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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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“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]
Experimental — accuracy not yet measuredThe cited source says what the claim attributes to it.
In the citing paper
“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]
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In the citing paper
“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]
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“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]
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In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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]
In the citing paper
“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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Citations
Cites
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BackgroundTefas, A., & Pitas, I. (2003) · Encyclopedia of Machine Learning · doi:10.1007/978-0-387-30164-8_665 · Cited by 29,409
Least squares quantization in PCM
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MethodIndependent Component Analysis
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BackgroundImproved side-chain torsion potentials for the Amber ff99SB protein force field
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MethodIndependent Component Analysis
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Essential dynamics of proteins
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“KID peptide analyzed below). Principal component analysis (PCA) is a frequently-used method to reducethedimensionofanorderparameterspacebyprojectingitonitslinearsubspaceofthelargestamplitude motions [4]. PCA has also been used successfully in Markov model construction [67, 65], however is suffers from the similar limit…”
BackgroundMethodA solution for the best rotation to relate two sets of vectors
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BackgroundMethodHow fast-folding proteins fold
Lindorff-Larsen, K., Piana, S., Dror, R. O., & Shaw, D. E. (2011) · Science · doi:10.1126/science.1208351 · Cited by 1,980 · cited 1×
“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].”
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Items 601–700 of 1,004
Dreßler, C., Kabbe, G., Brehm, M., & Sebastiani, D. (2020) · The Journal of Chemical Physics · doi:10.1063/5.0002167 · Cited by 7
Dynamical matrix propagator scheme for large-scale proton dynamics simulations
Dreßler, C., Kabbe, G., Brehm, M., & Sebastiani, D. (2020) · The Journal of Chemical Physics · doi:10.1063/1.5140635 · Cited by 9
Maruyama, Y., Takano, H., & Mitsutake, A. (2019) · Biophysics and Physicobiology · doi:10.2142/biophysico.16.0_407 · Cited by 10
On the role of solvent in hydrophobic cavity-ligand recognition kinetics.
Ahalawat, N., Bandyopadhyay, S., & Mondal, J. (2019) · Journal of Chemical Physics · doi:10.1063/1.5139584 · Cited by 9
Howard, R. J., Carnevale, V., Delemotte, L., Hellmich, U. A., & Rothberg, B. S. (2017) · Biochimica et Biophysica Acta (BBA) - Biomembranes · doi:10.1016/j.bbamem.2017.12.013 · Cited by 9
“Through the years, user input (e.g. choice of collective variables to discretize the conformational space, number of microstates, or time scales over which transitions are evaluated) has been reduced by machine-learning based automation [156].”
BackgroundEnhanced Sampling for Efficient Learning of Coarse-Grained Machine Learning Potentials
Chen, W., Görlich, F., Fuchs, P., & Zavadlav, J. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c01712 · Cited by 9
Cao, S., Nüske, F., Liu, B., Soley, M. B., & Huang, X. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00076 · Cited by 7
Roessner, R. A., Floquet, N., & Louet, M. (2025) · bioRxiv · doi:10.1101/2025.01.21.634062 · Cited by 8
Lionello, C., Becchi, M., Martino, S., & Pavan, G. M. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5c00374 · Cited by 8
Muscat, S., Errico, S., Danani, A., Chiti, F., & Grasso, G. (2024) · bioRxiv · doi:10.1101/2024.01.31.578042 · Cited by 8
“An approach to design an effective CV involves utilizing TICA, which focused on identifying the most slowly decorrelating modes, through the variational principle 68,69 .”
MethodKemeny Constant-Based Optimization of Network Clustering Using Graph Neural Networks
Martino, S., Morado, J., Li, C., Lu, Z., & Rosta, E. (2024) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.3c08213 · Cited by 5
“The simulation initially underwent clustering into 250 states using K-means on tICA projected data, followed by the calculation of a Markov matrix [58,59] , which served as the input to our method.”
MethodLearning Markovian dynamics with spectral maps
Rydzewski, J., & Gökdemir, T. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0189241 · Cited by 9
Thermodynamically Optimized Machine-Learned Reaction Coordinates for Hydrophobic Ligand Dissociation
Beyerle, E. R., & Tiwary, P. (2024) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.3c08304 · Cited by 8
Kinetic network models to elucidate aggregation dynamics of aggregation‐induced emission systems
Liu, Z., Kalin, M. L., Liu, B., Cao, S., & Huang, X. (2023) · Aggregate · doi:10.1002/agt2.422 · Cited by 11
Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model
Sisk, T., & Robustelli, P. J. (2023) · bioRxiv · doi:10.1101/2023.07.21.550103 · Cited by 8
Resolving Protein Conformational Plasticity and Substrate Binding via Machine Learning.
Ahalawat, N., Sahil, M., & Mondal, J. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00932 · Cited by 8
Mori, T., & Saito, S. (2022) · Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.2c02095 · Cited by 8
Molecular dynamics study of conformation transition from helix to sheet of Aβ42 peptide.
Zhou, M., Wen, H.-L., Lei, H., & Zhang, T. (2021) · Journal of Molecular Graphics and Modelling · doi:10.1016/j.jmgm.2021.108027 · Cited by 8
Enhanced sampling protocol to elucidate fusion peptide opening of SARS-CoV-2 spike protein
Remington, J. M., McKay, K. T., Ferrell, J. B., Schneebeli, S. T., & Li, J. (2021) · Biophysical Journal · doi:10.1016/j.bpj.2021.05.022 · Cited by 13
Error Bounds for Dynamical Spectral Estimation
Webber, R., Thiede, E., Dow, D., Dinner, A., & Weare, J. (2020) · SIAM Journal on Mathematics of Data Science · doi:10.1137/20m1335984 · Cited by 8
Karasawa, N., Mitsutake, A., & Takano, H. (2019) · Journal of Chemical Physics · doi:10.1063/1.5083891 · Cited by 8
Remington, J. M., McCullagh, M., & Kohler, B. (2019) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.8b12172 · Cited by 8
Narayan, B., Herbert, C., Yuan, Y., Rodriguez, B. J., Brooks, B. R., & Buchete, N. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5027580 · Cited by 8
Rudzinski, J. F., & Bereau, T. (2017) · bioRxiv · doi:10.1101/237875 · Cited by 8
“To determine the MSM microstate representation, time-lagged independent component analysis [41] was performed on the configurational space characterized by the φ/ψ dihedral angles of each residue along the peptide backbone.”
MethodIn silicoExploration of the Conformational Universe of GPCRs
Rodríguez‐Espigares, I., Kaczor, A. A., & Selent, J. (2016) · Molecular Informatics · doi:10.1002/minf.201600012 · Cited by 7
Šponer, J., Islam, B., Stadlbauer, P., & Haider, S. M. (2020) · Annual reports in medicinal chemistry · doi:10.1016/bs.armc.2020.04.002 · Cited by 13
Sadiq, S. K., Muñiz Chicharro, A., Friedrich, P., & Wade, R. C. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c00673 · Cited by 8
Sadiq, S. K., Chicharro, A. M., Friedrich, P., & Wade, R. C. (2021) · doi:10.1101/2021.06.22.449380 · Cited by 8
“Finding the appropriate CV space is still a major challenge, despite considerable efforts at systemisation [54–56].”
BackgroundPhysically Grounded Generative Modeling of All-Atom Biomolecular DynamicsPreprint
Feng, B., Zhang, J., Zhang, X., He, C., Zhang, M., Barth, P., Li, Y., & Li, Y. (2026) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.64898/2026.02.15.705956 · Cited by 4
“In the TICA basis, each component d decorrelates exponentially with a characteristic rate given by the TICA eigenvalue λ d : where τ is the TICA lag time and n is the number of lag steps.”
InfluentialData efficient learning of molecular slow modes from nonequilibrium metadynamics.
Hanni, J., & Ray, D. (2025) · Journal of Chemical Physics · doi:10.1063/5.0258483 · Cited by 7
Molecular Mechanisms Underlying the Loop-Closing Dynamics of β-1,4 Galactosyltransferase 1
Tian, J., Jia, W., Dong, H., Luo, X., Gong, L., Ren, Y., Zhong, L., Wang, J., & Shi, D. (2024) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.4c02010 · Cited by 8
A Sinking Approach to Explore Arbitrary Areas in Free Energy Landscapes
Pan, Z.-J., Li, M.-D., Chen, D.-C., & Yang, Y. (2024) · JACS Au · doi:10.1021/jacsau.5c00460 · Cited by 7
Shen, W., Wan, K., Li, D.-C., Gao, H.-J., & Shi, X.-H. (2024) · Proceedings of the National Academy of Sciences of the United States of America · doi:10.1073/pnas.2414205121 · Cited by 7
Force-Guided Bridge Matching for Full-Atom Time-Coarsened Dynamics of Peptides
Yu, Z., Huang, W.-B., & Liu, Y. (2024) · arXiv.org · doi:10.48550/arxiv.2408.15126 · Cited by 7
“Only the slowest components, TIC 0 and TIC 1, are taken for further evaluation (P´erez-Hern´andez et al., 2013).”
Sarkar, D. K., Surpeta, B., & Brezovský, J. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c00452 · Cited by 9
Araki, M., Ekimoto, T., Takemura, K., Matsumoto, S., Tamura, Y., Kokubo, H., Bekker, G., Yamane, T., Isaka, Y., Sagae, Y., et al. (2024) · bioRxiv · doi:10.1101/2024.03.27.586990 · Cited by 7
Huang, Y., Zhang, H.-L., Lin, Z.-L., Wei, Y., & Xi, W.-H. (2024) · bioRxiv · doi:10.1101/2024.03.11.584426 · Cited by 7
Yuan, S., Han, X., Zhang, J., Xie, Z., Fan, C., Xiao, Y.-L., Gao, Y.-Q., & Yang, Y. (2023) · Journal of Physical Chemistry A · doi:10.48550/arxiv.2401.00499 · Cited by 7
“As a result, some optimization methods for CVs have been developed, including Harmonic Linear Discriminant Analysis (HLDA) 43,44 , time-lagged component analysis (TICA) 45,46 , Skewed-Momenta method 47 and spectral gap optimization method for order parameters (SGOOP) 48 .”
MethodtICA-Metadynamics for Identifying Slow Dynamics in Membrane Permeation
Oh, M., da Hora, G. C. A., & Swanson, J. M. J. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00526 · Cited by 7
Coupling of conformational dynamics and inhibitor binding in the phosphodiesterase‐5 family
Tripathi, S., Cote, R. H., & Vashisth, H. (2023) · Protein Science · doi:10.1002/pro.4720 · Cited by 7
Yang, X., Gao, Y., Cao, F., & Wang, S. (2023) · International Journal of Molecular Sciences · doi:10.3390/ijms241310831 · Cited by 7
“This feature enables TICA to effectively extract slow order parameters from molecular dynamics data, making it an excellent choice for processing molecular simulation data before k-means clustering [58].”
MethodGiordano, D., Langini, C., Caflisch, A., Marabotti, A., & Facchiano, A. M. (2022) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2022.07.024 · Cited by 9
Identifying a Feasible Transition Pathway between Two Conformational States for a Protein
Li, Y., & Gong, H. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00390 · Cited by 6
Activation Pathways of Neurotensin Receptor 1 Elucidated Using Statistical Machine Learning
Yadav, P., & Farimani, A. B. (2022) · ACS Chemical Neuroscience · doi:10.1021/acschemneuro.2c00154 · Cited by 7
Linker, S. M., Schellhaas, C., Ries, B., ROTH, H. ‐., Fouché, M., Rodde, S., & Riniker, S. (2022) · RSC Advances · doi:10.1039/d1ra09025a · Cited by 24
Wenz, M. T., Bertazzon, M., Sticht, J., Aleksić, S., Gjorgjevikj, D., Freund, C., & Keller, B. (2021) · bioRxiv · doi:10.1101/2021.11.22.469489 · Cited by 7
FSATOOL 2.0: An integrated molecular dynamics simulation and trajectory data analysis program
Shu, Z., Wu, M., Liao, J., & Chen, C. (2021) · Journal of Computational Chemistry · doi:10.1002/jcc.26772 · Cited by 8
Nonlinear Model Reduction for Slow–Fast Stochastic Systems Near Unknown Invariant Manifolds
Ye, F. X.-F., Yang, S., & Maggioni, M. (2023) · Journal of Nonlinear Science · doi:10.1007/s00332-023-09998-8 · Cited by 7
Networks of interbasin traffic in intrinsically disordered proteins
de Aquino, B. R. H., Chwastyk, M., Mioduszewski, Ł., & Cieplak, M. (2020) · Physical Review Research · doi:10.1103/physrevresearch.2.013242 · Cited by 9
Simulating ion channel activation mechanisms using swarms of trajectories
Lev, B. B., & Allen, T. W. (2019) · Journal of Computational Chemistry · doi:10.1002/jcc.26102 · Cited by 8
Tian, J., Liu, F., Xu, Z.-J., Shi, J., Liang, T., Zhang, Y., & Da, L.-T. (2019) · ACS Catalysis · doi:10.1021/acscatal.9b03782 · Cited by 7
Highly Interactive, Steered Scientific Workflows on HPC Systems: Optimizing Design Solutions
Ossyra, J. R., Sedova, A., Baker, M., & Smith, J. C. (2019) · ISC High Performance · doi:10.1007/978-3-030-34356-9_39 · Cited by 7
Curado-Carballada, C., Feixas, F., & Osuna, S. (2019) · Advanced Synthesis and Catalysis · doi:10.1002/adsc.201900158 · Cited by 7
Elucidating the role of key structural motifs in antifreeze glycoproteins
Pandey, P., & Mallajosyula, S. S. (2019) · Physical Chemistry Chemical Physics · doi:10.1039/c8cp06743k · Cited by 18
Kots, E. D., Khrenova, M. G., & Nemukhin, A. V. (2018) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.8b00666 · Cited by 8
Folding a viral peptide in different membrane environments: pathway and sampling analyses
Nangia, S., Pattis, J. G., & May, E. R. (2018) · Journal of Biological Physics · doi:10.1007/s10867-018-9490-y · Cited by 8
“We performed a global TICA analysis by combining the systems into a single, master system, which allows us to obtain global tICs, and compare the systems on a consistent basis.”
MethodInfluentialUnfolding dynamics of small peptides biased by constant mechanical forces
Knoch, F., & Speck, T. (2017) · Molecular Systems Design & Engineering · doi:10.1039/c7me00080d · Cited by 7
Karasawa, N., Mitsutake, A., & Takano, H. (2017) · Physical review. E · doi:10.1103/physreve.96.062408 · Cited by 8
Nonequilibrium Markov state modeling of the globule-stretch transition
Knoch, F., & Speck, T. (2017) · Physical review. E · doi:10.1103/physreve.95.012503 · Cited by 12
Tanaka, S. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4942861 · Cited by 6
Challenges and Opportunities in Drug Discovery of Biased Ligands
Rodríguez‐Espigares, I., Kaczor, A. A., Stępniewski, T. M., & Selent, J. (2017) · Methods in molecular biology · doi:10.1007/978-1-4939-7465-8_14 · Cited by 8
Becker, R. A., & Hub, J. S. (2023) · Communications Biology · doi:10.1038/s42003-023-04751-z · Cited by 7
Characterizing RNA Tetramer Conformational Landscape Using Explainable Machine Learning.
Chatterjee, S., & Ray, D. (2026) · Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.5c03438 · Cited by 6
Bonneau, K., Lederer, J., Templeton, C., Rosenberger, D., Giambagli, L., Müller, K., & Clementi, C. (2025) · Nature Communications · doi:10.1038/s41467-025-65863-0 · Cited by 18
“A comparison of the Free Energy Surface (FES) projected onto the fi rst two TICA components (collective variables capturing the slow motions of the system, 69 ) is shown in Fig.”
Beyond Ensembles: Simulating All-Atom Protein Dynamics in a Learned Latent SpacePreprint
Sengar, A., Zhang, J., Vandergheynst, P., & Barth, P. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2509.02196 · Cited by 1
“While linear methods like time-lagged independent component analysis (TICA) remain strong baselines for identifying slow variables [17], deep learning has enabled far more expressive encoders.”
Operator Forces For Coarse-Grained Molecular Dynamics
Klein, L., Kelkar, A., Durumeric, A. E. P., Chen, Y.-Y., & Noé, F. (2025) · Journal of Chemical Physics · doi:10.48550/arxiv.2506.19628 · Cited by 6
“…that generative model-based kernels preserve local structure, whereas the previously proposed random noise kernels introduce significant distortions in local behavior (e.g., bond lengths) despite preserving slow motion as described via time-lagged independent component analysis (TICA) features 63 .”
Self-citationMitra, S., Biswas, R., & Chakrabarty, S. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0239713 · Cited by 7
Erastova, V., Evans, I. R., Glossop, W. N., Güryel, S., Hodgkinson, P., Kerr, H. E., Oganesyan, V. S., Softley, L. K., Wickins, H. M., & Wilson, M. R. (2024) · Journal of the American Chemical Society · doi:10.1021/jacs.4c03246 · Cited by 9
Wang, D.-D., & Tiwary, P. (2024) · arXiv.org · doi:10.48550/arxiv.2406.14839 · Cited by 6
“24 This is unlike commonly used dynamics-based dimension reduction methods such as tICA, 35,36 which focus on learning a given number of slow processes.”
Implementation of Girsanov Reweighting in OpenMM and Deeptime
Schäfer, J.-L., & Keller, B. G. (2024) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.4c01702 · Cited by 5
Free energy profile of the substrate‐induced occlusion of the human serotonin transporter
da Silva, L. A., Lazzarin, E., Gradisch, R., Clarke, A., & Stockner, T. (2024) · Journal of Neurochemistry · doi:10.1111/jnc.16061 · Cited by 7
“Here, we used time-lagged independent component analysis (tICA) (Molgedey & Schuster, 1994; Pérez-Hernández et al., 2013; Schwantes & Pande, 2013), which is a linear transformation method that maximizes the autocorrelation of the molecular descriptors or features to identify the slowest kinetic…”
Hardie, A., Cossins, B. P., Lovera, S., & Michel, J. (2023) · Communications Chemistry · doi:10.1038/s42004-023-00926-1 · Cited by 10
A deep encoder–decoder framework for identifying distinct ligand binding pathways
Bandyopadhyay, S., & Mondal, J. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0145197 · Cited by 6
Hsueh, S. C. C., Aina, A., & Plotkin, S. S. (2022) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.2c05470 · Cited by 8
Maltarollo, V., Shevchenko, E., Lima, I. D. D. M., Cino, E., Ferreira, G. M., Poso, A., & Kronenberger, T. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c01178 · Cited by 6
LINES: Log-Probability Estimation via Invertible Neural Networks for Enhanced Sampling.
Odstrcil, R. E., Dutta, P., & Liu, J. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.2c00254 · Cited by 6
Early aggregation mechanism of Aβ16-22 revealed by Markov state models.
Rahman, M., Song, K.-Y., Da, L.-T., & Chen, H.-F. (2022) · International Journal of Biological Macromolecules · doi:10.1016/j.ijbiomac.2022.02.001 · Cited by 6
Benchmarking ensemble docking methods in D3R Grand Challenge 4
Gan, J. L., Kumar, D., Chen, C., Taylor, B. C., Jagger, B. R., Amaro, R. E., & Lee, C. T. (2022) · Journal of Computer-Aided Molecular Design · doi:10.1007/s10822-021-00433-2 · Cited by 10
Nijhawan, A. K., Chan, A. M., Hsu, D. J., Chen, L. X., & Kohlstedt, K. L. (2021) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.1c05820 · Cited by 7
Liu, S., Cao, S., Suarez, M., Goonetillek, E. C., & Huang, X. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.06.09.447666 · Cited by 5
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Goossens, K., Neves, R. P. P., Fernandes, P. A., & Winter, H. L. D. (2020) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.0c00377 · Cited by 7
Kabir, K. L., Akhter, N., & Shehu, A. (2019) · Journal of Bioinformatics and Computational Biology · doi:10.1142/s0219720019400146 · Cited by 9
Opening dynamics of HIV-1 gp120 upon receptor binding is dictated by a key hydrophobic core.
Da, L.-T., & Lin, M. (2019) · Physical Chemistry, Chemical Physics - PCCP · doi:10.1039/c9cp04613e · Cited by 6
Thermal versus Mechanical Unfolding in a Model Protein
Tapia-Rojo, R., Mazo, J., & Falo, F. (2019) · bioRxiv · doi:10.1101/816801 · Cited by 6
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ACAP1 assembles into an unusual protein lattice for membrane deformation through multiple stages
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“Further analysis employing the time-lagged independent component analysis (TICA) [41,42], which finds a subspace with maximized autocorrelation, also show that the two dynamical states are distinguishable and independent of minor revision to molecular force-field (S8 Fig).”
Agarwal, A., Hengartner, N., Gnanakaran, S., & Voter, A. F. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5094457 · Cited by 5
Automatic Feature Selection in Markov State Models Using Genetic Algorithm
Chen, Q., Feng, J., Mittal, S., & Shukla, D. (2018) · The Journal of Computational Science Education · doi:10.22369/issn.2153-4136/9/2/2 · Cited by 6
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Markov State Models to Elucidate Ligand Binding Mechanism
Ge, Y., & Voelz, V. A. (2021) · Methods in molecular biology · doi:10.1007/978-1-0716-1209-5_14 · Cited by 14
Markov state modelling reveals heterogeneous drug-inhibition mechanism of Calmodulin
Westerlund, A. M., Sridhar, A., Dahl, L., Andersson, A., Bodnar, A.-Y., & Delemotte, L. (2022) · PLOS Computational Biology · doi:10.1371/journal.pcbi.1010583 · Cited by 6
“The data was projected with time-lagged independent component analysis (tICA) [52] using time-lagged correlation matrices (tICA time-lag of 20 ns).”
MethodWang, B., Wang, C., Chen, J., Liu, D., Sun, C., Zhang, J., Zhang, K., & Li, H. (2026) · Nature Machine Intelligence · doi:10.1038/s42256-026-01198-9 · Cited by 5
Wang, B., Wang, C., Chen, J., Liu, D., Sun, C., Zhang, J., Zhang, K., & Li, H. (2025) · doi:10.1101/2025.02.21.639488 · Cited by 5
“4a visualized the conformations produced by MD simulation and six generative models for α 3D, Protein B and Homeodomain, in which each conformation generated was projected (as a dot) to the top-2 TICA-components 47,48 .”
Clark, R., Smith, L. G., Leighton, M. P., Szukalo, R. J., Khalid, S., Debenedetti, P. G., Cossio, P., Astore, M. A., & Hanson, S. M. (2026) · Proceedings of the National Academy of Sciences · doi:10.64898/2026.04.21.720011 · Cited by 4
“Dimensionality reduction was performed with time-lagged independent component analysis (TICA) from the deeptime package [28, 55–58], by retaining 90% of the kinetic variance in these features.”
Scalable Spatio-Temporal SE(3) Diffusion for Long-Horizon Protein DynamicsPreprint
Shoghi, N., Liu, Y., Shen, Y., Brekelmans, R., Li, P., & Gu, Q. (2026) · arXiv (Cornell University) · doi:10.48550/arxiv.2602.02128 · Cited by 3
“First, we use tICA lag-time correlation to quantify the preservation of slow collective variables [22, 25, 26]; crucially, this is computed only on valid transitions to avoid artifacts from broken structures.”
Zhao, D., Liu, M.-T., Duan, H., Zhu, J., Yang, L., & Sang, P. (2025) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.5c01201 · Cited by 6
AutoSIM: Redesigning and automating umbrella sampling for biomolecular conformational transitions
Das, M., & Venkatramani, R. (2025) · The Journal of Chemical Physics · doi:10.1063/5.0268626 · Cited by 3
From closed to open: three dynamic states of membrane-bound cytochrome P450 3A4
Spanke, V. A., Hoerschinger, V. J., Ruzsányi, V., & Liedl, K. R. (2025) · Journal of Computer-Aided Molecular Design · doi:10.1007/s10822-025-00589-1 · Cited by 6
Pérez-Lemus, G. R., Xu, Y., Jin, Y., Rico, P. Z. Z., & de Pablo, J. D. (2024) · Journal of Chemical Physics · doi:10.1063/5.0237399 · Cited by 5
Metadata
- 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
- 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
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.
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