Coarse master equations for peptide folding dynamics

Buchete, Nicolae-Viorel; Hummer, Gerhard

doi:10.1021/jp0761665

Cited by 477Protein Structure and DynamicsAdvanced Physical and Chemical Molecular InteractionsRNA and protein synthesis mechanisms

Coarse master equations for peptide folding dynamics

Buchete, Nicolae-Viorel, Hummer, Gerhard·2008·The Journal of Physical Chemistry B

DOI 10.1021/jp0761665

Open this paper in CoChat — free account

Abstract

We construct coarse master equations for peptide folding dynamics from atomistic molecular dynamics simulations. A maximum-likelihood propagator-based method allows us to extract accurate rates for the transitions between the different conformational states of the small helix-forming peptide Ala5. Assigning the conformational states by using transition paths instead of instantaneous molecular coordinates suppresses the effects of fast non-Markovian dynamics. The resulting master equations are validated by comparing their analytical correlation functions with those obtained directly from the molecular dynamics simulations. We find that the master equations properly capture the character and relaxation times of the entire spectrum of conformational relaxation processes. By using the eigenvectors of the transition rate matrix, we are able to systematically coarse-grain the system. We find that a two-state description, with a folded and an unfolded state, roughly captures the slow conformational dynamics. A four-state model, with two folded and two unfolded states, accurately recovers the three slowest relaxation process with time scales between 1.5 and 7 ns. The master equation models not only give access to the slow conformational dynamics but also shed light on the molecular mechanisms of the helix-coil transition.

Integrity signals

Registry

Crossref · 10.1021/jp0761665

Cites

64 of 64 references verified0 citation errors · 0 not checkable

Statistics

Recomputing p-values needs the paper’s full text.

Claims the paper makes

This paper’s full text isn’t openly available, so its claims and self-check weren’t run. The registry and citation checks still apply.

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 core-based projection method was first introduced for MSM construction in [22].
“An alternative approach is the core-based projection method, long familiar to the transition path sampling community but first introduced for MSM construction in [22].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [22]

Comparison of simple potential functions for simulating liquid water
Jorgensen, W. L., Chandrasekhar, J., Madura, J., Impey, R., & Klein, M. (1983) · The Journal of Chemical Physics · doi:10.1063/1.445869 · Cited by 38,335 · see citing works
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
A smooth particle mesh Ewald method
Essmann, U., Perera, L., Berkowitz, M., Darden, T., Lee, H.-C., & Pedersen, L. (1995) · The Journal of Chemical Physics · doi:10.1063/1.470117 · Cited by 21,329 · 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 19,187 · 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
A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules
Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M., Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., & Kollman, P. A. (1995) · Journal of the American Chemical Society · doi:10.1021/ja00124a002 · Cited by 13,111 · see citing works
Laplacian Eigenmaps for Dimensionality Reduction and Data Representation
Belkin, M., & Niyogi, P. (2003) · Neural Computation · doi:10.1162/089976603321780317 · Cited by 7,562 · see citing works
Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models
Miyamoto, S., & Kollman, P. A. (1992) · Journal of Computational Chemistry · doi:10.1002/jcc.540130805 · Cited by 7,268 · see citing works
GROMACS 3.0: a package for molecular simulation and trajectory analysis
Lindahl, E. R., Hess, B., & van der Spoel, D. (2001) · Journal of Molecular Modeling · doi:10.1007/s008940100045 · Cited by 6,953 · see citing works
T <scp>RANSITION</scp> P <scp>ATH</scp> S <scp>AMPLING</scp> : Throwing Ropes Over Rough Mountain Passes, in the Dark
Bolhuis, P. G., Chandler, D., Dellago, C., & Geissler, P. L. (2002) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.53.082301.113146 · Cited by 1,972 · see citing works
Initial Recombination of Ions
Onsager, L. (1938) · Physical Review · doi:10.1103/physrev.54.554 · Cited by 1,889 · see citing works
The topology of multidimensional potential energy surfaces: Theory and application to peptide structure and kinetics
Becker, O. M., & Karplus, M. (1997) · The Journal of Chemical Physics · doi:10.1063/1.473299 · Cited by 808 · see citing works
Intermediates and barrier crossing in a random energy model (with applications to protein folding)
Bryngelson, J. D., & Wolynes, P. G. (1989) · The Journal of Physical Chemistry · doi:10.1021/j100356a007 · Cited by 746 · see citing works
Automatic discovery of metastable states for the construction of Markov models of macromolecular conformational dynamics.
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
Position-dependent diffusion coefficients and free energies from Bayesian analysis of equilibrium and replica molecular dynamics simulations
Hummer, G. (2005) · New Journal of Physics · doi:10.1088/1367-2630/7/1/034 · Cited by 530 · see citing works
Self-citation
Levinthal's paradox.
Zwanzig, R., Szabo, A., & Bagchi, B. (1992) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.89.1.20 · Cited by 527 · 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
α-Helical stabilization by side chain shielding of backbone hydrogen bonds
Garcı́a, A. E., & Sanbonmatsu, K. Y. (2002) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.042496899 · Cited by 442 · see citing works
From transition paths to transition states and rate coefficients
Hummer, G. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1630572 · Cited by 417 · see citing works
Self-citation
Discrete path sampling
Wales, D. J. (2002) · Molecular Physics · doi:10.1080/00268970210162691 · Cited by 399 · 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
Hierarchical analysis of conformational dynamics in biomolecules: transition networks of metastable states.
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
Kinetic Pathways of Ion Pair Dissociation in Water
Geissler, P. L., Dellago, C., & Chandler, D. (1999) · The Journal of Physical Chemistry B · doi:10.1021/jp984837g · Cited by 351 · see citing works
Structure and Dynamics of the Homologous Series of Alanine Peptides: A Joint Molecular Dynamics/NMR Study
Graf, J., Nguyen, P. H., Stock, G., & Schwalbe, H. (2007) · Journal of the American Chemical Society · doi:10.1021/ja0660406 · Cited by 333 · see citing works
On the calculation of reaction rate constants in the transition path ensemble
Dellago, C., Bolhuis, P. G., & Chandler, D. (1999) · The Journal of Chemical Physics · doi:10.1063/1.478569 · Cited by 322 · see citing works
Identification 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
Using path sampling to build better Markovian state models: Predicting the folding rate and mechanism of a tryptophan zipper beta hairpin
Singhal, N., Snow, C. D., & Pande, V. S. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1738647 · Cited by 269 · see citing works
Simulation of the folding equilibrium of α-helical peptides: A comparison of the generalized Born approximation with explicit solvent
Nymeyer, H., & Garcı́a, A. E. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2232868100 · Cited by 261 · see citing works
Coarse molecular dynamics of a peptide fragment: Free energy, kinetics, and long-time dynamics computations
Hummer, G., & Kevrekidis, I. G. (2003) · The Journal of Chemical Physics · doi:10.1063/1.1574777 · Cited by 235 · see citing works
Self-citation
Long‐Time Protein Folding Dynamics from Short‐Time Molecular Dynamics Simulations
Chodera, J. D., Swope, W. C., Pitera, J. W., & Dill, K. A. (2006) · Multiscale Modeling and Simulation · doi:10.1137/06065146x · Cited by 220 · see citing works
Transition pathways in complex systems: Application of the finite-temperature string method to the alanine dipeptide.
Ren, W.-Q., Vanden-Eijnden, E., Maragakis, P., & E, W. (2005) · Journal of Chemical Physics · doi:10.1063/1.2013256 · Cited by 205 · see citing works
Diffusive Model of Protein Folding Dynamics with Kramers Turnover in Rate
Best, R. B., & Hummer, G. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.228104 · Cited by 191 · see citing works
Self-citation
One-dimensional reaction coordinates for diffusive activated rate processes in many dimensions
Berezhkovskii, A. M., & Szabó, A. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1818091 · Cited by 187 · see citing works
Error 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
Using massively parallel simulation and Markovian models to study protein folding: Examining the dynamics of the villin headpiece
Jayachandran, G., Vishal, V., & Pande, V. S. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2186317 · Cited by 165 · see citing works
Electron transfer reaction dynamics in non-Debye solvents
Bicout, D., & Szabó, A. (1998) · The Journal of Chemical Physics · doi:10.1063/1.476800 · Cited by 143 · see citing works
Protein folding pathways from replica exchange simulations and a kinetic network model
Andrec, M., Felts, A. K., Gallicchio, E., & Levy, R. M. (2005) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0408970102 · Cited by 137 · see citing works
Direct Determination of Kinetic Rates from Single-Molecule Photon Arrival Trajectories Using Hidden Markov Models
Andrec, M., Levy, R. M., & Talaga, D. S. (2003) · The Journal of Physical Chemistry A · doi:10.1021/jp035514+ · Cited by 130 · see citing works
Calculation of the distribution of eigenvalues and eigenvectors in Markovian state models for molecular dynamics.
Hinrichs, N., & Pande, V. (2007) · Journal of Chemical Physics · doi:10.1063/1.2740261 · Cited by 123 · see citing works
A 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
Essential dynamics of reversible peptide folding: memory-free conformational dynamics governed by internal hydrogen bonds.
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
Entropic barriers, transition states, funnels, and exponential protein folding kinetics: A simple model
Bicout, D., & Szabó, A. (2000) · Protein Science · doi:10.1110/ps.9.3.452 · Cited by 116 · see citing works
Coarse master equation from Bayesian analysis of replica molecular dynamics simulations.
Sriraman, S., Kevrekidis, I., & Hummer, G. (2005) · Journal of Physical Chemistry B · doi:10.1021/jp046448u · Cited by 115 · see citing works
Self-citation
Helix nucleation kinetics from molecular simulations in explicit solvent
Hummer, G., Garcı́a, A. E., & Garde, S. (2000) · Proteins Structure Function and Bioinformatics · doi:10.1002/1097-0134(20010101)42:1 · Cited by 107 · see citing works
Self-citation
From classical dynamics to continuous time random walks
Zwanzig, R. W. (1983) · Journal of Statistical Physics · doi:10.1007/bf01012300 · Cited by 101 · see citing works
Better Nonlinear Models from Noisy Data: Attractors with Maximum Likelihood
McSharry, P., & Smith, L. A. (1999) · Physical Review Letters · doi:10.1103/physrevlett.83.4285 · Cited by 99 · see citing works
Protein Folding Kinetics and Thermodynamics from Atomistic Simulations
van der Spoel, D., & Seibert, M. M. (2006) · Physical Review Letters · doi:10.1103/physrevlett.96.238102 · Cited by 97 · see citing works
Conformational Diffusion and Helix Formation Kinetics
Hummer, G., Garcı́a, A. E., & Garde, S. (2000) · Physical Review Letters · doi:10.1103/physrevlett.85.2637 · Cited by 95 · see citing works
Self-citation
Long-Time Conformational Transitions of Alanine Dipeptide in Aqueous Solution: Continuous and Discrete-State Kinetic Models
Chekmarev, D. S., Ishida, T., & Levy, R. M. (2004) · The Journal of Physical Chemistry B · doi:10.1021/jp048540w · Cited by 88 · see citing works
Bonding Patterns in Benzene Triradicals from Structural, Spectroscopic, and Thermochemical Perspectives
Cristian, A.-M. C., Shao, Y., & Krylov, A. I. (2004) · The Journal of Physical Chemistry A · doi:10.1021/jp049007j · Cited by 73 · see citing works
Kinetics of peptide folding: computer simulations of SYPFDV and peptide variants in water 1 1Edited by G. von Heijne
Mohanty, D., Elber, R., Thirumalai, D., Beglov, D., & Roux, B. (1997) · Journal of Molecular Biology · doi:10.1006/jmbi.1997.1246 · Cited by 68 · see citing works
Estimation, Computation, and Experimental Correction of Molecular Zero-Point Vibrational Energies
Csonka, G. I., Ruzsinszky, A., & Perdew, J. P. (2005) · The Journal of Physical Chemistry A · doi:10.1021/jp0519464 · Cited by 58 · see citing works
Fast protein folding kinetics
Schonbrun, J., & Dill, K. A. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1735417100 · Cited by 56 · see citing works
Foldamer dynamics expressed via Markov state models. I. Explicit solvent molecular-dynamics simulations in acetonitrile, chloroform, methanol, and water
Elmer, S. P., Park, S., & Pande, V. S. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2001648 · Cited by 54 · see citing works
Theoretical Characterization of α-Helix and β-Hairpin Folding Kinetics
Daidone, I., D’Abramo, M., Nola, A. D., & Amadei, A. (2005) · Journal of the American Chemical Society · doi:10.1021/ja053383f · Cited by 43 · see citing works
Extracting macroscopic stochastic dynamics: Model problems
Huisinga, W., Schütte, C., & Stuart, A. M. (2002) · Communications on Pure and Applied Mathematics · doi:10.1002/cpa.10057 · Cited by 38 · see citing works
Monte Carlo simulations of polyalanine using a reduced model and statistics-based interaction potentials
van Giessen, A. E., & Straub, J. E. (2004) · The Journal of Chemical Physics · doi:10.1063/1.1833354 · Cited by 33 · see citing works
Mean First-Passage Time Calculations for the Coil-to-Helix Transition: The Active Helix Ising Model
Buchete, N., & Straub, J. E. (2001) · The Journal of Physical Chemistry B · doi:10.1021/jp0104031 · Cited by 33 · see citing works
Self-citation
Foldamer dynamics expressed via Markov state models. II. State space decomposition
Elmer, S. P., Park, S., & Pande, V. S. (2005) · The Journal of Chemical Physics · doi:10.1063/1.2008230 · Cited by 32 · see citing works
Eigenvalue spectrum of the master equation for hierarchical dynamics of complex systems
Levy, Y., Jortner, J., & Berry, R. S. (2002) · Physical Chemistry Chemical Physics · doi:10.1039/b203534k · Cited by 32 · see citing works
Coarse-Grained Model of Coil-to-Helix Kinetics Demonstrates the Importance of Multiple Nucleation Sites in Helix Folding
van Giessen, A. E., & Straub, J. E. (2006) · Journal of Chemical Theory and Computation · doi:10.1021/ct0503318 · Cited by 22 · see citing works
Action of a microbial lipase/acyltransferase on phospholipid monolayers
Hilton, S., & Buckley, J. T. (1991) · Biochemistry · doi:10.1021/bi00238a034 · Cited by 22 · see citing works
Kinetics of α-helix formation as diffusion on a one-dimensional free energy surface
Doshi, U., & Muñoz, V. (2004) · Chemical Physics · doi:10.1016/j.chemphys.2004.05.022 · Cited by 19 · see citing works
Perturbation theory of Φ-value analysis of two-state protein folding: Relation between pfold and Φ values
Berezhkovskii, A. M., & Szabó, A. (2006) · The Journal of Chemical Physics · doi:10.1063/1.2347708 · Cited by 11 · see citing works

Flagged first, then by citations

1 of the 65 references couldn’t be matched to a known paper.

Sorted by citations

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
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
Major Histocompatibility Complex (MHC) Class I and MHC Class II Proteins: Conformational Plasticity in Antigen Presentation
Wieczorek, M., Abualrous, E. T., Sticht, J., Álvaro‐Benito, M., Stolzenberg, S., Noé, F., & Freund, C. (2017) · Frontiers in Immunology · doi:10.3389/fimmu.2017.00292 · Cited by 998 · see citing works
Identification of slow molecular order parameters for Markov model construction
Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G., & Noé, F. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4811489 · Cited by 990 · see citing works
“…The Journal of Chemical Physics 126, 155101 (2007); 10.1063/1.2714538 Identification of slow molecular order parameters for Markov model construction Guillermo Pérez-Hernández,1 Fabian Paul,2,a),b) Toni Giorgino,3,a) Gianni De Fabritiis,4,c) and Frank Noé1,c) 1Department of Mathematics and…”
BackgroundInfluential
Machine Learning for Molecular Simulation
Noé, F., Tkatchenko, A., Müller, K.-R., & Clementi, C. (2020) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-042018-052331 · Cited by 956 · 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
Constructing 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
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
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 657 · see citing works
Transition-Path Theory and Path-Finding Algorithms for the Study of Rare Events
Weinan, E., & Vanden‐Eijnden, E. (2008) · Annual Review of Physical Chemistry · doi:10.1146/annurev.physchem.040808.090412 · 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 631 · see citing works
Native contacts determine protein folding mechanisms in atomistic simulations
Best, R. B., Hummer, G., & Eaton, W. A. (2013) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1311599110 · Cited by 593 · see citing works
Self-citation
RNA Structural Dynamics As Captured by Molecular Simulations: A Comprehensive Overview
Šponer, J., Bussi, G., Krepl, M., Banáš, P., Bottaro, S., Cunha, R. A., Gil-Ley, A., Pinamonti, G., Poblete, S., Jurečka, P., et al. (2018) · Chemical Reviews · doi:10.1021/acs.chemrev.7b00427 · Cited by 584 · see citing works
Machine Learning of Coarse-Grained Molecular Dynamics Force Fields
Wang, J., Olsson, S., Wehmeyer, C., Pérez, A., Charron, N. E., Fabritiis, G. D., Noé, F., & Clementi, C. (2019) · ACS Central Science · doi:10.1021/acscentsci.8b00913 · Cited by 519 · see citing works
Are Current Molecular Dynamics Force Fields too Helical?
Best, R. B., Buchete, N., & Hummer, G. (2008) · Biophysical Journal · doi:10.1529/biophysj.108.132696 · Cited by 452 · see citing works
Self-citation
To milliseconds and beyond: challenges in the simulation of protein folding
Lane, T. J., Shukla, D., Beauchamp, K. A., & Pande, V. S. (2013) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2012.11.002 · Cited by 409 · see citing works
Unsupervised 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
Progress and challenges in the automated construction of Markov state models for full protein systems
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
MSMBuilder2: 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
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
Variational approach to molecular kinetics
Nüske, F., Keller, B. G., Pérez-Hernández, G., Mey, A. S. J. S., & Noé, F. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct4009156 · Cited by 308 · see citing works
Using generalized ensemble simulations and Markov state models to identify conformational states
Bowman, G. R., Huang, X., & Pande, V. S. (2009) · Methods · doi:10.1016/j.ymeth.2009.04.013 · Cited by 301 · see citing works
Thermodynamics and Kinetics of Drug-Target Binding by Molecular Simulation
Decherchi, S., & Cavalli, A. (2020) · Chemical Reviews · doi:10.1021/acs.chemrev.0c00534 · Cited by 301 · see citing works
Protein folding kinetics and thermodynamics from atomistic simulation
Piana, S., Lindorff‐Larsen, K., & Shaw, D. E. (2012) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1201811109 · Cited by 297 · see citing works
A Kinetic Model of Trp-Cage Folding from Multiple Biased Molecular Dynamics Simulations
Marinelli, F., Pietrucci, F., Laio, A., & Piana, S. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000452 · Cited by 271 · see citing works
Principal component analysis of molecular dynamics: On the use of Cartesian vs. internal coordinates
Sittel, F., Jain, A., & Stock, G. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4885338 · Cited by 268 · 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
A Role for Both Conformational Selection and Induced Fit in Ligand Binding by the LAO Protein
Silva, D., Bowman, G. R., Sosa‐Peinado, A., & Huang, X. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002054 · Cited by 224 · see citing works
Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry
Abyzov, A., Blackledge, M., & Zweckstetter, M. (2022) · Chemical Reviews · doi:10.1021/acs.chemrev.1c00774 · Cited by 215 · 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 214 · see citing works
Protein folded states are kinetic hubs
Bowman, G. R., & Pande, V. S. (2010) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1003962107 · Cited by 210 · see citing works
Coarse graining molecular dynamics with graph neural networks
Husic, B. E., Charron, N. E., Lemm, D., Wang, J., Pérez, A., Majewski, M., Krämer, A., Chen, Y., Olsson, S., Fabritiis, G. D., et al. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0026133 · Cited by 206 · see citing works
Reaction Coordinates and Mechanistic Hypothesis Tests
Peters, B. (2016) · Annual Review of Physical Chemistry · doi:10.1146/annurev-physchem-040215-112215 · Cited by 202 · see citing works
Markovian milestoning with Voronoi tessellations
Vanden‐Eijnden, E., & Venturoli, M. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3129843 · Cited by 190 · see citing works
Dynamics of an Intrinsically Disordered Protein Reveal Metastable Conformations That Potentially Seed Aggregation
Qiao, Q., Bowman, G. R., & Huang, X. (2013) · Journal of the American Chemical Society · doi:10.1021/ja403147m · Cited by 182 · 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
On the assumptions underlying milestoning
Vanden‐Eijnden, E., Venturoli, M., Ciccotti, G., & Elber, R. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2996509 · Cited by 178 · see citing works
Projected and hidden Markov models for calculating kinetics and metastable states of complex molecules
Noé, F., Wu, H., Prinz, J.-H., & Plattner, N. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4828816 · Cited by 173 · 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
Taming the complexity of protein folding
Bowman, G. R., Voelz, V. A., & Pande, V. S. (2010) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2010.10.006 · Cited by 170 · see citing works
The Theory of Ultra-Coarse-Graining. 1. General Principles
Dama, J. F., Sinitskiy, A. V., McCullagh, M., Weare, J., Roux, B., Dinner, A. R., & Voth, G. A. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct4000444 · Cited by 169 · see citing works
Reaching biological timescales with all-atom molecular dynamics simulations
Zwier, M. C., & Chong, L. T. (2010) · Current Opinion in Pharmacology · doi:10.1016/j.coph.2010.09.008 · Cited by 168 · see citing works
Reactive flux and folding pathways in network models of coarse-grained protein dynamics
Berezhkovskii, A. M., Hummer, G., & Szabó, A. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3139063 · Cited by 168 · see citing works
Self-citation
Exploring the Free Energy Landscape: From Dynamics to Networks and Back
Prada‐Gracia, D., Gómez‐Gardeñes, J., Echenique, P. M., & Falo, F. (2009) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1000415 · Cited by 167 · see citing works
Thermodynamics and kinetics of protein folding under confinement
Mittal, J., & Best, R. B. (2008) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0807742105 · Cited by 161 · see citing works
Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods
Noé, F., & Clementi, C. (2017) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2017.02.006 · Cited by 161 · see citing works
Rapid equilibrium sampling initiated from nonequilibrium data
Huang, X., Bowman, G. R., Bacallado, S., & Pande, V. S. (2009) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0909088106 · Cited by 161 · 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
Protein-peptide association kinetics beyond the seconds timescale from atomistic simulations
Paul, F., Wehmeyer, C., Abualrous, E. T., Wu, H., Crabtree, M., Schöneberg, J., Clarke, J., Freund, C., Weikl, T. R., & Noé, F. (2017) · Nature Communications · doi:10.1038/s41467-017-01163-6 · Cited by 158 · see citing works
Conformational selection in protein binding and function
Weikl, T. R., & Paul, F. (2014) · Protein Science · doi:10.1002/pro.2539 · Cited by 152 · 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
Perspective: Identification of collective variables and metastable states of protein dynamics
Sittel, F., & Stock, G. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5049637 · Cited by 146 · see citing works
Constructing Markov State Models to elucidate the functional conformational changes of complex biomolecules
Wang, W., Cao, S., Zhu, L., & Huang, X. (2017) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1343 · Cited by 145 · see citing works
Slow Unfolded-State Structuring in Acyl-CoA Binding Protein Folding Revealed by Simulation and Experiment
Voelz, V. A., Jäger, M., Yao, S., Chen, Y., Zhu, L., Waldauer, S. A., Bowman, G. R., Friedrichs, M., Bakajin, O., Lapidus, L. J., et al. (2012) · Journal of the American Chemical Society · doi:10.1021/ja302528z · Cited by 140 · see citing works
Variational Koopman models: Slow collective variables and molecular kinetics from short off-equilibrium simulations
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
Graph dynamical networks for unsupervised learning of atomic scale dynamics in materials
Xie, T., France‐Lanord, A., Wang, Y., Shao‐Horn, Y., & Grossman, J. C. (2019) · Nature Communications · doi:10.1038/s41467-019-10663-6 · Cited by 139 · see citing works
Protein functional landscapes, dynamics, allostery: a tortuous path towards a universal theoretical framework
Zhuravlev, P. I., & Papoian, G. A. (2010) · Quarterly Reviews of Biophysics · doi:10.1017/s0033583510000119 · Cited by 138 · 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
Rate theories for biologists
Zhou, H. (2010) · Quarterly Reviews of Biophysics · doi:10.1017/s0033583510000120 · Cited by 135 · see citing works
Free Energies from Dynamic Weighted Histogram Analysis Using Unbiased Markov State Model
Rosta, E., & Hummer, G. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500719p · Cited by 134 · see citing works
Self-citation
Free energy of conformational transition paths in biomolecules: The string method and its application to myosin VI
Ovchinnikov, V., Karplus, M., & Vanden‐Eijnden, E. (2011) · The Journal of Chemical Physics · doi:10.1063/1.3544209 · Cited by 131 · see citing works
Comparing 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 125 · see citing works
Fibril Elongation by Aβ17–42: Kinetic Network Analysis of Hybrid-Resolution Molecular Dynamics Simulations
Han, W., & Schulten, K. J. (2014) · Journal of the American Chemical Society · doi:10.1021/ja507002p · Cited by 124 · see citing works
A theoretical view of protein dynamics
Orozco, M. (2014) · Chemical Society Reviews · doi:10.1039/c3cs60474h · Cited by 123 · see citing works
Thermostat Artifacts in Replica Exchange Molecular Dynamics Simulations
Rosta, E., Buchete, N., & Hummer, G. (2009) · Journal of Chemical Theory and Computation · doi:10.1021/ct800557h · Cited by 120 · see citing works
Self-citation
Markov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning
Konovalov, K. A., Unarta, I. C., Cao, S., Goonetilleke, E. C., & Huang, X. (2021) · JACS Au · doi:10.1021/jacsau.1c00254 · Cited by 120 · see citing works
Probing molecular kinetics with Markov models: metastable states, transition pathways and spectroscopic observables
Prinz, J.-H., Keller, B. G., & Noé, F. (2011) · Physical Chemistry Chemical Physics · doi:10.1039/c1cp21258c · Cited by 119 · see citing works
Molecular origins of internal friction effects on protein-folding rates
Sancho, D. D., Sirur, A., & Best, R. B. (2014) · Nature Communications · doi:10.1038/ncomms5307 · Cited by 118 · see citing works
The Free Energy Landscape of Small Molecule Unbinding
Huang, D., & Caflisch, A. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002002 · Cited by 116 · see citing works
Dynamical fingerprints for probing individual relaxation processes in biomolecular dynamics with simulations and kinetic experiments
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
Contact- and distance-based principal component analysis of protein dynamics
Ernst, M., Sittel, F., & Stock, G. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4938249 · Cited by 105 · see citing works
Kinetic 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
Error and efficiency of replica exchange molecular dynamics simulations
Rosta, E., & Hummer, G. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3249608 · Cited by 100 · see citing works
Self-citation
Evaluating the Effects of Cutoffs and Treatment of Long-range Electrostatics in Protein Folding Simulations
Piana, S., Lindorff‐Larsen, K., Dirks, R. M., Salmon, J. K., Dror, R. O., & Shaw, D. E. (2012) · PLoS ONE · doi:10.1371/journal.pone.0039918 · Cited by 100 · 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 99 · see citing works
Self-citation
Artificial Intelligence Enhanced Molecular Simulations
Zhang, J., Chen, D., Xia, Y., Huang, Y., Lin, X., Han, X., Ni, N., Wang, Z., Fan, Y., Yang, L., et al. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00214 · Cited by 96 · see citing works
Bridge helix bending promotes RNA polymerase II backtracking through a critical and conserved threonine residue
Da, L., Pardo‐Ávila, F., Xu, L., Silva, D., Zhang, L., Gao, X., Wang, D., & Huang, X. (2016) · Nature Communications · doi:10.1038/ncomms11244 · Cited by 91 · see citing works
Perspective: Markov models for long-timescale biomolecular dynamics
Schwantes, C. R., McGibbon, R. T., & Pande, V. S. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4895044 · Cited by 86 · see citing works
Integration of network models and evolutionary analysis into high-throughput modeling of protein dynamics and allosteric regulation: theory, tools and applications
Liang, Z. T., Verkhivker, G. M., & Hu, G. (2019) · Briefings in Bioinformatics · doi:10.1093/bib/bbz029 · Cited by 85 · see citing works
Statistically optimal analysis of state-discretized trajectory data from multiple thermodynamic states
Wu, H., Mey, A. S. J. S., Rosta, E., & Noé, F. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4902240 · Cited by 83 · see citing works
Exact rate calculations by trajectory parallelization and tilting
Vanden‐Eijnden, E., & Venturoli, M. (2009) · The Journal of Chemical Physics · doi:10.1063/1.3180821 · Cited by 83 · see citing works
Markov Models of Molecular Kinetics
Noé, F., & Rosta, E. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5134029 · Cited by 82 · see citing works
Diffusion models of protein folding
Best, R. B., & Hummer, G. (2011) · Physical Chemistry Chemical Physics · doi:10.1039/c1cp21541h · Cited by 80 · see citing works
Self-citation
Dynamic properties of force fields
Vitalini, F., Mey, A. S. J. S., Noé, F., & Keller, B. G. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4909549 · Cited by 79 · see citing works
Kinetics from Replica Exchange Molecular Dynamics Simulations
Stelzl, L. S., & Hummer, G. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00372 · Cited by 79 · see citing works
Self-citation
Multiscale Simulation Reveals Multiple Pathways for H2 and O2 Transport in a [NiFe]-Hydrogenase
Wang, P.-H., Best, R. B., & Blumberger, J. (2011) · Journal of the American Chemical Society · doi:10.1021/ja109712q · Cited by 78 · see citing works
Uncertainty quantification for quantum chemical models of complex reaction networks
Proppe, J., Husch, T., Simm, G. N. C., & Reiher, M. (2016) · Faraday Discussions · doi:10.1039/c6fd00144k · Cited by 78 · see citing works
Disordered RNA chaperones can enhance nucleic acid folding via local charge screening
Holmstrom, E. D., Liu, Z., Nettels, D., Best, R. B., & Schuler, B. (2019) · Nature Communications · doi:10.1038/s41467-019-10356-0 · Cited by 78 · see citing works
Mechanisms of protein–ligand association and its modulation by protein mutations
Held, M., Metzner, P., Prinz, J.-H., & Noé, F. (2011) · Biophysical Journal · doi:10.1016/j.bpj.2010.12.3699 · Cited by 77 · see citing works
Protein storytelling through physics
Brini, E., Simmerling, C. L., & Dill, K. A. (2020) · Science · doi:10.1126/science.aaz3041 · Cited by 77 · see citing works
Improved coarse-graining of Markov state models via explicit consideration of statistical uncertainty
Bowman, G. R. (2012) · The Journal of Chemical Physics · doi:10.1063/1.4755751 · Cited by 76 · see citing works
Robust Density-Based Clustering To Identify Metastable Conformational States of Proteins
Sittel, F., & Stock, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b01233 · Cited by 76 · see citing works
Hierarchical Time-Lagged Independent Component Analysis: Computing Slow Modes and Reaction Coordinates for Large Molecular Systems
Pérez‐Hernández, G., & Noé, F. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00738 · Cited by 76 · see citing works
Identifying metastable states of folding proteins
Jain, A., & Stock, G. (2012) · Journal of Chemical Theory and Computation · doi:10.1021/ct300077q · Cited by 75 · see citing works
Committors, first-passage times, fluxes, Markov states, milestones, and all that
Berezhkovskii, A. M., & Szabó, A. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5079742 · Cited by 74 · see citing works
Multiscale Estimation of Binding Kinetics Using Brownian Dynamics, Molecular Dynamics and Milestoning
Votapka, L. W., & Amaro, R. E. (2015) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1004381 · Cited by 74 · see citing works
Machine Learning of Biomolecular Reaction Coordinates
Brandt, S., Sittel, F., Ernst, M., & Stock, G. (2018) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.8b00759 · Cited by 73 · see citing works
The molecular recognition of phosphatidic acid by an amphipathic helix in Opi1
Hofbauer, H. F., Gecht, M., Fischer, S., Seybert, A., Frangakis, A. S., Stelzer, E. H. K., Covino, R., Hummer, G., & Ernst, R. (2018) · The Journal of Cell Biology · doi:10.1083/jcb.201802027 · Cited by 73 · see citing works
Self-citation
Temperature-dependent kinetic pathways of heterogeneous ice nucleation competing between classical and non-classical nucleation
Li, C., Liu, Z., Goonetilleke, E. C., & Huang, X. (2021) · Nature Communications · doi:10.1038/s41467-021-25267-2 · Cited by 72 · see citing works
Revisiting and Computing Reaction Coordinates with Directional Milestoning
Kırmızıaltın, S., & Elber, R. (2011) · The Journal of Physical Chemistry A · doi:10.1021/jp111093c · Cited by 72 · see citing works

Probing the Kinetic Network of Folding-Unfolding Transitions in Proteins
Murphy, R. D., & Buchete, N. (2011) · Biophysical Journal · doi:10.1016/j.bpj.2010.12.3130
Self-citation
Helix−Coil Kinetics: Folding Time Scales for Helical Peptides from a Sequential Kinetic Model
Brooks, C. L. (1996) · The Journal of Physical Chemistry · doi:10.1021/jp952674f · Cited by 63 · see citing works
Peptide folding kinetics from replica exchange molecular dynamics
Buchete, N.-V., & Hummer, G. (2008) · Physical Review E · doi:10.1103/physreve.77.030902 · Cited by 121 · see citing works
Self-citation
Kinetics of α-helix formation as diffusion on a one-dimensional free energy surface
Doshi, U., & Muñoz, V. (2004) · Chemical Physics · doi:10.1016/j.chemphys.2004.05.022 · Cited by 19 · see citing works
Helix–Coil Transition Courses Through Multiple Pathways and Intermediates: Fast Kinetic Measurements and Dimensionality Reduction
Jas, G. S., & Kuczera, K. (2018) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.8b07924 · Cited by 14 · see citing works

Authors: Buchete, N.-V., & Hummer, G.
Affiliations: National Institutes of Health (US)
Corresponding author: Hummer, Gerhard
ORCID: Buchete, Nicolae-Viorel
Hummer, Gerhard
Venue: The Journal of Physical Chemistry B
Publisher: American Chemical Society (ACS)
Published: 2008-01-31
Volume: 112
Issue: 19
Pages: 6057-6069
ISSN: 1520-5207 (ISSN-L)
1520-6106
DOI: 10.1021/jp0761665
OpenAlex: W2025899185
Cited by: 477
References: 65
Citations by year: 2026: 8 · 2025: 17 · 2024: 14 · 2023: 20 · 2022: 23 · 2021: 23 · 2020: 30 · 2019: 34 · 2018: 35 · 2017: 32 · 2016: 37 · 2015: 31 · 2014: 26 · 2013: 34 · 2012: 31
FWCI: 11.02
Type: journal article
Language: en
Open access: closed
Locations: The Journal of Physical Chemistry B (publishedVersion)
PubMed (publishedVersion)
MPG.PuRe (Max Planck Society) (submittedVersion)
Funders: National Institutes of Health
Topics: Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
Keywords: helix-coil transition, conformational relaxation, transition rate matrix, transition pathways, non-Markovian dynamics, two-state model, four-state model, relaxation time, correlation functions
MeSH terms: Computer Simulation, Models, Molecular, Peptides, Temperature, Time Factors, Protein Structure, Tertiary, Protein Folding

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

Coarse master equations for peptide folding dynamics

Abstract

Integrity signals

Claims the paper makes

Claims other papers make about this one

Cites

Cited by

Related

Record

About these checks