cited by 65 · see citing works
Optimized parameter selection reveals trends in Markov state models for protein folding.
Husic, B., McGibbon, R., Sultan, M. M., & Pande, V. (2016) · Journal of Chemical Physics · doi:10.1063/1.4967809 · Cited by 59 · see citing works
Ligand diffusion in proteins via enhanced sampling in molecular dynamics
Rydzewski, J., & Nowak, W. (2017) · Physics of Life Reviews · doi:10.1016/j.plrev.2017.03.003 · Cited by 63 · see citing works
Suárez, E., Wiewiora, R. P., Wehmeyer, C., Noé, F., Chodera, J. D., & Zuckerman, D. M. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01154 · Cited by 65 · see citing works
Self-citationParsimony as the ultimate regularizer for physics-informed machine learning
Kutz, J., & Brunton, S. (2022) · Nonlinear dynamics · doi:10.1007/s11071-021-07118-3 · Cited by 67 · see citing works
Characterizing magnetized plasmas with dynamic mode decomposition
Kaptanoglu, A., Morgan, K., Hansen, C., & Brunton, S. (2019) · Physics of Plasmas · doi:10.1063/1.5138932 · Cited by 71 · see citing works
Computational methods for exploring protein conformations
Allison, J. R. (2020) · Biochemical Society Transactions · doi:10.1042/bst20200193 · Cited by 54 · see citing works
Nüske, F., Wu, H., Prinz, J.-H., Wehmeyer, C., Clementi, C., & Noé, F. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4976518 · Cited by 60 · see citing works
Self-citationCooperative Changes in Solvent Exposure Identify Cryptic Pockets, Switches, and Allosteric Coupling.
Porter, J., Moeder, K. E., Sibbald, C., Zimmerman, M. I., Hart, K., Greenberg, M. J., & Bowman, G. (2019) · Biophysical Journal · doi:10.1016/j.bpj.2018.11.3144 · Cited by 68 · see citing works
Zhang, L., Pardo‐Ávila, F., Unarta, I. C., Cheung, P. P., Guo, W., Wang, D., & Huang, X. (2016) · Accounts of Chemical Research · doi:10.1021/acs.accounts.5b00536 · Cited by 58 · see citing works
Girsanov reweighting for metadynamics simulations.
Donati, L., & Keller, B. (2018) · Journal of Chemical Physics · doi:10.1063/1.5027728 · Cited by 66 · see citing works
Self-citationThe dynamic conformational landscape of the protein methyltransferase SETD8
Chen, S., Wiewiora, R. P., Meng, F.-W., Babault, N., Ma, A., Yu, W.-Y., Qian, K., Hu, H., Zou, H., Wang, J., et al. (2019) · eLife · doi:10.7554/elife.45403 · Cited by 41 · see citing works
Deep learning models for global coordinate transformations that linearise PDEs
Gin, C., Lusch, B., Brunton, S., & Kutz, J. (2019) · European journal of applied mathematics · doi:10.1017/s0956792520000327 · Cited by 47 · see citing works
Investigating Molecular Kinetics by Variationally Optimized Diffusion Maps
Boninsegna, L., Gobbo, G., Noé, F., & Clementi, C. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00749 · Cited by 56 · see citing works
Self-citationMeng, Y., Gao, C., Clawson, D. K., Atwell, S., Russell, M., Vieth, M., & Roux, B. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b01170 · Cited by 56 · see citing works
Recognizing Local and Global Structural Motifs at the Atomic Scale
Gasparotto, P., Meißner, R. H., & Ceriotti, M. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00993 · Cited by 50 · see citing works
Deep learning collective variables from transition path ensemble.
Ray, D., Trizio, E., & Parrinello, M. (2023) · Journal of Chemical Physics · doi:10.1063/5.0148872 · Cited by 54 · see citing works
Enhanced Sampling in the Age of Machine Learning: Algorithms and Applications
Zhu, K., Trizio, E., Zhang, J., Hu, R., Jiang, L., Hou, T., & Bonati, L. (2025) · Chemical Reviews · doi:10.1021/acs.chemrev.5c00700 · Cited by 54 · see citing works
Molecular latent space simulators
Sidky, H., Chen, W., & Ferguson, A. L. (2020) · Chemical Science · doi:10.1039/d0sc03635h · Cited by 52 · see citing works
Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling.
Noé, F., Banisch, R., & Clementi, C. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00762 · Cited by 58 · see citing works
Self-citationGirsanov reweighting for path ensembles and Markov state models
Donati, L., Hartmann, C., & Keller, B. G. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4989474 · Cited by 52 · see citing works
Self-citationGhorbani, M., Prasad, S., Klauda, J. B., & Brooks, B. R. (2022) · The Journal of Chemical Physics · doi:10.1063/5.0085607 · Cited by 51 · see citing works
Banushkina, P. V., & Krivov, S. V. (2016) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1276 · Cited by 50 · see citing works
Transition rate theory, spectral analysis, and reactive paths
Roux, B. (2022) · Journal of Chemical Physics · doi:10.1063/5.0084209 · Cited by 50 · see citing works
Ward Clustering Improves Cross-Validated Markov State Models of Protein Folding.
Husic, B., & Pande, V. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b01238 · Cited by 46 · see citing works
Sultan, M. M., Denny, R., Unwalla, R., Lovering, F., & Pande, V. (2017) · Scientific Reports · doi:10.1038/s41598-017-10697-0 · Cited by 50 · see citing works
String Method with Swarms-of-Trajectories, Mean Drifts, Lag Time, and Committor
Roux, B. (2021) · The Journal of Physical Chemistry A · doi:10.1021/acs.jpca.1c04110 · Cited by 48 · see citing works
Sheong, F. K., Silva, D., Meng, L., Zhao, Y., & Huang, X. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct5007168 · Cited by 43 · see citing works
Dynamic graphical models of molecular kinetics
Olsson, S., & Noé, F. (2018) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1901692116 · Cited by 40 · see citing works
Self-citationA Maximum-Caliber Approach to Predicting Perturbed Folding Kinetics Due to Mutations.
Wan, H., Zhou, G., & Voelz, V. A. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00938 · Cited by 42 · see citing works
Accelerated Simulations of Molecular Systems through Learning of Effective Dynamics
Vlachas, P. R., Zavadlav, J., Praprotnik, M., & Koumoutsakos, P. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c00809 · Cited by 45 · see citing works
Lin, Y.-T., Tian, Y.-F., Livescu, D., & Anghel, M. (2021) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/21m1401759 · Cited by 56 · see citing works
Strahan, J., Antoszewski, A., Lorpaiboon, C., Vani, B. P., Weare, J., & Dinner, A. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00933 · Cited by 46 · see citing works
Coarse-graining molecular systems by spectral matching.
Nüske, F., Boninsegna, L., & Clementi, C. (2019) · Journal of Chemical Physics · doi:10.1063/1.5100131 · Cited by 35 · see citing works
Self-citationSmith, Z., Pramanik, D., Tsai, S.-T., & Tiwary, P. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5064856 · Cited by 40 · see citing works
- Authors
- Nüske, F., Keller, B. G., Pérez-Hernández, G., Mey, A. S. J. S., & Noé, F.
- Affiliations
- Freie Universität Berlin (DE)
- Department for Mathematics and Computer Science, Freie Universität Berlin, 14195 Berlin, Germany
- Corresponding author
- Keller, Bettina G.
- Noé, Frank
- Venue
- Journal of Chemical Theory and Computation
- Publisher
- American Chemical Society (ACS)
- Published
- 2014-03-06
- Volume
- 10
- Issue
- 4
- Pages
- 1739-1752
- ISSN
- 1549-9618 (ISSN-L)
- 1549-9626
- OpenAlex
- W1989544083
- Cited by
- 308
- References
- 66
- Citations by year
- 2026: 18 · 2025: 19 · 2024: 23 · 2023: 27 · 2022: 26 · 2021: 25 · 2020: 26 · 2019: 43 · 2018: 32 · 2017: 27 · 2016: 21 · 2015: 15 · 2014: 6
- FWCI
- 14.75
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Chemical Theory and Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Advanced Thermodynamics and Statistical Mechanics
- Keywords
- molecular kinetics, transfer operator, stationary distribution, metastable states, correlation matrix, conformational change, variational methods
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
