Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation

Sidky, Hythem; Chen, Wei; Ferguson, Andrew L.

doi:10.1080/00268976.2020.1737742

Title: Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation

Journal Article · Tue Mar 10 00:00:00 EDT 2020 · Molecular Physics

DOI:https://doi.org/10.1080/00268976.2020.1737742· OSTI ID:1651117

Sidky, Hythem ^[1]; Chen, Wei ^[2];

^[1]

University of Chicago, IL (United States)
University of Illinois at Urbana-Champaign, IL (United States)

Classical molecular dynamics simulates the time evolution of molecular systems through the phase space spanned by the positions and velocities of the constituent atoms. Molecular-level thermodynamic, kinetic, and structural data extracted from the resulting trajectories provide valuable information for the understanding, engineering, and design of biological and molecular materials. The cost of simulating many-body atomic systems makes simulations of large molecules prohibitively expensive, and the high-dimensionality of the resulting trajectories presents a challenge for analysis. Driven by advances in algorithms, hardware, and data availability, there has been a flare of interest in recent years in the applications of machine learning – especially deep learning – to molecular simulation. Furthermore, these techniques have demonstrated great power and flexibility in both extracting mechanistic understanding of the important nonlinear collective variables governing the dynamics of a molecular system, and in furnishing good low-dimensional system representations with which to perform enhanced sampling or develop long-timescale dynamical models. It is the purpose of this article to introduce the key machine learning approaches, describe how they are married with statistical mechanical theory into domain-specific tools, and detail applications of these approaches in understanding and accelerating biomolecular simulation.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES). Materials Sciences & Engineering Division

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1651117

Journal Information:: Molecular Physics, Vol. 118, Issue 5; ISSN 0026-8976

Publisher:: Taylor & FrancisCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 77 works

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References (150)

Reduced Models in Chemical Kinetics via Nonlinear Data-Mining Chiavazzo, Eliodoro; Gear, Charles; Dsilva, Carmeline Processes, Vol. 2, Issue 1 https://doi.org/10.3390/pr2010112	journal	January 2014
Charting molecular free-energy landscapes with an atlas of collective variables Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino The Journal of Chemical Physics, Vol. 145, Issue 17 https://doi.org/10.1063/1.4966262	journal	November 2016
A self-learning algorithm for biased molecular dynamics Tribello, Gareth A.; Ceriotti, Michele; Parrinello, Michele Proceedings of the National Academy of Sciences, Vol. 107, Issue 41 https://doi.org/10.1073/pnas.1011511107	journal	September 2010
Girsanov reweighting for metadynamics simulations Donati, Luca; Keller, Bettina G. The Journal of Chemical Physics, Vol. 149, Issue 7 https://doi.org/10.1063/1.5027728	journal	August 2018
Using sketch-map coordinates to analyze and bias molecular dynamics simulations Tribello, G. A.; Ceriotti, M.; Parrinello, M. Proceedings of the National Academy of Sciences, Vol. 109, Issue 14 https://doi.org/10.1073/pnas.1201152109	journal	March 2012
Graph Laplacian Tomography From Unknown Random Projections Coifman, R. R.; Shkolnisky, Y.; Sigworth, F. J. IEEE Transactions on Image Processing, Vol. 17, Issue 10 https://doi.org/10.1109/TIP.2008.2002305	journal	October 2008
Nonphysical sampling distributions in Monte Carlo free-energy estimation: Umbrella sampling Torrie, G. M.; Valleau, J. P. Journal of Computational Physics, Vol. 23, Issue 2 https://doi.org/10.1016/0021-9991(77)90121-8	journal	February 1977
Transferable Neural Networks for Enhanced Sampling of Protein Dynamics Sultan, Mohammad M.; Wayment-Steele, Hannah K.; Pande, Vijay S. Journal of Chemical Theory and Computation, Vol. 14, Issue 4 https://doi.org/10.1021/acs.jctc.8b00025	journal	March 2018
Machine learning of single molecule free energy surfaces and the impact of chemistry and environment upon structure and dynamics Mansbach, Rachael A.; Ferguson, Andrew L. The Journal of Chemical Physics, Vol. 142, Issue 10 https://doi.org/10.1063/1.4914144	journal	March 2015
Molecular modeling studies of peptoid polymers J. Weiser, Laura; E. Santiso, Erik AIMS Materials Science, Vol. 4, Issue 5 https://doi.org/10.3934/matersci.2017.5.1029	journal	January 2017
Nonlinear machine learning in simulations of soft and biological materials Wang, J.; Ferguson, A. L. Molecular Simulation, Vol. 44, Issue 13-14 https://doi.org/10.1080/08927022.2017.1400164	journal	November 2017
Reaction coordinates and transition pathways of rare events via forward flux sampling Borrero, Ernesto E.; Escobedo, Fernando A. The Journal of Chemical Physics, Vol. 127, Issue 16 https://doi.org/10.1063/1.2776270	journal	October 2007
Large-amplitude nonlinear motions in proteins García, Angel E. Physical Review Letters, Vol. 68, Issue 17 https://doi.org/10.1103/PhysRevLett.68.2696	journal	April 1992
Dynamical reweighting: Improved estimates of dynamical properties from simulations at multiple temperatures Chodera, John D.; Swope, William C.; Noé, Frank The Journal of Chemical Physics, Vol. 134, Issue 24 https://doi.org/10.1063/1.3592152	journal	June 2011
Optimal use of data in parallel tempering simulations for the construction of discrete-state Markov models of biomolecular dynamics Prinz, Jan-Hendrik; Chodera, John D.; Pande, Vijay S. The Journal of Chemical Physics, Vol. 134, Issue 24 https://doi.org/10.1063/1.3592153	journal	June 2011
Diffusion maps Coifman, Ronald R.; Lafon, Stéphane Applied and Computational Harmonic Analysis, Vol. 21, Issue 1 https://doi.org/10.1016/j.acha.2006.04.006	journal	July 2006
VAMPnets for deep learning of molecular kinetics Mardt, Andreas; Pasquali, Luca; Wu, Hao Nature Communications, Vol. 9, Issue 1 https://doi.org/10.1038/s41467-017-02388-1	journal	January 2018
Kinetic Distance and Kinetic Maps from Molecular Dynamics Simulation Noé, Frank; Clementi, Cecilia Journal of Chemical Theory and Computation, Vol. 11, Issue 10 https://doi.org/10.1021/acs.jctc.5b00553	journal	September 2015
Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations Wu, Hao; Nüske, Feliks; Paul, Fabian The Journal of Chemical Physics, Vol. 146, Issue 15 https://doi.org/10.1063/1.4979344	journal	April 2017
Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling Noé, Frank; Banisch, Ralf; Clementi, Cecilia Journal of Chemical Theory and Computation, Vol. 12, Issue 11 https://doi.org/10.1021/acs.jctc.6b00762	journal	October 2016
Demonstrating the Transferability and the Descriptive Power of Sketch-Map Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 9, Issue 3 https://doi.org/10.1021/ct3010563	journal	February 2013
Collective variable discovery and enhanced sampling using autoencoders: Innovations in network architecture and error function design Chen, Wei; Tan, Aik Rui; Ferguson, Andrew L. The Journal of Chemical Physics, Vol. 149, Issue 7 https://doi.org/10.1063/1.5023804	journal	August 2018
How Fast-Folding Proteins Fold Lindorff-Larsen, K.; Piana, S.; Dror, R. O. Science, Vol. 334, Issue 6055 https://doi.org/10.1126/science.1208351	journal	October 2011
Nonlinear Machine Learning of Patchy Colloid Self-Assembly Pathways and Mechanisms Long, Andrew W.; Ferguson, Andrew L. The Journal of Physical Chemistry B, Vol. 118, Issue 15 https://doi.org/10.1021/jp500350b	journal	April 2014
A Study of the Morphology, Dynamics, and Folding Pathways of Ring Polymers with Supramolecular Topological Constraints Using Molecular Simulation and Nonlinear Manifold Learning Wang, Jiang; Ferguson, Andrew L. Macromolecules, Vol. 51, Issue 2 https://doi.org/10.1021/acs.macromol.7b01684	journal	January 2018
Discovering Mountain Passes via Torchlight: Methods for the Definition of Reaction Coordinates and Pathways in Complex Macromolecular Reactions Rohrdanz, Mary A.; Zheng, Wenwei; Clementi, Cecilia Annual Review of Physical Chemistry, Vol. 64, Issue 1 https://doi.org/10.1146/annurev-physchem-040412-110006	journal	April 2013
High-Resolution Markov State Models for the Dynamics of Trp-Cage Miniprotein Constructed Over Slow Folding Modes Identified by State-Free Reversible VAMPnets Sidky, Hythem; Chen, Wei; Ferguson, Andrew L. The Journal of Physical Chemistry B, Vol. 123, Issue 38 https://doi.org/10.1021/acs.jpcb.9b05578	journal	August 2019
Variational Approach to Molecular Kinetics Nüske, Feliks; Keller, Bettina G.; Pérez-Hernández, Guillermo Journal of Chemical Theory and Computation, Vol. 10, Issue 4 https://doi.org/10.1021/ct4009156	journal	March 2014
Unmasking Clever Hans predictors and assessing what machines really learn Lapuschkin, Sebastian; Wäldchen, Stephan; Binder, Alexander Nature Communications, Vol. 10, Issue 1 https://doi.org/10.1038/s41467-019-08987-4	journal	March 2019
SchNet – A deep learning architecture for molecules and materials Schütt, K. T.; Sauceda, H. E.; Kindermans, P. -J. The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5019779	journal	June 2018
Deep clustering of protein folding simulations Bhowmik, Debsindhu; Gao, Shang; Young, Michael T. BMC Bioinformatics, Vol. 19, Issue S18 https://doi.org/10.1186/s12859-018-2507-5	journal	December 2018
Automated design of collective variables using supervised machine learning Sultan, Mohammad M.; Pande, Vijay S. The Journal of Chemical Physics, Vol. 149, Issue 9 https://doi.org/10.1063/1.5029972	journal	September 2018
Automatic Method for Identifying Reaction Coordinates in Complex Systems ^† Ma, Ao; Dinner, Aaron R. The Journal of Physical Chemistry B, Vol. 109, Issue 14 https://doi.org/10.1021/jp045546c	journal	April 2005
Molecular enhanced sampling with autoencoders: On-the-fly collective variable discovery and accelerated free energy landscape exploration: Molecular Enhanced Sampling with Autoencoders: On-The-Fly Collective Variable Discovery and Accelerated Free Energy Landscape Exploration Chen, Wei; Ferguson, Andrew L. Journal of Computational Chemistry, Vol. 39, Issue 25 https://doi.org/10.1002/jcc.25520	journal	September 2018
Integrating diffusion maps with umbrella sampling: Application to alanine dipeptide Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Debenedetti, Pablo G. The Journal of Chemical Physics, Vol. 134, Issue 13 https://doi.org/10.1063/1.3574394	journal	April 2011
Spectral gap optimization of order parameters for sampling complex molecular systems Tiwary, Pratyush; Berne, B. J. Proceedings of the National Academy of Sciences, Vol. 113, Issue 11 https://doi.org/10.1073/pnas.1600917113	journal	February 2016
Collective motions in proteins: A covariance analysis of atomic fluctuations in molecular dynamics and normal mode simulations Ichiye, Toshiko; Karplus, Martin Proteins: Structure, Function, and Genetics, Vol. 11, Issue 3 https://doi.org/10.1002/prot.340110305	journal	November 1991
Machine Calculation of Thermodynamic Properties of a Simple Fluid at Supercritical Temperatures McDonald, I. R.; Singer, K. The Journal of Chemical Physics, Vol. 47, Issue 11 https://doi.org/10.1063/1.1701695	journal	December 1967
Design of therapeutic proteins with enhanced stability Chennamsetty, N.; Voynov, V.; Kayser, V. Proceedings of the National Academy of Sciences, Vol. 106, Issue 29 https://doi.org/10.1073/pnas.0904191106	journal	July 2009
Koopman operator-based model reduction for switched-system control of PDEs Peitz, Sebastian; Klus, Stefan Automatica, Vol. 106 https://doi.org/10.1016/j.automatica.2019.05.016	journal	August 2019
Stochastic Gradient Descent Tricks Bottou, Léon Lecture Notes in Computer Science https://doi.org/10.1007/978-3-642-35289-8_25	book	January 2012
Markov models of molecular kinetics: Generation and validation Prinz, Jan-Hendrik; Wu, Hao; Sarich, Marco The Journal of Chemical Physics, Vol. 134, Issue 17 https://doi.org/10.1063/1.3565032	journal	May 2011
Intrinsic map dynamics exploration for uncharted effective free-energy landscapes Chiavazzo, Eliodoro; Covino, Roberto; Coifman, Ronald R. Proceedings of the National Academy of Sciences, Vol. 114, Issue 28 https://doi.org/10.1073/pnas.1621481114	journal	June 2017
Modeling Molecular Kinetics with tICA and the Kernel Trick Schwantes, Christian R.; Pande, Vijay S. Journal of Chemical Theory and Computation, Vol. 11, Issue 2 https://doi.org/10.1021/ct5007357	journal	January 2015
A Variational Approach to Modeling Slow Processes in Stochastic Dynamical Systems Noé, Frank; Nüske, Feliks Multiscale Modeling & Simulation, Vol. 11, Issue 2 https://doi.org/10.1137/110858616	journal	January 2013
Markov state models of biomolecular conformational dynamics Chodera, John D.; Noé, Frank Current Opinion in Structural Biology, Vol. 25 https://doi.org/10.1016/j.sbi.2014.04.002	journal	April 2014
A variational conformational dynamics approach to the selection of collective variables in metadynamics McCarty, James; Parrinello, Michele The Journal of Chemical Physics, Vol. 147, Issue 20 https://doi.org/10.1063/1.4998598	journal	November 2017
A Data–Driven Approximation of the Koopman Operator: Extending Dynamic Mode Decomposition Williams, Matthew O.; Kevrekidis, Ioannis G.; Rowley, Clarence W. Journal of Nonlinear Science, Vol. 25, Issue 6 https://doi.org/10.1007/s00332-015-9258-5	journal	June 2015
Finite approximations of Frobenius-Perron operators. A solution of Ulam's conjecture to multi-dimensional transformations Ding, Jiu; Zhou, Aihui Physica D: Nonlinear Phenomena, Vol. 92, Issue 1-2 https://doi.org/10.1016/0167-2789(95)00292-8	journal	April 1996
Collective Variables from Local Fluctuations Mendels, Dan; Piccini, GiovanniMaria; Parrinello, Michele The Journal of Physical Chemistry Letters, Vol. 9, Issue 11 https://doi.org/10.1021/acs.jpclett.8b00733	journal	May 2018
Reweighted autoencoded variational Bayes for enhanced sampling (RAVE) Ribeiro, João Marcelo Lamim; Bravo, Pablo; Wang, Yihang The Journal of Chemical Physics, Vol. 149, Issue 7 https://doi.org/10.1063/1.5025487	journal	August 2018
Simplifying the representation of complex free-energy landscapes using sketch-map Ceriotti, Michele; Tribello, Gareth A.; Parrinello, Michele Proceedings of the National Academy of Sciences, Vol. 108, Issue 32 https://doi.org/10.1073/pnas.1108486108	journal	July 2011
Learning free energy landscapes using artificial neural networks Sidky, Hythem; Whitmer, Jonathan K. The Journal of Chemical Physics, Vol. 148, Issue 10 https://doi.org/10.1063/1.5018708	journal	March 2018
Enhancing Important Fluctuations: Rare Events and Metadynamics from a Conceptual Viewpoint Valsson, Omar; Tiwary, Pratyush; Parrinello, Michele Annual Review of Physical Chemistry, Vol. 67, Issue 1 https://doi.org/10.1146/annurev-physchem-040215-112229	journal	May 2016
Data-Driven Model Reduction and Transfer Operator Approximation Klus, Stefan; Nüske, Feliks; Koltai, Péter Journal of Nonlinear Science, Vol. 28, Issue 3 https://doi.org/10.1007/s00332-017-9437-7	journal	January 2018
Generalized Neural-Network Representation of High-Dimensional Potential-Energy Surfaces Behler, Jörg; Parrinello, Michele Physical Review Letters, Vol. 98, Issue 14 https://doi.org/10.1103/PhysRevLett.98.146401	journal	April 2007
Nonlinear discovery of slow molecular modes using state-free reversible VAMPnets Chen, Wei; Sidky, Hythem; Ferguson, Andrew L. The Journal of Chemical Physics, Vol. 150, Issue 21 https://doi.org/10.1063/1.5092521	journal	June 2019
tICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables M. Sultan, Mohammad; Pande, Vijay S. Journal of Chemical Theory and Computation, Vol. 13, Issue 6 https://doi.org/10.1021/acs.jctc.7b00182	journal	May 2017
Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias Nüske, Feliks; Wu, Hao; Prinz, Jan-Hendrik The Journal of Chemical Physics, Vol. 146, Issue 9 https://doi.org/10.1063/1.4976518	journal	March 2017
A generalized deep learning approach for local structure identification in molecular simulations DeFever, Ryan S.; Targonski, Colin; Hall, Steven W. Chemical Science, Vol. 10, Issue 32 https://doi.org/10.1039/C9SC02097G	journal	January 2019
Universal approximation to nonlinear operators by neural networks with arbitrary activation functions and its application to dynamical systems IEEE Transactions on Neural Networks, Vol. 6, Issue 4 https://doi.org/10.1109/72.392253	journal	July 1995
Enhanced sampling in molecular dynamics Yang, Yi Isaac; Shao, Qiang; Zhang, Jun The Journal of Chemical Physics, Vol. 151, Issue 7 https://doi.org/10.1063/1.5109531	journal	August 2019
Metadynamics: Metadynamics Barducci, Alessandro; Bonomi, Massimiliano; Parrinello, Michele Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 1, Issue 5 https://doi.org/10.1002/wcms.31	journal	February 2011
Systematic characterization of protein folding pathways using diffusion maps: Application to Trp-cage miniprotein Kim, Sang Beom; Dsilva, Carmeline J.; Kevrekidis, Ioannis G. The Journal of Chemical Physics, Vol. 142, Issue 8 https://doi.org/10.1063/1.4913322	journal	February 2015
Simulating materials failure by using up to one billion atoms and the world's fastest computer: Brittle fracture Abraham, F. F.; Walkup, R.; Gao, H. Proceedings of the National Academy of Sciences, Vol. 99, Issue 9 https://doi.org/10.1073/pnas.062012699	journal	April 2002
What Is the Relation Between Slow Feature Analysis and Independent Component Analysis? Blaschke, Tobias; Berkes, Pietro; Wiskott, Laurenz Neural Computation, Vol. 18, Issue 10 https://doi.org/10.1162/neco.2006.18.10.2495	journal	October 2006
Local elevation: A method for improving the searching properties of molecular dynamics simulation Huber, Thomas; Torda, Andrew E.; van Gunsteren, Wilfred F. Journal of Computer-Aided Molecular Design, Vol. 8, Issue 6 https://doi.org/10.1007/BF00124016	journal	December 1994
On the Use of Experimental Observations to Bias Simulated Ensembles Pitera, Jed W.; Chodera, John D. Journal of Chemical Theory and Computation, Vol. 8, Issue 10 https://doi.org/10.1021/ct300112v	journal	March 2012
Machine learning for molecular and materials science Butler, Keith T.; Davies, Daniel W.; Cartwright, Hugh Nature, Vol. 559, Issue 7715 https://doi.org/10.1038/s41586-018-0337-2	journal	July 2018
Unconstrained enhanced sampling for free energy calculations of biomolecules: a review Miao, Yinglong; McCammon, J. Andrew Molecular Simulation, Vol. 42, Issue 13 https://doi.org/10.1080/08927022.2015.1121541	journal	July 2016
Predicting slow structural transitions in macromolecular systems: Conformational flooding Grubmüller, Helmut Physical Review E, Vol. 52, Issue 3 https://doi.org/10.1103/PhysRevE.52.2893	journal	September 1995
NSF’s Inaugural Software Institutes: The Science Gateways Community Institute and the Molecular Sciences Software Institute Wilkins-Diehr, Nancy; Crawford, T. Daniel Computing in Science & Engineering, Vol. 20, Issue 5 https://doi.org/10.1109/MCSE.2018.05329813	journal	September 2018
Perspective: Computational chemistry software and its advancement as illustrated through three grand challenge cases for molecular science Krylov, Anna; Windus, Theresa L.; Barnes, Taylor The Journal of Chemical Physics, Vol. 149, Issue 18 https://doi.org/10.1063/1.5052551	journal	November 2018
Neural Network and Nearest Neighbor Algorithms for Enhancing Sampling of Molecular Dynamics Galvelis, Raimondas; Sugita, Yuji Journal of Chemical Theory and Computation, Vol. 13, Issue 6 https://doi.org/10.1021/acs.jctc.7b00188	journal	May 2017
The Protein Folding Problem Dill, Ken A.; Ozkan, S. Banu; Shell, M. Scott Annual Review of Biophysics, Vol. 37, Issue 1 https://doi.org/10.1146/annurev.biophys.37.092707.153558	journal	June 2008
The reweighted path ensemble Rogal, Jutta; Lechner, Wolfgang; Juraszek, Jarek The Journal of Chemical Physics, Vol. 133, Issue 17 https://doi.org/10.1063/1.3491817	journal	November 2010
Determination of reaction coordinates via locally scaled diffusion map Rohrdanz, Mary A.; Zheng, Wenwei; Maggioni, Mauro The Journal of Chemical Physics, Vol. 134, Issue 12 https://doi.org/10.1063/1.3569857	journal	March 2011
A Global Geometric Framework for Nonlinear Dimensionality Reduction Tenenbaum, J. B. Science, Vol. 290, Issue 5500 https://doi.org/10.1126/science.290.5500.2319	journal	December 2000
Nonlinear principal component analysis using autoassociative neural networks Kramer, Mark A. AIChE Journal, Vol. 37, Issue 2 https://doi.org/10.1002/aic.690370209	journal	February 1991
Coarse-grained dynamics of an activity bump in a neural field model Laing, C. R.; Frewen, T. A.; Kevrekidis, I. G. Nonlinearity, Vol. 20, Issue 9 https://doi.org/10.1088/0951-7715/20/9/007	journal	July 2007
Enhanced Sampling in Molecular Dynamics Using Metadynamics, Replica-Exchange, and Temperature-Acceleration Abrams, Cameron; Bussi, Giovanni Entropy, Vol. 16, Issue 1 https://doi.org/10.3390/e16010163	journal	December 2013
BayesWHAM: A Bayesian approach for free energy estimation, reweighting, and uncertainty quantification in the weighted histogram analysis method Ferguson, Andrew L. Journal of Computational Chemistry, Vol. 38, Issue 18 https://doi.org/10.1002/jcc.24800	journal	May 2017
Atomic-Level Characterization of the Structural Dynamics of Proteins Shaw, D. E.; Maragakis, P.; Lindorff-Larsen, K. Science, Vol. 330, Issue 6002 https://doi.org/10.1126/science.1187409	journal	October 2010
Toward Achieving Efficient and Accurate Ligand-Protein Unbinding with Deep Learning and Molecular Dynamics through RAVE Lamim Ribeiro, João Marcelo; Tiwary, Pratyush Journal of Chemical Theory and Computation, Vol. 15, Issue 1 https://doi.org/10.1021/acs.jctc.8b00869	journal	November 2018
TweTriS: Twenty trillion-atom simulation Tchipev, Nikola; Seckler, Steffen; Heinen, Matthias The International Journal of High Performance Computing Applications, Vol. 33, Issue 5 https://doi.org/10.1177/1094342018819741	journal	January 2019
Studies in Molecular Dynamics. I. General Method Alder, B. J.; Wainwright, T. E. The Journal of Chemical Physics, Vol. 31, Issue 2 https://doi.org/10.1063/1.1730376	journal	August 1959
LIII. On lines and planes of closest fit to systems of points in space Pearson, Karl The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 2, Issue 11 https://doi.org/10.1080/14786440109462720	journal	November 1901
Protein folding and de novo protein design for biotechnological applications Khoury, George A.; Smadbeck, James; Kieslich, Chris A. Trends in Biotechnology, Vol. 32, Issue 2 https://doi.org/10.1016/j.tibtech.2013.10.008	journal	February 2014
The perceptron: A probabilistic model for information storage and organization in the brain. Rosenblatt, F. Psychological Review, Vol. 65, Issue 6 https://doi.org/10.1037/h0042519	journal	January 1958
Obtaining reaction coordinates by likelihood maximization Peters, Baron; Trout, Bernhardt L. The Journal of Chemical Physics, Vol. 125, Issue 5 https://doi.org/10.1063/1.2234477	journal	August 2006
Dynamic Mode Decomposition with Control Proctor, Joshua L.; Brunton, Steven L.; Kutz, J. Nathan SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue 1 https://doi.org/10.1137/15M1013857	journal	January 2016
Molecular dynamics simulations in biology Karplus, Martin; Petsko, Gregory A. Nature, Vol. 347, Issue 6294 https://doi.org/10.1038/347631a0	journal	October 1990
Adaptive enhanced sampling by force-biasing using neural networks Guo, Ashley Z.; Sevgen, Emre; Sidky, Hythem The Journal of Chemical Physics, Vol. 148, Issue 13 https://doi.org/10.1063/1.5020733	journal	April 2018
ACS Central Science Virtual Issue on Machine Learning Ferguson, Andrew L. ACS Central Science, Vol. 4, Issue 8 https://doi.org/10.1021/acscentsci.8b00528	journal	August 2018
Rapid Exploration of Configuration Space with Diffusion-Map-Directed Molecular Dynamics Zheng, Wenwei; Rohrdanz, Mary A.; Clementi, Cecilia The Journal of Physical Chemistry B, Vol. 117, Issue 42 https://doi.org/10.1021/jp401911h	journal	July 2013
Multiensemble Markov models of molecular thermodynamics and kinetics Wu, Hao; Paul, Fabian; Wehmeyer, Christoph Proceedings of the National Academy of Sciences, Vol. 113, Issue 23 https://doi.org/10.1073/pnas.1525092113	journal	May 2016
Landmark diffusion maps (L-dMaps): Accelerated manifold learning out-of-sample extension Long, Andrew W.; Ferguson, Andrew L. Applied and Computational Harmonic Analysis, Vol. 47, Issue 1 https://doi.org/10.1016/j.acha.2017.08.004	journal	July 2019
Simulating materials failure by using up to one billion atoms and the world's fastest computer: Work-hardening Abraham, F. F.; Walkup, R.; Gao, H. Proceedings of the National Academy of Sciences, Vol. 99, Issue 9 https://doi.org/10.1073/pnas.062054999	journal	April 2002
Extending Data-Driven Koopman Analysis to Actuated Systems Williams, Matthew O.; Hemati, Maziar S.; Dawson, Scott T. M. IFAC-PapersOnLine, Vol. 49, Issue 18 https://doi.org/10.1016/j.ifacol.2016.10.248	journal	January 2016
Molecular Dynamics with On-the-Fly Machine Learning of Quantum-Mechanical Forces Li, Zhenwei; Kermode, James R.; De Vita, Alessandro Physical Review Letters, Vol. 114, Issue 9 https://doi.org/10.1103/PhysRevLett.114.096405	journal	March 2015
Using Ulam's method to calculate entropy and other dynamical invariants Froyland, Gary Nonlinearity, Vol. 12, Issue 1 https://doi.org/10.1088/0951-7715/12/1/006	journal	January 1999
Calculation of absolute protein-ligand binding free energy from computer simulations Woo, H. -J.; Roux, B. Proceedings of the National Academy of Sciences, Vol. 102, Issue 19 https://doi.org/10.1073/pnas.0409005102	journal	May 2005
Metadynamics: a method to simulate rare events and reconstruct the free energy in biophysics, chemistry and material science Laio, Alessandro; Gervasio, Francesco L. Reports on Progress in Physics, Vol. 71, Issue 12 https://doi.org/10.1088/0034-4885/71/12/126601	journal	November 2008
Extended dynamic mode decomposition with dictionary learning: A data-driven adaptive spectral decomposition of the Koopman operator Li, Qianxiao; Dietrich, Felix; Bollt, Erik M. Chaos: An Interdisciplinary Journal of Nonlinear Science, Vol. 27, Issue 10 https://doi.org/10.1063/1.4993854	journal	October 2017
Hessian eigenmaps: Locally linear embedding techniques for high-dimensional data Donoho, D. L.; Grimes, C. Proceedings of the National Academy of Sciences, Vol. 100, Issue 10 https://doi.org/10.1073/pnas.1031596100	journal	April 2003
Metadynamics with Discriminants: A Tool for Understanding Chemistry Piccini, GiovanniMaria; Mendels, Dan; Parrinello, Michele Journal of Chemical Theory and Computation, Vol. 14, Issue 10 https://doi.org/10.1021/acs.jctc.8b00634	journal	August 2018
A Computational Method to Extract Macroscopic Variables and Their Dynamics in Multiscale Systems Froyland, Gary; Gottwald, Georg A.; Hammerlindl, Andy SIAM Journal on Applied Dynamical Systems, Vol. 13, Issue 4 https://doi.org/10.1137/130943637	journal	January 2014
Markov State Models: From an Art to a Science Husic, Brooke E.; Pande, Vijay S. Journal of the American Chemical Society, Vol. 140, Issue 7 https://doi.org/10.1021/jacs.7b12191	journal	February 2018
Multiresolution Dynamic Mode Decomposition Kutz, J. Nathan; Fu, Xing; Brunton, Steven L. SIAM Journal on Applied Dynamical Systems, Vol. 15, Issue 2 https://doi.org/10.1137/15M1023543	journal	January 2016
Nonlinear Dimensionality Reduction by Locally Linear Embedding Roweis, S. T. Science, Vol. 290, Issue 5500 https://doi.org/10.1126/science.290.5500.2323	journal	December 2000
Modeling and enhanced sampling of molecular systems with smooth and nonlinear data-driven collective variables Hashemian, Behrooz; Millán, Daniel; Arroyo, Marino The Journal of Chemical Physics, Vol. 139, Issue 21 https://doi.org/10.1063/1.4830403	journal	December 2013
Everything you wanted to know about Markov State Models but were afraid to ask Pande, Vijay S.; Beauchamp, Kyle; Bowman, Gregory R. Methods, Vol. 52, Issue 1 https://doi.org/10.1016/j.ymeth.2010.06.002	journal	September 2010
Capabilities and limitations of time-lagged autoencoders for slow mode discovery in dynamical systems Chen, Wei; Sidky, Hythem; Ferguson, Andrew L. The Journal of Chemical Physics, Vol. 151, Issue 6 https://doi.org/10.1063/1.5112048	journal	August 2019
Hierarchical Time-Lagged Independent Component Analysis: Computing Slow Modes and Reaction Coordinates for Large Molecular Systems Pérez-Hernández, Guillermo; Noé, Frank Journal of Chemical Theory and Computation, Vol. 12, Issue 12 https://doi.org/10.1021/acs.jctc.6b00738	journal	November 2016
Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9 Schwantes, Christian R.; Pande, Vijay S. Journal of Chemical Theory and Computation, Vol. 9, Issue 4 https://doi.org/10.1021/ct300878a	journal	March 2013
Time-Scale Separation from Diffusion-Mapped Delay Coordinates Berry, T.; Cressman, J. R.; Gregurić-Ferenček, Z. SIAM Journal on Applied Dynamical Systems, Vol. 12, Issue 2 https://doi.org/10.1137/12088183X	journal	January 2013
Rational design of patchy colloids via landscape engineering Long, Andrew W.; Ferguson, Andrew L. Molecular Systems Design & Engineering, Vol. 3, Issue 1 https://doi.org/10.1039/C7ME00077D	journal	January 2018
Density of States–Based Molecular Simulations Singh, Sadanand; Chopra, Manan; de Pablo, Juan J. Annual Review of Chemical and Biomolecular Engineering, Vol. 3, Issue 1 https://doi.org/10.1146/annurev-chembioeng-062011-081032	journal	July 2012
On Convergence of Extended Dynamic Mode Decomposition to the Koopman Operator Korda, Milan; Mezić, Igor Journal of Nonlinear Science, Vol. 28, Issue 2 https://doi.org/10.1007/s00332-017-9423-0	journal	November 2017
Beating the Millisecond Barrier in Molecular Dynamics Simulations Noé, Frank Biophysical Journal, Vol. 108, Issue 2 https://doi.org/10.1016/j.bpj.2014.11.3477	journal	January 2015
Phase Transition for a Hard Sphere System Alder, B. J.; Wainwright, T. E. The Journal of Chemical Physics, Vol. 27, Issue 5 https://doi.org/10.1063/1.1743957	journal	November 1957
Graphite-diamond phase coexistence study employing a neural-network mapping of the ab initio potential energy surface Khaliullin, Rustam Z.; Eshet, Hagai; Kühne, Thomas D. Physical Review B, Vol. 81, Issue 10 https://doi.org/10.1103/PhysRevB.81.100103	journal	March 2010
Boltzmann generators: Sampling equilibrium states of many-body systems with deep learning Noé, Frank; Olsson, Simon; Köhler, Jonas Science, Vol. 365, Issue 6457 https://doi.org/10.1126/science.aaw1147	journal	September 2019
The Protein-Folding Problem, 50 Years On Dill, K. A.; MacCallum, J. L. Science, Vol. 338, Issue 6110 https://doi.org/10.1126/science.1219021	journal	November 2012
Nonlinear dimensionality reduction in molecular simulation: The diffusion map approach Ferguson, Andrew L.; Panagiotopoulos, Athanassios Z.; Kevrekidis, Ioannis G. Chemical Physics Letters, Vol. 509, Issue 1-3 https://doi.org/10.1016/j.cplett.2011.04.066	journal	June 2011
Systematic determination of order parameters for chain dynamics using diffusion maps Ferguson, A. L.; Panagiotopoulos, A. Z.; Debenedetti, P. G. Proceedings of the National Academy of Sciences, Vol. 107, Issue 31 https://doi.org/10.1073/pnas.1003293107	journal	July 2010
Deflation reveals dynamical structure in nondominant reaction coordinates Husic, Brooke E.; Noé, Frank The Journal of Chemical Physics, Vol. 151, Issue 5 https://doi.org/10.1063/1.5099194	journal	August 2019
Low-dimensional, free-energy landscapes of protein-folding reactions by nonlinear dimensionality reduction Das, P.; Moll, M.; Stamati, H. Proceedings of the National Academy of Sciences, Vol. 103, Issue 26 https://doi.org/10.1073/pnas.0603553103	journal	June 2006
Time-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics Wehmeyer, Christoph; Noé, Frank The Journal of Chemical Physics, Vol. 148, Issue 24 https://doi.org/10.1063/1.5011399	journal	June 2018
Fuzzy spectral clustering by PCCA+: application to Markov state models and data classification Röblitz, Susanna; Weber, Marcus Advances in Data Analysis and Classification, Vol. 7, Issue 2 https://doi.org/10.1007/s11634-013-0134-6	journal	May 2013
Discovery Through the Computational Microscope Lee, Eric H.; Hsin, Jen; Sotomayor, Marcos Structure, Vol. 17, Issue 10 https://doi.org/10.1016/j.str.2009.09.001	journal	October 2009
PotentialNet for Molecular Property Prediction Feinberg, Evan N.; Sur, Debnil; Wu, Zhenqin ACS Central Science, Vol. 4, Issue 11 https://doi.org/10.1021/acscentsci.8b00507	journal	November 2018
Recent advances in machine learning towards multiscale soft materials design Jackson, Nicholas E.; Webb, Michael A.; de Pablo, Juan J. Current Opinion in Chemical Engineering, Vol. 23 https://doi.org/10.1016/j.coche.2019.03.005	journal	March 2019
Dynamic Mode Decomposition Kutz, J. Nathan; Brunton, Steven L.; Brunton, Bingni W. Society for Industrial and Applied Mathematics https://doi.org/10.1137/1.9781611974508	book	January 2016
On Pixel-Wise Explanations for Non-Linear Classifier Decisions by Layer-Wise Relevance Propagation Bach, Sebastian; Binder, Alexander; Montavon, Grégoire PLOS ONE, Vol. 10, Issue 7 https://doi.org/10.1371/journal.pone.0130140	journal	July 2015
Dynamic mode decomposition for large and streaming datasets Hemati, Maziar S.; Williams, Matthew O.; Rowley, Clarence W. Physics of Fluids, Vol. 26, Issue 11 https://doi.org/10.1063/1.4901016	journal	November 2014
Girsanov reweighting for path ensembles and Markov state models Donati, L.; Hartmann, C.; Keller, B. G. The Journal of Chemical Physics, Vol. 146, Issue 24 https://doi.org/10.1063/1.4989474	journal	June 2017
Relations Between two sets of Variates Hotelling, H. Biometrika, Vol. 28, Issue 3-4 https://doi.org/10.1093/biomet/28.3-4.321	journal	December 1936
Variants of Dynamic Mode Decomposition: Boundary Condition, Koopman, and Fourier Analyses Chen, Kevin K.; Tu, Jonathan H.; Rowley, Clarence W. Journal of Nonlinear Science, Vol. 22, Issue 6, p. 887-915 https://doi.org/10.1007/s00332-012-9130-9	journal	April 2012
Extensions to the likelihood maximization approach for finding reaction coordinates Peters, Baron; Beckham, Gregg T.; Trout, Bernhardt L. The Journal of Chemical Physics, Vol. 127, Issue 3 https://doi.org/10.1063/1.2748396	journal	July 2007
Separation of a mixture of independent signals using time delayed correlations Molgedey, L.; Schuster, H. G. Physical Review Letters, Vol. 72, Issue 23 https://doi.org/10.1103/PhysRevLett.72.3634	journal	June 1994
Escaping free-energy minima Laio, A.; Parrinello, M. Proceedings of the National Academy of Sciences, Vol. 99, Issue 20 https://doi.org/10.1073/pnas.202427399	journal	September 2002
Geometric diffusions as a tool for harmonic analysis and structure definition of data: Diffusion maps Coifman, R. R.; Lafon, S.; Lee, A. B. Proceedings of the National Academy of Sciences, Vol. 102, Issue 21 https://doi.org/10.1073/pnas.0500334102	journal	May 2005
Folding a small protein using harmonic linear discriminant analysis Mendels, Dan; Piccini, Giovannimaria; Brotzakis, Z. Faidon The Journal of Chemical Physics, Vol. 149, Issue 19 https://doi.org/10.1063/1.5053566	journal	November 2018
Tensor-based dynamic mode decomposition Klus, Stefan; Gelß, Patrick; Peitz, Sebastian Nonlinearity, Vol. 31, Issue 7 https://doi.org/10.1088/1361-6544/aabc8f	journal	June 2018
Unsupervised Learning of Image Manifolds by Semidefinite Programming Weinberger, Kilian Q.; Saul, Lawrence K. International Journal of Computer Vision, Vol. 70, Issue 1 https://doi.org/10.1007/s11263-005-4939-z	journal	May 2006
De-biasing the dynamic mode decomposition for applied Koopman spectral analysis of noisy datasets Hemati, Maziar S.; Rowley, Clarence W.; Deem, Eric A. Theoretical and Computational Fluid Dynamics, Vol. 31, Issue 4 https://doi.org/10.1007/s00162-017-0432-2	journal	April 2017
Adaptive biasing force method for scalar and vector free energy calculations Darve, Eric; Rodríguez-Gómez, David; Pohorille, Andrew The Journal of Chemical Physics, Vol. 128, Issue 14 https://doi.org/10.1063/1.2829861	journal	April 2008
Identification of slow molecular order parameters for Markov model construction Pérez-Hernández, Guillermo; Paul, Fabian; Giorgino, Toni The Journal of Chemical Physics, Vol. 139, Issue 1 https://doi.org/10.1063/1.4811489	journal	July 2013
Machine Learning of Coarse-Grained Molecular Dynamics Force Fields Wang, Jiang; Olsson, Simon; Wehmeyer, Christoph ACS Central Science https://doi.org/10.1021/acscentsci.8b00913	journal	April 2019

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