Identification of slow molecular order parameters for Markov model construction
Open accessAbstract
A goal in the kinetic characterization of a macromolecular system is the description of its slow relaxation processes via (i) identification of the structural changes involved in these processes and (ii) estimation of the rates or timescales at which these slow processes occur. Most of the approaches to this task, including Markov models, master-equation models, and kinetic network models, start by discretizing the high-dimensional state space and then characterize relaxation processes in terms of the eigenvectors and eigenvalues of a discrete transition matrix. The practical success of such an approach depends very much on the ability to finely discretize the slow order parameters. How can this task be achieved in a high-dimensional configuration space without relying on subjective guesses of the slow order parameters? In this paper, we use the variational principle of conformation dynamics to derive an optimal way of identifying the “slow subspace” of a large set of prior order parameters – either generic internal coordinates or a user-defined set of parameters. Using a variational formulation of conformational dynamics, it is shown that an existing method—the time-lagged independent component analysis—provides the optional solution to this problem. In addition, optimal indicators—order parameters indicating the progress of the slow transitions and thus may serve as reaction coordinates—are readily identified. We demonstrate that the slow subspace is well suited to construct accurate kinetic models of two sets of molecular dynamics simulations, the 6-residue fluorescent peptide MR121-GSGSW and the 30-residue intrinsically disordered peptide kinase inducible domain (KID). The identified optimal indicators reveal the structural changes associated with the slow processes of the molecular system under analysis.
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The intrinsically disordered KID peptide was found to adopt a conformation that may precede its KIX-bound geometry even in the absence of its binding partner.
“which was found to adopt a conformation that may precede its KIX-bound geometry even in the absence of its binding partner [21].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [21]
The Results describe intrinsically disordered KID forming partial helices and hairpin-like structures in simulations without a binding partner. They do not compare those structures with KIX-bound KID or establish that any observed conformation may precede its bound geometry. Page numbers are unavailable in our copy. (LLM, conf=0.84)
Experimental — accuracy not yet measuredtICA solves the variational problem for the specific choice of basis functions identical to the input coordinates.
“This approach can also be shown to solve the variational problem for the specific choice of basis functions identical to the input coordinates [21].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [21]
tICA linearly transforms input coordinates into collective coordinates sorted by slowness, providing an excellent dimension reduction method for MSM construction.
“This approach, independently rediscovered by two groups [20, 21], linearly transforms the input coordinates (e.g. torsions, distances, contacts) into collective coordinates sorted by “slowness”, thus providing an excellent dimension reduction method for MSM construction.”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [21]
tICA can be understood as a generalization of principal component analysis, solving a generalized eigenvalue problem with the instantaneous and time-lagged correlation matrices of the input coordinates.
“This can be understood as a generalization of principal component analysis, as it solves a generalized eigenvalue problem with the instantaneous and time-lagged correlation matrices of the input coordinates [20, 21].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [21]
tICA proved critical in enabling the construction of MSMs for the intrinsically disordered KID peptide.
“This proved critical in enabling the construction of MSMs for the intrinsically disordered KID peptide”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [21]
The main drawback of TICA is the large amount of simulation data that is necessary to reliably estimate the autocorrelation function.
“the main drawback being the large amount of simulation data that is necessary to reliably estimate the autocorrelation function.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [81]
TICA identifies linear combinations of features from a time-dependent trajectory that not only have the largest variance, but that also have the longest autocorrelation time.
“The time-lagged independent component analysis method (TICA) 80,81 identifies linear combinations of features from a time-dependent trajectory that not only have the largest variance, but that also have the longest autocorrelation time”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [81]
Dimensionality reduction algorithms such as TICA or SGOOP, that incorporate information on the system's dynamics, implicitly ensure that the order parameter(s) perform well as descriptors of the slowest molecular motion.
“Dimensionality reduction algorithms as TICA 80,81 or SGOOP 82 , that incorporate information on the system's dynamics, implicitly ensure that the order parameter(s) perform well as descriptors of the slowest molecular motion.”
From Unsupervised machine learning in atomistic simulations, between predictions and understanding (2019) · cites this paper as [81]
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“Like PCA, TICA [55] uses a linear transform to map the original order parameters r ( t ) to a new set of order parameters z ( t ) — the independent components (ICs).”
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ResultComplete reconstruction of an enzyme-inhibitor binding process by molecular dynamics simulations
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Molecular simulation of ab initio protein folding for a millisecond folder NTL9(1–39)
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BackgroundTransition Path Theory for Markov Jump Processes
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BackgroundInfluentialTransition networks for modeling the kinetics of conformational change in macromolecules.
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Self-citationDescribing Protein Folding Kinetics by Molecular Dynamics Simulations. 1. Theory
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Intrinsically disordered proteins from A to Z
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“The TICA problem can easily be solved by subsequently solving two simple eigenvalue problems.”
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BackgroundMSMBuilder2: 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 · cited 1× · see citing works
“For clustering and Markov model construction of molecular dynamics data, the packages EMMA [83], MSMbuilder [5], Wordom [82] and METAGUI [8] are currently available.”
MethodObservation of a power-law memory kernel for fluctuations within a single protein molecule.
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“Conformational transitions between long-lived, or “metastable” states are essential to the function of biomolecules [27, 58, 52, 24, 78, 28, 95].”
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“…Markovian in (i.e., the time step to xt+τ is computed based on the current value of xt only), and gives rise to a unique stationary density μ(x), usually the Boltzmann density: μ(x) = Z−1e−βH (x), where H is the Hamiltonian, Z is the partition function, and β = (kBT)−1 is the inverse temperature.”
BackgroundDetermination of reaction coordinates via locally scaled diffusion map
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“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundPerformance guarantees for hierarchical clustering
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“The TICA problem can easily be solved by subsequently solving two simple eigenvalue problems.”
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“For clustering and Markov model construction of molecular dynamics data, the packages EMMA [83], MSMbuilder [5], Wordom [82] and METAGUI [8] are currently available.”
MethodConformational transitions in DNA polymerase I revealed by single-molecule FRET
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“Conformational transitions between long-lived, or “metastable” states are essential to the function of biomolecules [27, 58, 52, 24, 78, 28, 95].”
BackgroundStructure-function-folding relationship in a WW domain.
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“These rare transitions are ubiquitously found in biomolecular processes, including folding [34, 44], complex conformational rearrangements between native protein substates [26, 63], and ligand binding [68].”
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“of only ˝ = 2 ns [67]. Stock and co-workers have exploredthepossibilityofusingdihedralanglesasaninputtoPCA(dPCA).Asangularcoordinates, theycannotbeaveragedinthesamewaylikenonperiodiccoordinates. Ref. [3]thussuggeststouse the sine and cosine of backbone dihedral angles as input coordinates. It is found for hepta-alanin…”
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“Kinetic models usually first partition the conformation space into discrete states [93, 61, 40, 33, 94, 14, 74, 56, 21, 80, 69].”
BackgroundFull distance-resolved folding energy landscape of one single protein molecule
Gebhardt, J., Bornschlögl, T., & Rief, M. (2010) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.0909854107 · Cited by 209 · cited 1× · see citing works
“pf.edu *frank.noe@fu-berlin.de 1 arXiv:1302.6614v1 [physics.chem-ph] 26 Feb 2013 1 Introduction Conformationaltransitionsbetweenlong-lived,or“metastable” statesareessentialtothefunctionof biomolecules[27,58,52,24,78,28,95]. Theseraretransitionsareubiquitouslyfoundinbiomolecularprocesses,includingfolding[34,44], comple…”
BackgroundNucleosome disassembly intermediates characterized by single-molecule FRET
Gansen, A., Valeri, A., Hauger, F., Felekyan, S., Kalinin, S., Toth, K., Langowski, J., & Seidel, C. (2009) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.0903005106 · Cited by 187 · cited 1× · see citing works
“Conformational transitions between long-lived, or “metastable” states are essential to the function of biomolecules [27, 58, 52, 24, 78, 28, 95].”
BackgroundHigh-Throughput All-Atom Molecular Dynamics Simulations Using Distributed Computing
Buch, I., Harvey, M., Giorgino, T., Anderson, D. P., & de Fabritiis, G. (2010) · Journal of Chemical Information and Modeling · doi:10.1021/ci900455r · Cited by 183 · cited 3× · see citing works
“Rare conformational transitions can be explicitly traced by either single-molecule experiments [70, 88, 17, 44] or by high-throughput molecular dynamics simulations, either realized with few long trajectories [84, 48] or with many shorter trajectories [92, 11, 67, 13, 77, 12].”
BackgroundMethodSelf-citationOn the Approximation Quality of Markov State Models
Sarich, M., Noé, F., & Schütte, C. (2010) · Multiscale Modeling & Simulation · doi:10.1137/090764049 · Cited by 182 · see citing works
Self-citationSingle-molecule fluorescence spectroscopy maps the folding landscape of a large protein
Pirchi, M., Ziv, G., Riven, I., Cohen, S. S., Zohar, N., Barak, Y., & Haran, G. (2011) · Nature Communications · doi:10.1038/ncomms1504 · Cited by 179 · cited 1× · see citing works
“…Published by the American Institute of Physics Articles you may be interested in Markov models of molecular kinetics: Generation and validation The Journal of Chemical Physics 134, 174105 (2011); 10.1063/1.3565032 Slow dynamics in protein fluctuations revealed by…”
BackgroundInfluentialStructural mechanism of the recovery stroke in the myosin molecular motor.
Fischer, S., Windshügel, B., Horák, D., Holmes, K., & Smith, J. C. (2005) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.0408784102 · Cited by 176 · cited 1× · see citing works
“These rare transitions are ubiquitously found in biomolecular processes, including folding [34, 44], complex conformational rearrangements between native protein substates [26, 63], and ligand binding [68].”
BackgroundError 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 · cited 1× · see citing works
“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundReactive 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 170 · cited 1× · see citing works
“From this propagator, many properties can be calculated, such as transition pathways between two sets of configurations [51, 7, 67].”
BackgroundBuilding Markov state models along pathways to determine free energies and rates of transitions.
Pan, A. C., & Roux, B. (2008) · Journal of Chemical Physics · doi:10.1063/1.2959573 · Cited by 163 · cited 2× · see citing works
“Identification of slow molecular order parameters for Markov model construction Guillermo Pérez-Hernández, Fabian Paul, Toni Giorgino, Gianni De Fabritiis, and Frank Noé Citation: The Journal of Chemical Physics 139, 015102 (2013); View online: https://doi.org/10.1063/1.4811489 View Table of Contents: http://aip.scita…”
BackgroundInfluentialSimple 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 · cited 2× · see citing works
“n many examples, especially protein folding (see [9, 72] and references therein). Recent applications include folding of MR121-GSGS-W peptide[72], folding of FiP35 WW domain, GTT, NTL9, and protein G [6] and discovery of cryptic allosteric sites in -lactamase, interleukin-2, and RNase H [10]. However, minimal RMSD ten…”
BackgroundMethodEMMA: 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 · cited 2× · see citing works
“inatespaceareselectedas cluster centers witha 8 clustering method. Various algorithms have been proposed in the literature, including k-means [50], k-centers[20],k-medoids[42],regularspatialclustering[83],regulartemporalclustering[83]andWard clustering[6]. The k-meansalgorithmrequiresthecoordinatespacetobeavectorspace…”
MethodInfluentialSelf-citationAtomistic folding simulations of the five helix bundle protein λ6–85
Bowman, G., Voelz, V. A., & Pande, V. (2011) · Journal of the American Chemical Society · doi:10.1021/ja106936n · Cited by 139 · see citing works
Probability distributions of molecular observables computed from Markov models
Noé, F. (2008) · The Journal of Chemical Physics · doi:10.1063/1.2916718 · Cited by 135 · cited 1× · see citing works
“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundSelf-citationHinrichs, 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 · cited 1× · see citing works
“• From the largest m Eigenvalues and their associated Eigenfunctions, a rank-m propagator can be assembled that can describe the dynamics slower than timescale t m [46].”
BackgroundExperimental evidence for a frustrated energy landscape in a 3-helix bundle protein family
Wensley, B., Batey, S., Bone, F. A. C., Chan, Z.-M., Tumelty, N. R., Steward, A., Kwa, L., Borgia, A., & Clarke, J. (2010) · Nature · doi:10.1038/nature08743 · Cited by 122 · cited 1× · see citing works
“Conformational transitions between long-lived, or “metastable” states are essential to the function of biomolecules [27, 58, 52, 24, 78, 28, 95].”
Backgroundde Groot, B. L., Daura, X., Mark, A., & Grubmüller, H. (2001) · Journal of Molecular Biology · doi:10.1006/jmbi.2001.4655 · Cited by 121 · cited 1× · see citing works
“…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 Computer Science,…”
BackgroundInfluentialNeuweiler, H., Löllmann, M., Doose, S., & Sauer, M. (2006) · Journal of Molecular Biology · doi:10.1016/j.jmb.2006.10.021 · Cited by 118 · cited 1× · see citing works
“MR121-GSGSW is a well-studied fluorescent peptide that has been extensively characterized by experiments [59], simulations [19] and also Markov models [60, 65].”
BackgroundNoé, 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 · cited 6× · see citing works
“PCA has also been used successfully in Markov model construction [67, 65], however is suffers from the similar limitations like minimal RMSD, as there is no general guarantee that large-amplitude motions are associated with slow transitions.”
BackgroundMethodInfluentialSelf-citationThe Free Energy Landscape of Small Molecule Unbinding
Huang, D., & Caflisch, A. (2011) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1002002 · Cited by 116 · cited 1× · see citing works
“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundCoarse 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 · cited 1× · see citing works
“The resulting models are often called transition networks [74, 62, 32], Diffusion maps [18, 76], Master equation models [87, 14], Markov models [64] or Markov state models [86, 16] (MSM), where “Markovianity” means that the kinetics are modeled by a memoryless jump process between states.”
BackgroundKinetic 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 · cited 1× · see citing works
“Rare conformational transitions can be explicitly traced by either single-molecule experiments [70, 88, 17, 44] or by high-throughput molecular dynamics simulations, either realized with few long trajectories [84, 48] or with many shorter trajectories [92, 11, 67, 13, 77, 12].”
BackgroundSelf-citationNoé, F., Krachtus, D., Smith, J. C., & Fischer, S. (2006) · Journal of Chemical Theory and Computation · doi:10.1021/ct050162r · Cited by 93 · cited 1× · see citing works
“These rare transitions are ubiquitously found in biomolecular processes, including folding [34, 44], complex conformational rearrangements between native protein substates [26, 63], and ligand binding [68].”
BackgroundSelf-citationMETAGUI. A VMD interface for analyzing metadynamics and molecular dynamics simulations
Biarnés, X., Pietrucci, F., Marinelli, F., & Laio, A. (2012) · Computer Physics Communications · doi:10.1016/j.cpc.2011.08.020 · Cited by 92 · cited 1× · see citing works
“For clustering and Markov model construction of molecular dynamics data, the packages EMMA [83], MSMbuilder [5], Wordom [82] and METAGUI [8] are currently available.”
MethodMuff, S., & Caflisch, A. (2008) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.21565 · Cited by 91 · cited 3× · see citing works
“Identification of slow molecular order parameters for Markov model construction Guillermo Pérez-Hernández, Fabian Paul, Toni Giorgino, Gianni De Fabritiis, and Frank Noé Citation: The Journal of Chemical Physics 139, 015102 (2013); View online: https://doi.org/10.1063/1.4811489 View Table of Contents: http://aip.scita…”
BackgroundInfluentialMg2+-dependent folding of a Diels-Alderase ribozyme probed by single-molecule FRET analysis
Kobitski, A., Nierth, A., Helm, M., Jäschke, A., & Nienhaus, G. U. (2007) · Nucleic Acids Research · doi:10.1093/nar/gkm072 · Cited by 81 · cited 2× · see citing works
“Rare conformational transitions can be explicitly traced by either single-molecule experiments [70, 88, 17, 44] or by high-throughput molecular dynamics simulations, either realized with few long trajectories [84, 48] or with many shorter trajectories [92, 11, 67, 13, 77, 12].”
BackgroundMechanisms 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 · cited 1× · see citing works
“[30, 13], the binding of a small ligand was analyzed by using the three-dimensional positions of the ligand with respect to the protein.”
BackgroundSelf-citationUnderstanding ensemble protein folding at atomic detail
Hubner, I. A., Deeds, E. J., & Shakhnovich, E. I. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0605580103 · Cited by 67 · cited 1× · see citing works
“Kinetic models usually first partition the conformation space into discrete states [93, 61, 40, 33, 94, 14, 74, 56, 21, 80, 69].”
BackgroundEstimating the Eigenvalue Error of Markov State Models
Djurdjevac, N., Sarich, M., & Schütte, C. (2012) · Multiscale Modeling & Simulation · doi:10.1137/100798910 · Cited by 63 · cited 2× · see citing works
“The approximation error of all of the above quantities can be cast in terms of the approximation error of the eigenvalues and eigenfunctions [79, 23, 72, 71].”
BackgroundMarkov models and dynamical fingerprints: Unraveling the complexity of molecular kinetics
Keller, B. G., Prinz, J.-H., & Noé, F. (2012) · Chemical Physics · doi:10.1016/j.chemphys.2011.08.021 · Cited by 59 · cited 1× · see citing works
“…correlation functions (e.g. fluorescence correlation, intermediate scattering function in dynamic neutron or X-ray scattering) can be computed as a sum of single-exponential relaxations with timescales computed from λ i and amplitudes from the φ i and the experimental observable [65, 43, 15].”
BackgroundSelf-citationNeubauer, H., Gaiko, N., Berger, S., Schaffer, J., Eggeling, C., Tuma, J., Verdier, L., Seidel, C., Griesinger, C., & Volkmer, A. (2007) · Journal of the American Chemical Society · doi:10.1021/ja0722574 · Cited by 58 · cited 1×
“Conformational transitions between long-lived, or “metastable” states are essential to the function of biomolecules [27, 58, 52, 24, 78, 28, 95].”
BackgroundBuchner, G. S., Murphy, R. D., Buchete, N.-V., & Kubelka, J. (2011) · Biochimica et Biophysica Acta · doi:10.1016/j.bbapap.2010.09.013 · Cited by 54 · cited 1× · see citing works
“The TICA problem can easily be solved by subsequently solving two simple eigenvalue problems.”
BackgroundHydrogen-Bond Driven Loop-Closure Kinetics in Unfolded Polypeptide Chains
Daidone, I., Neuweiler, H., Doose, S., Sauer, M., & Smith, J. C. (2010) · PLoS Comput. Biol. · doi:10.1371/journal.pcbi.1000645 · Cited by 48 · cited 1× · see citing works
“MR121-GSGSW is a well-studied fluorescent peptide that has been extensively characterized by experiments [59], simulations [19] and also Markov models [60, 65].”
BackgroundRelaxation mode analysis of a peptide system: comparison with principal component analysis.
Mitsutake, A., Iijima, H., & Takano, H. (2011) · Journal of Chemical Physics · doi:10.1063/1.3652959 · Cited by 45 · cited 1×
“Mitsutake et al [53] used relaxation mode analysis, a related technique, to analyze the dynamics of Met-enkephalin.”
MethodExtracting Markov Models of Peptide Conformational Dynamics from Simulation Data.
Schultheis, V., Hirschberger, T., Carstens, H., & Tavan, P. (2005) · Journal of Chemical Theory and Computation · doi:10.1021/ct050020x · Cited by 44 · cited 2× · see citing works
“Kinetic models usually first partition the conformation space into discrete states [93, 61, 40, 33, 94, 14, 74, 56, 21, 80, 69].”
BackgroundJain, A., Hegger, R., & Stock, G. (2010) · The Journal of Physical Chemistry Letters · doi:10.1021/jz101069e · Cited by 28 · cited 1× · see citing works
“In subsequent work [35], the approach was extended to the “dihedral PCA by parts” method.”
MethodSpectral rate theory for two-state kinetics
Prinz, J.-H., Chodera, J. D., & Noé, F. (2014) · Physical Review X · doi:10.1103/physrevx.4.011020 · Cited by 21 · see citing works
Self-citationBerezovska, G., Prada-Gracia, D., Mostarda, S., & Rao, F. (2012) · Journal of Chemical Physics · doi:10.1063/1.4764868 · Cited by 17 · see citing works
Noé, F., Daidone, I., Smith, J. C., Nola, A. D., & Amadei, A. (2008) · Journal of Physical Chemistry B · doi:10.1021/jp801391t.s001 · Cited by 10 · cited 1×
“MR121-GSGSW is a well-studied fluorescent peptide that has been extensively characterized by experiments [59], simulations [19] and also Markov models [60, 65].”
BackgroundSelf-citationA variational approach to modeling slow processes in stochastic dynamical systems
Noé, F., & Nüske, F. (2012) · arXiv · doi:10.48550/arxiv.1211.7103
Self-citation
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Cited by
Sorted by citations
PyEMMA 2: A Software Package for Estimation, Validation, and Analysis of Markov Models
Scherer, M. K., Trendelkamp-Schroer, B., Paul, F., Pérez‐Hernández, G., Hoffmann, M., Plattner, N., Wehmeyer, C., Prinz, J.-H., & Noé, F. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00743 · Cited by 1,135 · see citing works
Self-citationBoltzmann generators: Sampling equilibrium states of many-body systems with deep learning
Noé, F., Olsson, S., Köhler, J., & Wu, H. (2019) · Science · doi:10.1126/science.aaw1147 · Cited by 747 · see citing works
“To promote simultaneous sampling of high-and low-probability configurations, we included an RC loss using two slow collective coordinates that have been used earlier in the analysis of this BPTI simulation (supplementary materials) ( 29 , 30 ).”
MethodSelf-citationMachine 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
Self-citationMarkov 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
“[21 ].”
BackgroundMethodInfluentialSelf-citationVAMPnets for deep learning of molecular kinetics
Mardt, A., Pasquali, L., Wu, H., & Noé, F. (2017) · Nature Communications · doi:10.1038/s41467-017-02388-1 · Cited by 557 · see citing works
Self-citationRNA 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
Self-citationTime-lagged autoencoders: Deep learning of slow collective variables for molecular kinetics
Wehmeyer, C., & Noé, F. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5011399 · Cited by 401 · see citing works
Self-citationHTMD: High-Throughput Molecular Dynamics for Molecular Discovery.
Doerr, S., Harvey, M., Noé, F., & de Fabritiis, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00049 · Cited by 421 · see citing works
Self-citationPlattner, N., & Noé, F. (2015) · Nature Communications · doi:10.1038/ncomms8653 · Cited by 391 · see citing works
Self-citationEffect of natural mutations of SARS-CoV-2 on spike structure, conformation, and antigenicity
Gobeil, S., Janowska, K., McDowell, S., Mansouri, K., Parks, R., Stalls, V., Kopp, M., Manne, K., Li, D., Wiehe, K. J., et al. (2021) · Science · doi:10.1126/science.abi6226 · Cited by 374 · see citing works
“MSMs were prepared in HTMD using a TICA lag time of 5 ns retaining five dimensions followed by K-means clustering using 500 cluster centers.”
MethodEnhanced sampling in molecular dynamics.
Yang, Y., Shao, Q., Zhang, J., Yang, L.-J., & Gao, Y. (2019) · Journal of Chemical Physics · doi:10.1063/1.5109531 · Cited by 362 · see citing works
Variational Approach for Learning Markov Processes from Time Series Data
Wu, H., & No'e, F. (2017) · Journal of nonlinear science · doi:10.1007/s00332-019-09567-y · Cited by 354 · see citing works
“…the variational approach of conformation dynamics (VAC) (Noé and Nüske 2013; Nüske et al. 2014), time-lagged independent component analysis (TICA) (Perez-Hernandez et al. 2013; Schwantes and Pande 2013), dynamic mode decomposition (DMD) (Rowley et al. 2009; Schmid 2010; Tu et al. 2014), extended…”
MethodScalable emulation of protein equilibrium ensembles with generative deep learning
Lewis, S., Hempel, T., Jiménez Luna, J., Gastegger, M., Xie, Y., Foong, A. Y. K., García Satorras, V., Abdin, O., Veeling, B. S., Zaporozhets, I., et al. (2024) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2024.12.05.626885 · Cited by 349 · see citing works
“[9], which consists of simulations for 24 systems and uses the amber ff03 force field [25].”
Self-citationUnsupervised Learning Methods for Molecular Simulation Data
Glielmo, A., Husic, B. E., Rodríguez, Á., Clementi, C., Noé, F., & Laio, A. (2021) · Chemical Reviews · doi:10.1021/acs.chemrev.0c01195 · Cited by 408 · see citing works
Self-citationData-Driven Model Reduction and Transfer Operator Approximation
Klus, S., Nüske, F., Koltai, P., Wu, H., Kevrekidis, I., Schütte, C., & Noé, F. (2018) · Journal of nonlinear science · doi:10.1007/s00332-017-9437-7
“The time-lagged independent components are required (a) to be uncorrelated and (b) to maximize the autocovariances at lag time τ , see (Hyvärinen et al. 2001; Pérez-Hernández et al. 2013) for more details.”
BackgroundMethodInfluentialSelf-citationScalable emulation of protein equilibrium ensembles with generative deep learning
Lewis, S., Hempel, T., Jiménez-Luna, J., Gastegger, M., Xie, Y., Foong, A. Y. K., Satorras, V. G., Abdin, O., Veeling, B. S., Zaporozhets, I., et al. (2025) · Science · doi:10.1126/science.adv9817 · Cited by 335 · see citing works
Self-citationPlattner, N., Doerr, S., Fabritiis, G. D., & Noé, F. (2017) · Nature Chemistry · doi:10.1038/nchem.2785 · Cited by 338 · see citing works
Self-citationVariational 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
Self-citationMachine learning approaches for analyzing and enhancing molecular dynamics simulations
Wang, Y., Lamim Ribeiro, J. M., & Tiwary, P. (2020) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2019.12.016 · Cited by 303 · see citing works
“Methods such as TICA [9] implement VAC directly by learning slow eigenvectors as linear combinations of pre-selected basis functions, and are at the heart of building MSMs.”
MethodBottom-up Coarse-Graining: Principles and Perspectives
Jin, J., Pak, A. J., Durumeric, A. E. P., Loose, T. D., & Voth, G. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00643 · Cited by 296 · see citing works
MSMBuilder: Statistical Models for Biomolecular Dynamics
Harrigan, M. P., Sultan, M. M., Hernández, C. X., Husic, B. E., Eastman, P., Schwantes, C. R., Beauchamp, K. A., McGibbon, R. T., & Pande, V. S. (2016) · doi:10.1101/084020 · Cited by 277 · see citing works
“In practice, this dimensionality reduction has proven to be very useful for capturing slow, biophysical conformational changes (20,21).”
BackgroundMarkov State Models Provide Insights into Dynamic Modulation of Protein Function
Shukla, D., Hernández, C. X., Weber, J. K., & Pande, V. S. (2015) · Accounts of Chemical Research · doi:10.1021/ar5002999 · Cited by 257 · see citing works
Deep learning the slow modes for rare events sampling
Bonati, L., Piccini, G., & Parrinello, M. (2021) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.2113533118 · Cited by 260 · see citing works
“In addition, we have used the property that the matrix elements of Tτ can be written in terms of timecorrelation function [25].”
Sittel, F., Jain, A., & Stock, G. (2014) · Journal of Chemical Physics · doi:10.1063/1.4885338 · Cited by 260 · see citing works
Spectral gap optimization of order parameters for sampling complex molecular systems
Tiwary, P., & Berne, B. J. (2016) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1600917113 · Cited by 259 · see citing works
“The identification of such order parameters poses another complicated problem, but as routinely done in other methods aimed at optimizing CVs (15, 18, 24), we assume such order parameters are a priori known.”
BackgroundTorchMD: A Deep Learning Framework for Molecular Simulations
Doerr, S., Majewski, M., Pérez, A., Krämer, A., Clementi, C., Noe, F., Giorgino, T., & De Fabritiis, G. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01343 · Cited by 230 · see citing works
“The energy landscapes are obtained from binning the configurations over the first two TICA dimensions and computing the average of the equilibrium probability on each bin, obtained by Markov state model analysis of the mi-crostate of each configuration.”
MethodInfluentialSelf-citationCoarse 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
Self-citationKinetic distance and kinetic maps from molecular dynamics simulation.
Noé, F., & Clementi, C. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00553 · Cited by 211 · see citing works
Self-citationPrinciples and Overview of Sampling Methods for Modeling Macromolecular Structure and Dynamics
Maximova, T., Moffatt, R., Ma, B., Nussinov, R., & Shehu, A. (2016) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1004619 · Cited by 211 · see citing works
“Several reviews discuss the fundamental principles of disorder in the biological function of IDPs/IDPRSs biological functions, including the role of disorder in cancer, neurodegeneration, genetic forms of Parkinson’s disease, and cardiovascular diseases [401–405].”
MethodInfluentialAnalysis of Protein Folding Simulation with Moving Root Mean Square Deviation
Maruyama, Y., Igarashi, R., Ushiku, Y., & Mitsutake, A. (2023) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c01444 · Cited by 199 · see citing works
Kinetics for Drug Discovery: an industry-driven effort to target drug residence time.
Schuetz, D., de Witte, W. D., Wong, Y., Knasmueller, B., Richter, L., Kokh, D., Sadiq, S., Bosma, R., Nederpelt, I., Heitman, L., et al. (2017) · Drug Discovery Today · doi:10.1016/j.drudis.2017.02.002 · Cited by 197 · see citing works
“motions [68] can reduce the required simulation time, taken together, by an order of”
BackgroundVariational cross-validation of slow dynamical modes in molecular kinetics
McGibbon, R. T., & Pande, V. S. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4916292 · Cited by 191 · see citing works
Deeptime: a Python library for machine learning dynamical models from time series data
Hoffmann, M., Scherer, M. K., Hempel, T., Mardt, A., de Silva, B. M., Husic, B., Klus, S., Wu, H., Kutz, N., Brunton, S., et al. (2021) · Machine Learning: Science and Technology · doi:10.1088/2632-2153/ac3de0 · Cited by 193 · see citing works
“TICA [4] is a linear transformation method which was introduced for molecular dynamics in [5], was independently derived as a method for extracting the slow molecular order parameters by invoking the variational approach for conformation dynamics (see below) [80], and introduced as a method for constructing high-accur…”
BackgroundMethodSelf-citationComprehensive computational design of ordered peptide macrocycles
Hosseinzadeh, P., Bhardwaj, G., Mulligan, V., Shortridge, M., Craven, T. W., Pardo-Avila, F., Rettie, S. A., Kim, D. E., Silva, D., Ibrahim, Y. M., et al. (2017) · Science · doi:10.1126/science.aap7577 · Cited by 192 · see citing works
Reaction Coordinates and Mechanistic Hypothesis Tests.
Peters, B. (2016) · Annual review of physical chemistry (Print) · doi:10.1146/annurev-physchem-040215-112215 · Cited by 184 · see citing works
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
“A practically feasible comparison could be constructed in a similar way as the Chapman-Kolmogorow test in [33].”
BackgroundMethodSelf-citationUnsupervised machine learning in atomistic simulations, between predictions and understanding
Ceriotti, M. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5091842 · Cited by 173 · see citing works
tICA-Metadynamics: Accelerating Metadynamics by Using Kinetically Selected Collective Variables
Sultan, M. M., & Pande, V. S. (2017) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.7b00182 · Cited by 167 · see citing works
Gkeka, P., Stoltz, G., Farimani, A. B., Belkacemi, Z., Ceriotti, M., Chodera, J. D., Dinner, A. R., Ferguson, A. L., Maillet, J., Minoux, H., et al. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00355 · Cited by 211 · see citing works
Noé, F., & Clementi, C. (2017) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2017.02.006 · Cited by 161 · see citing works
Self-citationEstimation and uncertainty of reversible Markov models
Trendelkamp-Schroer, B., Wu, H., Paul, F., & Noé, F. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4934536 · Cited by 137 · see citing works
Self-citationMachine 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
“For this reason, much method development has been made in the past 10-15 years in order to optimize the pipeline for the construction of MSMs, that is: finding suitable molecular features to work with [50], reducing the dimensionality of feature space [51, 52], clustering the resulting space [53, 49], estimating the M…”
MethodSelf-citationWu, H., Nüske, F., Paul, F., Klus, S., Koltai, P., & Noé, F. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4979344 · Cited by 140 · see citing works
Self-citationModeling Molecular Kinetics with tICA and the Kernel Trick
Schwantes, C. R., & Pande, V. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/ct5007357 · Cited by 157 · see citing works
Machine learning coarse-grained potentials of protein thermodynamics
Majewski, M., Pérez, A., Thölke, P., Doerr, S. H., Charron, N. E., Toni Giorgino, A., Husic, B. E., Clementi, C., Noé, F., & Fabritiis, G. D. (2023) · Nature Communications · doi:10.1038/s41467-023-41343-1 · Cited by 119 · see citing works
“For the all-atom MD simulations, we featurized the simulation data into pairwise C α distances and applied TICA to project the featurized data into the first 4 components.”
MethodInfluentialSelf-citationEigendecompositions of Transfer Operators in Reproducing Kernel Hilbert Spaces
Klus, S., Schuster, I., & Muandet, K. (2017) · Journal of nonlinear science · doi:10.1007/s00332-019-09574-z · Cited by 153 · see citing works
Variational encoding of complex dynamics
Hernández, C. X., Wayment-Steele, H. K., Sultan, M. M., Husic, B. E., & Pande, V. S. (2018) · Physical review. E · doi:10.1103/physreve.97.062412 · Cited by 176 · see citing works
Two for One: Diffusion Models and Force Fields for Coarse-Grained Molecular Dynamics
Arts, M., Satorras, V. G., Huang, C.-W., Zugner, D., Federici, M., Clementi, C., No'e, F., Pinsler, R., & van den Berg, R. (2023) · Journal of Chemical Theory and Computation · doi:10.48550/arxiv.2302.00600 · Cited by 150
“For this, we calculate the time-lagged independent component analysis (TICA) (Naritomi & Fuchigami, 2011; Pérez-Hernández et al., 2013; Schwantes & Pande, 2013) using the Deeptime library (Hoffmann et al.”
MethodLigand binding free-energy calculations with funnel metadynamics
Raniolo, S., & Limongelli, V. (2020) · Nature Protocols · doi:10.1038/s41596-020-0342-4 · Cited by 166 · see citing works
“As reported in Box 1, in complex cases, system-speci fi c CVs might be considered (e.g., torsion angles, water coordination and path CVs) 5,21 – 26, 81 , 82 .”
BackgroundProtein-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
Self-citationTaming Rugged Free Energy Landscapes Using an Average Force
Fu, H., Shao, X., Cai, W., & Chipot, C. J. (2019) · Accounts of Chemical Research · doi:10.1021/acs.accounts.9b00473 · Cited by 166 · see citing works
Perspective: Identification of collective variables and metastable states of protein dynamics.
Sittel, F., & Stock, G. (2018) · Journal of Chemical Physics · doi:10.1063/1.5049637 · Cited by 137 · see citing works
Machine learning and data science in soft materials engineering
Ferguson, A. L. (2018) · Journal of Physics: Condensed Matter · doi:10.1088/1361-648x/aa98bd · Cited by 137 · see citing works
Wang, W., Cao, S.-Q., Zhu, L.-Z., & Huang, X.-H. (2018) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.1343 · Cited by 137 · see citing works
Automated design of collective variables using supervised machine learning
Sultan, M. M., & Pande, V. S. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5029972 · Cited by 137 · see citing works
Chen, W., Tan, A. R., & Ferguson, A. L. (2018) · Journal of Chemical Physics · doi:10.1063/1.5023804 · Cited by 133 · see citing works
Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation
Sidky, H., Chen, W., & Ferguson, A. L. (2020) · Molecular Physics · doi:10.1080/00268976.2020.1737742 · Cited by 147 · see citing works
Nonlinear Discovery of Slow Molecular Modes using Hierarchical Dynamics Encoders
Chen, W., Sidky, H., & Ferguson, A. L. (2019) · Journal of Chemical Physics · doi:10.1063/1.5092521 · Cited by 124 · see citing works
Accelerating Cryptic Pocket Discovery Using AlphaFold
Meller, A., Bhakat, S., Solieva, S. O., & Bowman, G. R. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c01189 · Cited by 132 · see citing works
“We also performed metadynamics simulations to generate a free energy landscape of Trp41 side chain orientations using an orthogonal technique that could be compared against our unperturbed simulations.”
Atomistic Simulations of Membrane Ion Channel Conduction, Gating, and Modulation
Flood, E., Boiteux, C., Lev, B. B., Vorobyov, I. V., & Allen, T. W. (2019) · Chemical Reviews · doi:10.1021/acs.chemrev.8b00630 · Cited by 145 · see citing works
McCarty, J. J., & Parrinello, M. (2017) · Journal of Chemical Physics · doi:10.1063/1.4998598 · Cited by 120 · see citing works
Kitao, A. (2022) · ET Journal · doi:10.3390/j5020021 · Cited by 118
Tsai, S.-T., Kuo, E.-J., & Tiwary, P. (2020) · Nature Communications · doi:10.1038/s41467-020-18959-8 · Cited by 109 · see citing works
Timewarp: Transferable Acceleration of Molecular Dynamics by Learning Time-Coarsened DynamicsPreprint
Klein, L., Foong, A. Y. K., Fjelde, T. E., Mlodozeniec, B., Brockschmidt, M., Nowozin, S., No'e, F., & Tomioka, R. (2023) · Neural Information Processing Systems · doi:10.48550/arxiv.2302.01170 · Cited by 114 · see citing works
Structural basis of ω−3 fatty acid transport across the blood-brain barrier
Cater, R., Chua, G., Erramilli, S., Keener, J., Choy, B., Tokarz, P., Chin, C., Quek, D., Kloss, B., Pepe, J., et al. (2021) · Nature · doi:10.1038/s41586-021-03650-9 · Cited by 113 · see citing works
Role of conformational dynamics in the evolution of novel enzyme function
Maria-Solano, M. A., Serrano-Hervás, E., Romero-Rivera, A., Iglesias-Fernández, J., & Osuna, S. (2018) · Chemical Communications · doi:10.1039/c8cc02426j · Cited by 112 · see citing works
Transferable Neural Networks for Enhanced Sampling of Protein Dynamics.
Sultan, M. M., Wayment-Steele, H. K., & Pande, V. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00025 · Cited by 110 · see citing works
“…showed 3,11 that time-structure based independent component analysis (tICA), a relatively recent advance in the Markov state model (MSM) field 12–14 , yields an excellent set of linear and non-linear collective variables (CVs) for enhanced sampling via Metadynamics or other methods. tICA and…”
MethodMarkov State Models to Study the Functional Dynamics of Proteins in the Wake of Machine Learning
Konovalov, K., Unarta, I., Cao, S.-Q., Goonetilleke, E. C., & Huang, X.-H. (2021) · JACS Au · doi:10.1021/jacsau.1c00254 · Cited by 109 · see citing works
Membrane proteins structures: A review on computational modeling tools
de Almeida, J. G., Preto, A. J., Koukos, P. I., Bonvin, A. M. J. J., & Moreira, I. S. (2017) · Biochimica et Biophysica Acta (BBA) - Biomembranes · doi:10.1016/j.bbamem.2017.07.008 · Cited by 115 · see citing works
“This requires an initial dimensionality reduction (which eliminates redundant data on atom coordinates) and grouping similar kinetic modes [133].”
Palma, J., & Pierdominici-Sottile, G. (2022) · ChemPhysChem · doi:10.1002/cphc.202200491 · Cited by 106 · see citing works
Flow-Matching: Efficient Coarse-Graining of Molecular Dynamics without Forces.
Köhler, J., Chen, Y.-Y., Krämer, A., Clementi, C., & Noé, F. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00016 · Cited by 102 · see citing works
Self-citationEncoderMap: Dimensionality Reduction and Generation of Molecule Conformations.
Lemke, T., & Peter, C. (2019) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00975 · Cited by 102 · see citing works
Combining experimental and simulation data of molecular processes via augmented Markov models
Olsson, S., Wu, H., Paul, F., Clementi, C., & Noé, F. (2017) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1704803114 · Cited by 101 · see citing works
“The simulations are embedded in a joint space of time-lagged independent components (TICs) (11, 45).”
BackgroundSelf-citationContact- and distance-based principal component analysis of protein dynamics.
Ernst, M., Sittel, F., & Stock, G. (2015) · Journal of Chemical Physics · doi:10.1063/1.4938249 · Cited by 101 · see citing works
Decherchi, S., Berteotti, A., Bottegoni, G., Rocchia, W., & Cavalli, A. (2015) · Nature Communications · doi:10.1038/ncomms7155 · Cited by 101 · see citing works
“Notable examples include the TSA inhibitors of human purine nucleoside phosphorylase (PNP), a homotrimeric enzyme that catalyzes the reversible phosphorolysis of 6-oxopurine nucleosides and deoxynucleosides to the corresponding purine base and a -d-(deoxy)ribose 1-phosphate 10 .”
BackgroundGenerative Modeling of Molecular Dynamics Trajectories
Jing, B., Stärk, H., Jaakkola, T., & Berger, B. (2024) · Neural Information Processing Systems · doi:10.48550/arxiv.2409.17808 · Cited by 100
“We then reduce dimensionality with Time-lagged Independent Components Analysis (TICA) (Pérez-Hernández et al., 2013) in PyEMMA (Scherer et al., 2015).”
InfluentialMultiensemble Markov models of molecular thermodynamics and kinetics
Wu, H., Paul, F., Wehmeyer, C., & Noé, F. (2016) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.1525092113 · Cited by 99 · see citing works
“μðxÞ= 1 P kN k iðxÞexp h f k iðxÞ − bkðxÞ i, for x∈ Si, [29]”
Self-citationCapturing the continuous complexity of behaviour in Caenorhabditis elegans
Ahamed, T., Costa, A. C., & Stephens, G. J. (2020) · Nature Physics · doi:10.1038/s41567-020-01036-8 · Cited by 80 · see citing works
Kutz, J., Proctor, J. L., & Brunton, S. (2018) · Complex · doi:10.1155/2018/6010634 · Cited by 98 · see citing works
“The authors further show that time-lagged independent component analysis (TICA) [20, 21], which was originally developed in 1994, is closely related to the DMD algorithm [17].”
ResultBonati, L., Trizio, E., Rizzi, A., & Parrinello, M. (2023) · Journal of Chemical Physics · doi:10.1063/5.0156343 · Cited by 96 · see citing works
Understanding and Modeling Polymers: The Challenge of Multiple Scales
Schmid, F. (2022) · ACS Polymers Au · doi:10.1021/acspolymersau.2c0004 · Cited by 95
“Techniques are available how to optimize the partitioning into macrostates [414], how to determine transition rates and the associated uncertainty [415], and even, how to use MSMs to connect theoretical models to experimental trajectory data [416].”
BackgroundCoarse-grained modelling out of equilibrium
Schilling, T. (2021) · Physics reports · doi:10.1016/j.physrep.2022.04.006 · Cited by 92 · see citing works
Time-Lagged Independent Component Analysis of Random Walks and Protein Dynamics
Schultze, S., & Grubmüller, H. (2021) · bioRxiv · doi:10.1101/2021.03.18.435940 · Cited by 92
“This property also renders these dimension reduction techniques highly useful as a preprocessing step to describing the conformational dynamics of macromolecules in terms of a discrete Markov process [17, 18, 19].”
Protein Conformation Generation via Force-Guided SE(3) Diffusion ModelsPreprint
Wang, Y., Wang, L., Shen, Y., Wang, Y.-Q., Yuan, H., Wu, Y., & Gu, Q. (2024) · International Conference on Machine Learning · doi:10.48550/arxiv.2403.14088 · Cited by 89 · see citing works
Navigating protein landscapes with a machine-learned transferable coarse-grained model
Charron, N., Bonneau, K., Pasos-Trejo, A. S., Guljas, A., Chen, Y.-Y., Musil, F., Venturin, J., Gusew, D., Zaporozhets, I., Krämer, A., et al. (2023) · Nature Chemistry · doi:10.1038/s41557-025-01874-0 · Cited by 89 · see citing works
“In the case of Homeodomain, the CG model stabilizes a state very close to the reference native structure, with higher relative flexibility at the N and C termini comparable with the all-atom simulations.”
Self-citationDistant residues modulate conformational opening in SARS-CoV-2 spike protein
Ray, D., Le, L., & Andricioaei, I. (2020) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1101/2020.12.07.415596 · Cited by 89
Identification of simple reaction coordinates from complex dynamics
McGibbon, R. T., Husic, B. E., & Pande, V. S. (2017) · The Journal of Chemical Physics · doi:10.1063/1.4974306 · Cited by 90 · see citing works
Gating mechanism of the extracellular entry to the lipid pathway in a TMEM16 scramblase
Lee, B., Khelashvili, G., Falzone, M. E., Menon, A. K., Weinstein, H., & Accardi, A. (2018) · Nature Communications · doi:10.1038/s41467-018-05724-1 · Cited by 93 · see citing works
Perspective: Markov models for long-timescale biomolecular dynamics.
Schwantes, C. R., McGibbon, R., & Pande, V. (2014) · Journal of Chemical Physics · doi:10.1063/1.4895044 · Cited by 88 · see citing works
Galerkin approximation of dynamical quantities using trajectory data
Thiede, E. H., Giannakis, D., Dinner, A. R., & Weare, J. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5063730 · Cited by 90 · see citing works
Pantsar, T., Rissanen, S., Dauch, D., Laitinen, T., Vattulainen, I., & Poso, A. (2018) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1006458 · Cited by 85 · see citing works
“In our work, we unlocked this issue through the analysis of the simulation data using PCA, interaction network analysis and MSMs that indeed revealed the differences, not only between the wild-type and the mutants, but also between the mutants.”
MethodInfluentialWhat makes a kinase promiscuous for inhibitors?
Hanson, S. M., Georghiou, G., Thakur, M., Miller, W., Rest, J., Chodera, J., & Seeliger, M. (2019) · Cell Chemical Biology · doi:10.1016/j.chembiol.2018.11.005 · Cited by 85 · see citing works
“The time-lagged independent component analysis (TICA) projection was then calculated from these coordinates to find the most kinetically relevant linear combination (Perez-Hernandez et al., 2013), and cumulative sum of the eigenvalues began to flatten despite the small number coordinates used (Figure S4A).”
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
Machine learning implicit solvation for molecular dynamics.
Chen, Y.-Y., Krämer, A., Charron, N., Husic, B., Clementi, C., & No'e, F. (2021) · Journal of Chemical Physics · doi:10.1063/5.0059915 · Cited by 83 · see citing works
Appadurai, R., Nagesh, J., & Srivastava, A. K. (2020) · Nature Communications · doi:10.1101/2020.06.02.124628 · Cited by 80
Str2Str: A Score-based Framework for Zero-shot Protein Conformation Sampling
Lu, J.-R., Zhong, B., Zhang, Z.-B., & Tang, J. (2023) · International Conference on Learning Representations · doi:10.48550/arxiv.2306.03117 · Cited by 79
“To better demonstrate the performance of S TR 2S TR , we present the TICA plots (P´erez-Hern´andez et al., 2013) for the sampled conformations from each method.”
BackgroundMethodMethods for data-driven multiscale model discovery for materials
Brunton, S., & Kutz, J. (2019) · Journal of Physics Materials · doi:10.1088/2515-7639/ab291e · Cited by 78 · see citing works
Accurate Estimation of Protein Folding and Unfolding Times: Beyond Markov State Models
Suárez, E., Adelman, J. L., & Zuckerman, D. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00339 · Cited by 78 · see citing works
Markov Models of Molecular Kinetics.
No'e, F., & Rosta, E. (2019) · Journal of Chemical Physics · doi:10.1063/1.5134029 · Cited by 77 · see citing works
- Authors
- Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G., & Noé, F.
- Affiliations
- Freie Universität Berlin (DE)
- Max Planck Institute of Colloids and Interfaces (DE)
- National Research Council (IT)
- GRIB 4 , Barcelona Biomedical Research Park (PRBB), C/Dr. Aiguader 88, 08003 Barcelona, Spain
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2013-07-03
- Volume
- 139
- Issue
- 1
- Pages
- 015102-015102
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W2143592395
- Cited by
- 990
- References
- 98
- Citations by year
- 2026: 92 · 2025: 89 · 2024: 95 · 2023: 106 · 2022: 103 · 2021: 102 · 2020: 80 · 2019: 87 · 2018: 89 · 2017: 61 · 2016: 42 · 2015: 27 · 2014: 14 · 2013: 2 · 2012: 1
- FWCI
- 12.69
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- Repositori digital de la UPF (Universitat Pompeu Fabra) (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- arXiv (Cornell University)
- Funders
- Deutsche Forschungsgemeinschaft
- Generalitat de Catalunya
- Max-Planck-Gesellschaft
- Ministerio de Ciencia e Innovación (BIO2011/27450)
- Agència de Gestió d'Ajuts Universitaris i de Recerca
- FP7 Ideas: European Research Council (307494)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Physical Sciences › Physics and Astronomy › Statistical and Nonlinear Physics › Model Reduction and Neural Networks
- Keywords
- Markov model, conformational dynamics, variational principle, time-lagged independent component analysis, reaction coordinate, master equation, peptide dynamics, intrinsically disordered proteins
- MeSH terms
- Algorithms, Kinetics, Markov Chains, Molecular Conformation, Phosphotransferases, Temperature, Protein Structure, Tertiary, Molecular Dynamics Simulation
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