On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Cao, Siqin; Montoya-Castillo, Andrés; Wang, Wei; Markland, Thomas E.; Huang, Xuhui

doi:10.1063/5.0010787

Title: On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Journal Article · Tue Jul 07 00:00:00 EDT 2020 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/5.0010787· OSTI ID:1683623

^[1];

^[2]; Wang, Wei ^[1];

^[2];

^[3]

Hong Kong Univ. of Science and Technology (Hong Kong)
Stanford Univ., CA (United States)
Hong Kong Univ. of Science and Technology (Hong Kong); Shenzhen Research Inst. (China)

Biomolecular dynamics play an important role in numerous biological processes. Markov State Models (MSMs) provide a powerful approach to study these dynamic processes by predicting long time scale dynamics based on many short molecular dynamics (MD) simulations. In an MSM, protein dynamics are modeled as a kinetic process consisting of a series of Markovian transitions between different conformational states at discrete time intervals (called “lag time”). To achieve this, a master equation must be constructed with a sufficiently long lag time to allow interstate transitions to become truly Markovian. This imposes a major challenge for MSM studies of proteins since the lag time is bound by the length of relatively short MD simulations available to estimate the frequency of transitions. Here, we show how one can employ the generalized master equation formalism to obtain an exact description of protein conformational dynamics both at short and long time scales without the time resolution restrictions imposed by the MSM lag time. Using a simple kinetic model, alanine dipeptide, and WW domain, we demonstrate that it is possible to construct these quasi-Markov State Models (qMSMs) using MD simulations that are 5–10 times shorter than those required by MSMs. These qMSMs only contain a handful of metastable states and, thus, can greatly facilitate the interpretation of mechanisms associated with protein dynamics. A qMSM opens the door to the study of conformational changes of complex biomolecules where a Markovian model with a few states is often difficult to construct due to the limited length of available MD simulations.

View Accepted Manuscript (DOE)

View Accepted Manuscript (Publisher)

Cite

Export

Save

Research Organization:: Univ. of California, Merced, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES); Research Grants Council (RGC); Shenzhen Science and Technology Innovation Committee; Innovation and Technology Commission

Grant/Contract Number:: SC0020203; 16303919; AoE/P-705/16; JCYJ20170413173837121; ITCPD/17-9

OSTI ID:: 1683623

Alternate ID(s):: OSTI ID: 1637559

Journal Information:: Journal of Chemical Physics, Vol. 153, Issue 1; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

Citation Metrics:

Cited by: 24 works

Citation information provided by
Web of Science

References (80)

Diffusive reaction dynamics on invariant free energy profiles Krivov, S. V.; Karplus, M. Proceedings of the National Academy of Sciences, Vol. 105, Issue 37 https://doi.org/10.1073/pnas.0800228105	journal	September 2008
A Role for Both Conformational Selection and Induced Fit in Ligand Binding by the LAO Protein Silva, Daniel-Adriano; Bowman, Gregory R.; Sosa-Peinado, Alejandro PLoS Computational Biology, Vol. 7, Issue 5 https://doi.org/10.1371/journal.pcbi.1002054	journal	May 2011
Protein conformational plasticity and complex ligand-binding kinetics explored by atomistic simulations and Markov models Plattner, Nuria; Noé, Frank Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8653	journal	July 2015
Dynamical coring of Markov state models Nagel, Daniel; Weber, Anna; Lickert, Benjamin The Journal of Chemical Physics, Vol. 150, Issue 9 https://doi.org/10.1063/1.5081767	journal	March 2019
Dielectric friction and the transition from adiabatic to nonadiabatic electron transfer. I. Solvation dynamics in Liouville space Sparpaglione, Massimo; Mukamel, Shaul The Journal of Chemical Physics, Vol. 88, Issue 5 https://doi.org/10.1063/1.453922	journal	March 1988
Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules Noé, Frank; Wu, Hao; Prinz, Jan-Hendrik The Journal of Chemical Physics, Vol. 139, Issue 18 https://doi.org/10.1063/1.4828816	journal	November 2013
An efficient Bayesian kinetic lumping algorithm to identify metastable conformational states via Gibbs sampling Wang, Wei; Liang, Tong; Sheong, Fu Kit The Journal of Chemical Physics, Vol. 149, Issue 7 https://doi.org/10.1063/1.5027001	journal	August 2018
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
GROMACS 4: Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation Hess, Berk; Kutzner, Carsten; van der Spoel, David Journal of Chemical Theory and Computation, Vol. 4, Issue 3 https://doi.org/10.1021/ct700301q	journal	February 2008
Robust Perron cluster analysis in conformation dynamics Deuflhard, Peter; Weber, Marcus Linear Algebra and its Applications, Vol. 398 https://doi.org/10.1016/j.laa.2004.10.026	journal	March 2005
Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics Chodera, John D.; Singhal, Nina; Pande, Vijay S. The Journal of Chemical Physics, Vol. 126, Issue 15 https://doi.org/10.1063/1.2714538	journal	April 2007
Complete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations Buch, I.; Giorgino, T.; De Fabritiis, G. Proceedings of the National Academy of Sciences, Vol. 108, Issue 25 https://doi.org/10.1073/pnas.1103547108	journal	June 2011
A modified approach for simulating electronically nonadiabatic dynamics via the generalized quantum master equation Mulvihill, Ellen; Schubert, Alexander; Sun, Xiang The Journal of Chemical Physics, Vol. 150, Issue 3 https://doi.org/10.1063/1.5055756	journal	January 2019
Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules Wang, Wei; Cao, Siqin; Zhu, Lizhe WIREs Computational Molecular Science, Vol. 8, Issue 1 https://doi.org/10.1002/wcms.1343	journal	September 2017
Application of Molecular-Dynamics Based Markov State Models to Functional Proteins Malmstrom, Robert D.; Lee, Christopher T.; Van Wart, Adam T. Journal of Chemical Theory and Computation, Vol. 10, Issue 7 https://doi.org/10.1021/ct5002363	journal	June 2014
QUANTUM MODE-COUPLING THEORY: Formulation and Applications to Normal and Supercooled Quantum Liquids Rabani, Eran; Reichman, David R. Annual Review of Physical Chemistry, Vol. 56, Issue 1 https://doi.org/10.1146/annurev.physchem.56.092503.141138	journal	May 2005
Comparison of simple potential functions for simulating liquid water Jorgensen, William L.; Chandrasekhar, Jayaraman; Madura, Jeffry D. The Journal of Chemical Physics, Vol. 79, Issue 2 https://doi.org/10.1063/1.445869	journal	July 1983
Microscopic theory of the dynamics of polymeric liquids: General formulation of a mode–mode‐coupling approach Schweizer, Kenneth S. The Journal of Chemical Physics, Vol. 91, Issue 9 https://doi.org/10.1063/1.457533	journal	November 1989
MSMBuilder: Statistical Models for Biomolecular Dynamics Harrigan, Matthew P.; Sultan, Mohammad M.; Hernández, Carlos X. Biophysical Journal, Vol. 112, Issue 1 https://doi.org/10.1016/j.bpj.2016.10.042	journal	January 2017
Optimized Markov state models for metastable systems Guarnera, Enrico; Vanden-Eijnden, Eric The Journal of Chemical Physics, Vol. 145, Issue 2 https://doi.org/10.1063/1.4954769	journal	July 2016
A Jump-from-Cavity Pyrophosphate Ion Release Assisted by a Key Lysine Residue in T7 RNA Polymerase Transcription Elongation Da, Lin-Tai; E., Chao; Duan, Baogen PLOS Computational Biology, Vol. 11, Issue 11 https://doi.org/10.1371/journal.pcbi.1004624	journal	November 2015
Millisecond dynamics of RNA polymerase II translocation at atomic resolution Silva, D. -A.; Weiss, D. R.; Pardo Avila, F. Proceedings of the National Academy of Sciences, Vol. 111, Issue 21 https://doi.org/10.1073/pnas.1315751111	journal	April 2014
Allostery through the computational microscope: cAMP activation of a canonical signalling domain Malmstrom, Robert D.; Kornev, Alexandr P.; Taylor, Susan S. Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms8588	journal	July 2015
Comparison of multiple Amber force fields and development of improved protein backbone parameters Hornak, Viktor; Abel, Robert; Okur, Asim Proteins: Structure, Function, and Bioinformatics, Vol. 65, Issue 3 https://doi.org/10.1002/prot.21123	journal	November 2006
Dynamics of an Intrinsically Disordered Protein Reveal Metastable Conformations That Potentially Seed Aggregation Qiao, Qin; Bowman, Gregory R.; Huang, Xuhui Journal of the American Chemical Society, Vol. 135, Issue 43 https://doi.org/10.1021/ja403147m	journal	October 2013
Optimal Dimensionality Reduction of Multistate Kinetic and Markov-State Models Hummer, Gerhard; Szabo, Attila The Journal of Physical Chemistry B, Vol. 119, Issue 29 https://doi.org/10.1021/jp508375q	journal	September 2014
A fast parallel clustering algorithm for molecular simulation trajectories Zhao, Yutong; Sheong, Fu Kit; Sun, Jian Journal of Computational Chemistry, Vol. 34, Issue 2 https://doi.org/10.1002/jcc.23110	journal	September 2012
Molecular Simulation of ab Initio Protein Folding for a Millisecond Folder NTL9(1−39) Voelz, Vincent A.; Bowman, Gregory R.; Beauchamp, Kyle Journal of the American Chemical Society, Vol. 132, Issue 5 https://doi.org/10.1021/ja9090353	journal	February 2010
A semiclassical generalized quantum master equation for an arbitrary system-bath coupling Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 120, Issue 22 https://doi.org/10.1063/1.1738109	journal	June 2004
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models Scherer, Martin K.; Trendelkamp-Schroer, Benjamin; Paul, Fabian Journal of Chemical Theory and Computation, Vol. 11, Issue 11 https://doi.org/10.1021/acs.jctc.5b00743	journal	October 2015
Mean first passage times in variational coarse graining using Markov state models Kells, Adam; Mihálka, Zsuzsanna É.; Annibale, Alessia The Journal of Chemical Physics, Vol. 150, Issue 13 https://doi.org/10.1063/1.5083924	journal	April 2019
Taming the complexity of protein folding Bowman, Gregory R.; Voelz, Vincent A.; Pande, Vijay S. Current Opinion in Structural Biology, Vol. 21, Issue 1 https://doi.org/10.1016/j.sbi.2010.10.006	journal	February 2011
Markov state models based on milestoning Schütte, Christof; Noé, Frank; Lu, Jianfeng The Journal of Chemical Physics, Vol. 134, Issue 20 https://doi.org/10.1063/1.3590108	journal	May 2011
Rapid equilibrium sampling initiated from nonequilibrium data Huang, X.; Bowman, G. R.; Bacallado, S. Proceedings of the National Academy of Sciences, Vol. 106, Issue 47 https://doi.org/10.1073/pnas.0909088106	journal	September 2009
Efficient and accurate surface hopping for long time nonadiabatic quantum dynamics Kelly, Aaron; Markland, Thomas E. The Journal of Chemical Physics, Vol. 139, Issue 1 https://doi.org/10.1063/1.4812355	journal	July 2013
Quantitative comparison of adaptive sampling methods for protein dynamics Hruska, Eugen; Abella, Jayvee R.; Nüske, Feliks The Journal of Chemical Physics, Vol. 149, Issue 24 https://doi.org/10.1063/1.5053582	journal	December 2018
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
Generalized quantum master equations in and out of equilibrium: When can one win? Kelly, Aaron; Montoya-Castillo, Andrés; Wang, Lu The Journal of Chemical Physics, Vol. 144, Issue 18 https://doi.org/10.1063/1.4948612	journal	May 2016
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
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
Correlation function formula for the intrinsic viscosity of dilute polymer solutions Felderhof, B. U.; Deutch, J. M.; Titulaer, U. M. The Journal of Chemical Physics, Vol. 63, Issue 2 https://doi.org/10.1063/1.431352	journal	July 1975
Two algorithms to compute projected correlation functions in molecular dynamics simulations Carof, Antoine; Vuilleumier, Rodolphe; Rotenberg, Benjamin The Journal of Chemical Physics, Vol. 140, Issue 12 https://doi.org/10.1063/1.4868653	journal	March 2014
Canonical sampling through velocity rescaling Bussi, Giovanni; Donadio, Davide; Parrinello, Michele The Journal of Chemical Physics, Vol. 126, Issue 1 https://doi.org/10.1063/1.2408420	journal	January 2007
Building Markov state models using optimal transport theory Dixit, Purushottam D.; Dill, Ken A. The Journal of Chemical Physics, Vol. 150, Issue 5 https://doi.org/10.1063/1.5086681	journal	February 2019
Slow dynamics in protein fluctuations revealed by time-structure based independent component analysis: The case of domain motions Naritomi, Yusuke; Fuchigami, Sotaro The Journal of Chemical Physics, Vol. 134, Issue 6 https://doi.org/10.1063/1.3554380	journal	February 2011
Simulating Replica Exchange: Markov State Models, Proposal Schemes, and the Infinite Swapping Limit Zhang, Bin W.; Dai, Wei; Gallicchio, Emilio The Journal of Physical Chemistry B, Vol. 120, Issue 33 https://doi.org/10.1021/acs.jpcb.6b02015	journal	April 2016
Simulation of spontaneous G protein activation reveals a new intermediate driving GDP unbinding Sun, Xianqiang; Singh, Sukrit; Blumer, Kendall J. eLife, Vol. 7 https://doi.org/10.7554/elife.38465	journal	October 2018
On mean-field theories of dynamics in supercooled liquids Baity-Jesi, Marco; Reichman, David R. The Journal of Chemical Physics, Vol. 151, Issue 8 https://doi.org/10.1063/1.5115042	journal	August 2019
Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue Da, Lin-Tai; Pardo-Avila, Fátima; Xu, Liang Nature Communications, Vol. 7, Issue 1 https://doi.org/10.1038/ncomms11244	journal	April 2016
Building Markov state models along pathways to determine free energies and rates of transitions Pan, Albert C.; Roux, Benoît The Journal of Chemical Physics, Vol. 129, Issue 6 https://doi.org/10.1063/1.2959573	journal	August 2008
Efficient construction of generalized master equation memory kernels for multi-state systems from nonadiabatic quantum-classical dynamics Pfalzgraff, William C.; Montoya-Castillo, Andrés; Kelly, Aaron The Journal of Chemical Physics, Vol. 150, Issue 24 https://doi.org/10.1063/1.5095715	journal	June 2019
Approximate but accurate quantum dynamics from the Mori formalism: I. Nonequilibrium dynamics Montoya-Castillo, Andrés; Reichman, David R. The Journal of Chemical Physics, Vol. 144, Issue 18 https://doi.org/10.1063/1.4948408	journal	May 2016
Ensemble Method in the Theory of Irreversibility Zwanzig, Robert The Journal of Chemical Physics, Vol. 33, Issue 5 https://doi.org/10.1063/1.1731409	journal	November 1960
A fully self-consistent treatment of collective fluctuations in quantum liquids Rabani, Eran; Reichman, David R. The Journal of Chemical Physics, Vol. 120, Issue 3 https://doi.org/10.1063/1.1631436	journal	January 2004
On Quantum Theory of Transport Phenomena: Steady Diffusion Nakajima, Sadao Progress of Theoretical Physics, Vol. 20, Issue 6 https://doi.org/10.1143/ptp.20.948	journal	December 1958
Polymorphic transitions in single crystals: A new molecular dynamics method Parrinello, M.; Rahman, A. Journal of Applied Physics, Vol. 52, Issue 12 https://doi.org/10.1063/1.328693	journal	December 1981
Nonadiabatic Dynamics in Atomistic Environments: Harnessing Quantum-Classical Theory with Generalized Quantum Master Equations Pfalzgraff, William C.; Kelly, Aaron; Markland, Thomas E. The Journal of Physical Chemistry Letters, Vol. 6, Issue 23 https://doi.org/10.1021/acs.jpclett.5b02131	journal	November 2015
On the memory kernel and the reduced system propagator Kidon, Lyran; Wang, Haobin; Thoss, Michael The Journal of Chemical Physics, Vol. 149, Issue 10 https://doi.org/10.1063/1.5047446	journal	September 2018
Dynamics of Pyrophosphate Ion Release and Its Coupled Trigger Loop Motion from Closed to Open State in RNA Polymerase II Da, Lin-Tai; Wang, Dong; Huang, Xuhui Journal of the American Chemical Society, Vol. 134, Issue 4 https://doi.org/10.1021/ja210656k	journal	January 2012
Density-based cluster algorithms for the identification of core sets Lemke, Oliver; Keller, Bettina G. The Journal of Chemical Physics, Vol. 145, Issue 16 https://doi.org/10.1063/1.4965440	journal	October 2016
Molecular Hydrodynamics from Memory Kernels Lesnicki, Dominika; Vuilleumier, Rodolphe; Carof, Antoine Physical Review Letters, Vol. 116, Issue 14 https://doi.org/10.1103/physrevlett.116.147804	journal	April 2016
Elucidation of the Dynamics of Transcription Elongation by RNA Polymerase II using Kinetic Network Models Zhang, Lu; Pardo-Avila, Fátima; Unarta, Ilona Christy Accounts of Chemical Research, Vol. 49, Issue 4 https://doi.org/10.1021/acs.accounts.5b00536	journal	March 2016
Clustering by fast search and find of density peaks Rodriguez, A.; Laio, A. Science, Vol. 344, Issue 6191 https://doi.org/10.1126/science.1242072	journal	June 2014
Modeling Conformational Ensembles of Slow Functional Motions in Pin1-WW Morcos, Faruck; Chatterjee, Santanu; McClendon, Christopher L. PLoS Computational Biology, Vol. 6, Issue 12 https://doi.org/10.1371/journal.pcbi.1001015	journal	December 2010
Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation Zhang, Ming-Liang; Ka, Being J.; Geva, Eitan The Journal of Chemical Physics, Vol. 125, Issue 4 https://doi.org/10.1063/1.2218342	journal	July 2006
Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations Noé, Frank; Schütte, Christof; Vanden-Eijnden, Eric Proceedings of the National Academy of Sciences, Vol. 106, Issue 45 https://doi.org/10.1073/pnas.0905466106	journal	November 2009
Mode-coupling theory Reichman, David R.; Charbonneau, Patrick Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 05 https://doi.org/10.1088/1742-5468/2005/05/p05013	journal	May 2005
Accurate nonadiabatic quantum dynamics on the cheap: Making the most of mean field theory with master equations Kelly, Aaron; Brackbill, Nora; Markland, Thomas E. The Journal of Chemical Physics, Vol. 142, Issue 9 https://doi.org/10.1063/1.4913686	journal	March 2015
Coarse Master Equations for Peptide Folding Dynamics ^† Buchete, Nicolae-Viorel; Hummer, Gerhard The Journal of Physical Chemistry B, Vol. 112, Issue 19 https://doi.org/10.1021/jp0761665	journal	May 2008
Cloud computing approaches for prediction of ligand binding poses and pathways Lawrenz, Morgan; Shukla, Diwakar; Pande, Vijay S. Scientific Reports, Vol. 5, Issue 1 https://doi.org/10.1038/srep07918	journal	January 2015
A new approach to calculating the memory kernel of the generalized quantum master equation for an arbitrary system–bath coupling Shi, Qiang; Geva, Eitan The Journal of Chemical Physics, Vol. 119, Issue 23 https://doi.org/10.1063/1.1624830	journal	December 2003
Theory of Spin Resonance and Relaxation Argyres, P. N.; Kelley, P. L. Physical Review, Vol. 134, Issue 1A https://doi.org/10.1103/physrev.134.a98	journal	April 1964
Quantum fluctuations can promote or inhibit glass formation Markland, Thomas E.; Morrone, Joseph A.; Berne, Bruce J. Nature Physics, Vol. 7, Issue 2 https://doi.org/10.1038/nphys1865	journal	January 2011
Theory of Dielectric Relaxation in Polar Liquids Nee, Tsu‐Wei; Zwanzig, Robert The Journal of Chemical Physics, Vol. 52, Issue 12 https://doi.org/10.1063/1.1672951	journal	June 1970
Adaptive Markov state model estimation using short reseeding trajectories Wan, Hongbin; Voelz, Vincent A. The Journal of Chemical Physics, Vol. 152, Issue 2 https://doi.org/10.1063/1.5142457	journal	January 2020
A smooth particle mesh Ewald method Essmann, Ulrich; Perera, Lalith; Berkowitz, Max L. The Journal of Chemical Physics, Vol. 103, Issue 19 https://doi.org/10.1063/1.470117	journal	November 1995
Memory Effects and the Autocorrelation Function of a Dynamical Variable Boon, Jean‐Pierre; Rice, Stuart A. The Journal of Chemical Physics, Vol. 47, Issue 7 https://doi.org/10.1063/1.1703333	journal	October 1967
The Theory of Open Quantum Systems Breuer, Heinz-Peter; Petruccione, Francesco Oxford University Press https://doi.org/10.1093/acprof:oso/9780199213900.001.0001	book	January 2007
A Best Possible Heuristic for the k -Center Problem Hochbaum, Dorit S.; Shmoys, David B. Mathematics of Operations Research, Vol. 10, Issue 2 https://doi.org/10.1287/moor.10.2.180	journal	May 1985
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

Figures / Tables (9)

Similar Records

Markov state models from short non-equilibrium simulations—Analysis and correction of estimation bias

Journal Article · Thu Mar 02 00:00:00 EST 2017 · Journal of Chemical Physics · OSTI ID:1683623

Nüske, Feliks; Wu, Hao; Prinz, Jan-Hendrik; +3 more

Dynamic neutron scattering from conformational dynamics. II. Application using molecular dynamics simulation and Markov modeling

Journal Article · Fri Nov 01 00:00:00 EDT 2013 · Journal of Chemical Physics · OSTI ID:1683623

Yi, Zheng; Lindner, Benjamin; Prinz, Jan -Hendrik; +2 more

Diffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions

Journal Article · Sun Sep 21 00:00:00 EDT 2014 · Journal of Chemical Physics · OSTI ID:1683623

Nedialkova, Lilia V.; Amat, Miguel A.; Hummer, Gerhard

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Markov processes
Conformational dynamics
Molecular dynamics
Protein folding
Biomolecular dynamics
Protein dynamics

Title: On the advantages of exploiting memory in Markov state models for biomolecular dynamics

Citation Formats

References (80)

Figures / Tables (9)

Similar Records

Related Subjects