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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]
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“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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“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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“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]
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“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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MethodIndependent Component Analysis
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MethodIndependent Component Analysis
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BackgroundMethodHow fast-folding proteins fold
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Items 301–400 of 1,004
Deep learning path-like collective variable for enhanced sampling molecular dynamics
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Efficient approximation of molecular kinetics using random Fourier features
Nüske, F., & Klus, S. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0162619 · Cited by 22
Caruso, C., Cardellini, A., Crippa, M., Rapetti, D., & Pavan, G. M. (2023) · The Journal of Chemical Physics · doi:10.1063/5.0147025 · Cited by 27
Solving eigenvalue PDEs of metastable diffusion processes using artificial neural networks
Zhang, W., Li, T., & Schütte, C. (2022) · Journal of Computational Physics · doi:10.1016/j.jcp.2022.111377 · Cited by 22
“…examples are the variational approach to conformational dynamics [44, 45] and its linear version, time lagged independent component analysis (tICA) [50], the variational approach for Markov processes (VAMP) [69], the extended dynamic mode decompositions [68, 27, 28], Markov state models (MSMs)…”
BackgroundMethodComputer-designed active human butyrylcholinesterase double mutant with a new catalytic triad
Grigorenko, B. L., Novichkova, D. A., Lushchekina, S. V., Zueva, I. V., Schopfer, L. M., Nemukhin, A. V., Varfolomeev, S. D., Lockridge, O., & Masson, P. (2019) · Chemico-Biological Interactions · doi:10.1016/j.cbi.2019.04.019 · Cited by 35
Dynamical coring of Markov state models
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Data-driven computation of molecular reaction coordinates
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Deep generative modeling of temperature-dependent structural ensembles of proteins
Janson, G., Jussupow, A., & Feig, M. (2025) · Communications Chemistry · doi:10.1038/s42004-025-01737-2 · Cited by 33
“Ensembles generated by aSAMt were projected onto coordinates from time-lagged independent component analysis 42 (TICA) based on the MD sampling (Fig.”
Selecting Features for Markov Modeling: A Case Study on HP35
Nagel, D., Sartore, S., & Stock, G. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00240 · Cited by 25
“Time-lagged independent component analysis 35 (and other timescale optimizing approaches 12,13 ) aims at maximizing the timescales of the first components and is therefore deceived by functionally irrelevant slow motion (such as left to right-handed transitions).”
BackgroundMethodChen, H., Ogden, D. S., Pant, S., Cai, W., Tajkhorshid, E., Moradi, M., Roux, B., & Chipot, C. J. (2022) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.1c01049 · Cited by 43
Jones, M. S., Ashwood, B., Tokmakoff, A., & Ferguson, A. L. (2021) · Journal of the American Chemical Society · doi:10.1021/jacs.1c05219 · Cited by 34
Markov state modeling of membrane transport proteins
Chan, M. C., & Shukla, D. (2021) · Journal of Structural Biology · doi:10.1016/j.jsb.2021.107800 · Cited by 24
Deep learning Markov and Koopman models with physical constraintsPreprint
Mardt, A., Pasquali, L., Noé, F., & Wu, H. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1912.07392 · Cited by 21
“…reduction, clustering, estimating the transition matrix K , etc, these choices have recently been guided by variational approaches Noé and Nüske (2013); Nüske et al. (2014); Schwantes and Pande (2013); Perez-Hernandez et al. (2013); Wu and Noé (2019); Mardt et al. (2018); Chen et al. (2019).”
MethodConev, A., Rigo, M. M., Devaurs, D., Fonseca, A. F., Kalavadwala, H., de Freitas, M. V., Clementi, C., Zanatta, G., Antunes, D. A., & Kavraki, L. E. (2023) · Briefings in Bioinformatics · doi:10.1093/bib/bbad242 · Cited by 28
“For example, SRV and UMAP perform nonlinear dimensionality reduction, while TICA and PCA are linear.”
InfluentialUnprotected peptide macrocyclization and stapling via a fluorine-thiol displacement reaction
Islam, M. S., Junod, S. L., Zhang, S., Buuh, Z. Y., Guan, Y., Zhao, M., Kaneria, K. H., Kafley, P., Cohen, C., Maloney, R., et al. (2022) · Nature Communications · doi:10.1038/s41467-022-27995-5 · Cited by 28
“69 This involved the following steps: (1) performing dimensionality reduction using time-structure-based independent component analysis (tICA), 70,71 (2) conformational clustering in the reduced space to define and assign the trajectory data to discrete metastable states, and (3) estimating the…”
MethodImplicit Transfer Operator Learning: Multiple Time-Resolution Surrogates for Molecular DynamicsPreprint
Schreiner, M., Winther, O., & Olsson, S. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2305.18046 · Cited by 23
“4) projected onto a linear subspace determined us-ing time-lagged independent component analysis (time-lagged independent components, tIC) [22] (see Appendix B.3).”
BackgroundDeciphering the Folding Mechanism of Proteins G and L and Their Mutants
Chang, L., & Pérez, A. (2022) · Journal of the American Chemical Society · doi:10.1021/jacs.2c04488 · Cited by 25
Physics‐based protein structure refinement in the era of artificial intelligence
Heo, L., Janson, G., & Feig, M. (2021) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.26161 · Cited by 33
“Time-lagged independent components analysis (tICA) 53 was employed to reduce the dimensionality of these input features and k-means clustering was then used to cluster the MD snapshots in the tICA space.”
MethodLorpaiboon, C., Thiede, E. H., Webber, R. J., Weare, J., & Dinner, A. R. (2020) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.0c06477 · Cited by 32
Khelashvili, G., Falzone, M. E., Cheng, X., Lee, B., Accardi, A., & Weinstein, H. (2019) · Nature Communications · doi:10.1038/s41467-019-12865-4 · Cited by 32
Dynamical reweighting methods for Markov models
Kieninger, S., Donati, L., & Keller, B. G. (2020) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2019.12.018 · Cited by 31
“Here, the first two time-independent components were used as reaction coordinates [40, 41], and this two-dimensional space was discretized into 1000 states.”
BackgroundMethodUnarta, I. C., Zhu, L., Tse, C. K. M., Cheung, P. P., Yu, J. H., & Huang, X. (2018) · Current Opinion in Structural Biology · doi:10.1016/j.sbi.2018.01.002 · Cited by 29
Predicting the Kinetics of RNA Oligonucleotides Using Markov State Models
Pinamonti, G., Zhao, J., Condon, D. E., Paul, F., Noé, F., Turner, D. H., & Bussi, G. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00982 · Cited by 33
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“[66] However, it has been shown that PCA can fail to find the most important processes in a system,[67–69] so some studies have turned to the use of maximizing the timescales of the low-dimensional RC space through either linear methods such as time-lagged independent component analysis (tICA)[67, 70, 71] or through n…”
BackgroundMeller, A., Lotthammer, J. M., Smith, L. G., Novak, B., Lee, L. A., Kuhn, C. C., Greenberg, L., Leinwand, L. A., Greenberg, M. J., & Bowman, G. R. (2023) · eLife · doi:10.7554/elife.83602 · Cited by 32
Characterizing Metastable States with the Help of Machine Learning
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“One is the Variational Approach to Conformation dynamics (VAC) [15, 16].”
InfluentialVariational embedding of protein folding simulations using gaussian mixture variational autoencoders
Ghorbani, M., Prasad, S., Klauda, J. B., & Brooks, B. (2021) · Journal of Chemical Physics · doi:10.1063/5.0069708 · Cited by 26
Binding mechanism of the matrix domain of HIV-1 gag on lipid membranes
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“Lastly, we carried time-lagged independent component analysis (tICA) (59-61) as a reduction technique to quantify the protein changes during Myr insertion.”
MethodExtensible and Scalable Adaptive Sampling on Supercomputers
Hruška, E., Balasubramanian, V., Lee, H., Jha, S., & Clementi, C. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c00991 · Cited by 24
Ancestral reconstruction reveals mechanisms of ERK regulatory evolution
Sang, D., Pinglay, S., Wiewiora, R., Selvan, M. E., Lou, H. J., Chodera, J. D., Turk, B. E., Gumus, Z. H., & Holt, L. J. (2019) · eLife · doi:10.7554/elife.38805 · Cited by 27
Demuynck, R., Wieme, J., Rogge, S., Dedecker, K., Vanduyfhuys, L., Waroquier, M., & Speybroeck, V. V. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00725 · Cited by 26
Model Selection Using BICePs: A Bayesian Approach for Force Field Validation and Parameterization
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A Data-Driven Perspective on the Hierarchical Assembly of Molecular Structures
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Coarse Master Equations for Binding Kinetics of Amyloid Peptide Dimers
Leahy, C. T., Murphy, R. D., Hummer, G., Rosta, E., & Buchete, N. (2016) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.6b00518 · Cited by 29
“1), and, in this case, offer a better discrimination between states then, for example, principal-component based collective variables that offer less local information but can be useful for larger systems.(19-25)”
BackgroundCumberworth, A., Bui, J. M., & Gsponer, J. (2016) · Journal of Computational Chemistry · doi:10.1002/jcc.24235 · Cited by 26
Statistical Model Selection for Markov Models of Biomolecular Dynamics
McGibbon, R. T., Schwantes, C. R., & Pande, V. S. (2014) · The Journal of Physical Chemistry B · doi:10.1021/jp411822r · Cited by 29
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Samantray, S., Schumann, W., Illig, A.-M., Carballo-Pacheco, M., Paul, A., Barz, B., & Strodel, B. (2020) · bioRxiv · doi:10.1101/2020.04.25.060269 · Cited by 25
“Here, the method of choice is usually time-lagged independent component analysis (TICA) [36].”
Lemke, T., Berg, A., Jain, A., & Peter, C. (2019) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.9b00675 · Cited by 25
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Self-citationDiez, J. V., Atance, S. R., Engkvist, O., & Olsson, S. (2024) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad3b64 · Cited by 20
“To find the slowest transitions between metastable states, we use time-lagged independent component analysis (TICA) [37], a linear dimensionality reduction technique that identifies the linear combinations of molecular features that maximizes the autocorrelation.”
MethodHerrera-Nieto, P., Pérez, A., & Fabritiis, G. D. (2020) · Scientific Reports · doi:10.1038/s41598-020-69322-2 · Cited by 26
Kahler, U., Kamenik, A. S., Waibl, F., Kraml, J., & Liedl, K. R. (2020) · Biophysical Journal · doi:10.1016/j.bpj.2020.06.032 · Cited by 28
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The E2.65A mutation disrupts dynamic binding poses of SB269652 at the dopamine D2 and D3 receptors
Verma, R. K., Abramyan, A. M., Michino, M., Free, R. B., Sibley, D. R., Javitch, J. A., Lane, J. R., & Shi, L. (2018) · PLoS Computational Biology · doi:10.1371/journal.pcbi.1005948 · Cited by 22
Deciphering the folding code of collagens
Malcor, J.-D. M., Ferruz, N., Romero-Romero, S., Dhingra, S., Sagar, V., & Jalan, A. A. (2025) · Nature Communications · doi:10.1038/s41467-024-54046-y · Cited by 23
“Weprojectedthemultidimensionaldataonto its slow-order parameters using TICA (time-lagged independent component analysis) 125 .”
EquiJump: Protein Dynamics Simulation via SO(3)-Equivariant Stochastic Interpolants
Costa, A. D. S., Mitnikov, I., Pellegrini, F., Daigavane, A., Geiger, M., Cao, Z., Kreis, K., Smidt, T., Kucukbenli, E., & Jacobson, J. (2024) · arXiv.org · doi:10.48550/arxiv.2410.09667 · Cited by 23
“A common projection for this task is represented by the Time-lagged Independent Component Analysis (TICA) (P´erez-Hern´andez et al., 2013).”
MethodInfluentialLearning data-efficient coarse-grained molecular dynamics from forces and noise
Durumeric, A. E. P., Chen, Y., Pasos-Trejo, A. S., Noé, F., & Clementi, C. (2026) · Nature Communications · doi:10.1038/s41467-026-70818-0 · Cited by 20
“To accurately approximate the potential of mean force U PMF implied by the atomistic simulation, a fl exible functional form is needed for U θ ( R ), and neural networks have been shown to be a formid-able choice 21 .”
Estimating Koopman operators with sketching to provably learn large scale dynamical systems
Meanti, G., Chatalic, A., Kostić, V., Novelli, P., Pontil, M., & Rosasco, L. (2023) · Neural Information Processing Systems · doi:10.48550/arxiv.2306.04520 · Cited by 23
“[41] Guillermo Pérez-Hernández, Fabian Paul, Toni Giorgino, Gianni De Fabritiis, and Frank Noé.”
BackgroundManifold learning in atomistic simulations: a conceptual review
Rydzewski, J., Chen, M., & Valsson, Ó. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ace81a · Cited by 24
“Features with zero-mean are usually taken as basis functions [157, 159, 160, 164].”
BackgroundMethodInfluentialProtein Function Analysis through Machine Learning
Avery, C., Patterson, J., Grear, T. J., Frater, T. D., & Jacobs, D. J. (2022) · Biomolecules · doi:10.3390/biom12091246 · Cited by 30
“Because tICA is able to identify long time-scale motions, it has been used to generate CVs for metadynamics [142] and is widely used for constructing Markov models [143].”
MethodBreathing and tilting: mesoscale simulations illuminate influenza glycoprotein vulnerabilities
Casalino, L., Seitz, C., Lederhofer, J., Tsybovsky, Y., Wilson, I. A., Kanekiyo, M., & Amaro, R. (2022) · bioRxiv · doi:10.1101/2022.08.02.502576 · Cited by 23
“We used one to two features, whose dimensionalities were then reduced and/or data reformatted through TICA ( 138 – 140 ).”
Bergh, C. C., Heusser, S. A., Howard, R. J., & Lindahl, E. R. (2021) · eLife · doi:10.7554/elife.68369 · Cited by 31
“…to account for the symmetry of the homopentameric protein (Figure 1E4), followed by dimensionality reduction by time-lagged independent component analysis (tICA) (Pérez-Hernández et al., 2013; Schwantes and Pande, 2013), to capture the slowest motions observed in the simulations (Figure 1E5).”
MethodImproving the analysis of biological ensembles through extended similarity measures
Chang, L., Pérez, A., & Miranda-Quintana, R. (2021) · bioRxiv · doi:10.1101/2021.08.08.455555 · Cited by 23
Wang, W., Liang, T., Sheong, F. K., Fan, X., & Huang, X. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5027001 · Cited by 27
Brotzakis, Z. F., & Parrinello, M. (2018) · bioRxiv · doi:10.1101/390278 · Cited by 23
Surprisal Metrics for Quantifying Perturbed Conformational Dynamics in Markov State Models
Voelz, V. A., Elman, B., Razavi, A. M., & Zhou, G. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500827g · Cited by 24
Sultan, M. M., Kiss, G., Shukla, D., & Pande, V. S. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500353m · Cited by 28
Molecular Dynamics and Simulation
Zheng, L., Alhossary, A., Kwoh, C.-K., & Mu, Y. (2018) · Elsevier eBooks · doi:10.1016/b978-0-12-809633-8.20284-7 · Cited by 43
Atomistic Insights into Structural Differences between E3 and E4 Isoforms of Apolipoprotein E
Ray, A., Ahalawat, N., & Mondal, J. (2017) · Biophysical Journal · doi:10.1016/j.bpj.2017.10.006 · Cited by 23
“The time-structure-based independent component analysis method (44)”
Principal Component Analysis of Molecular Dynamic Trajectories: Concepts, Tools, and Applications
Roccatano, D. (2025) · Wiley Interdisciplinary Reviews Computational Molecular Science · doi:10.1002/wcms.70060 · Cited by 22
“Large k correspond to slow transitions between metastable states, whereas small ones capture fast noise. tICA is widely used as a preprocessing step for Markov state models, as it provides a kinetic map of conformational dynamics [37, 38].”
Bourgeois, B., Spreitzer, E., Platero-Rochart, D., Paar, M., Zhou, Q., Usluer, S., de Keizer, P. L. J., Burgering, B. M. T., Sánchez-Murcia, P. A., & Madl, T. (2025) · Nature Communications · doi:10.1038/s41467-025-60844-9 · Cited by 23
Thermodynamic Interpolation: A Generative Approach to Molecular Thermodynamics and Kinetics
Moqvist, S., Chen, W., Schreiner, M., Nüske, F., & Olsson, S. (2025) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.4c01557 · Cited by 22
Markov State Models: To Optimize or Not to Optimize
Arbon, R. E., Zhu, Y., & Mey, A. S. J. S. (2024) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c01134 · Cited by 18
Data-driven path collective variables
France-Lanord, A., Vroylandt, H., Salanne, M., Rotenberg, B., Saitta, A. M., & Pietrucci, F. (2023) · Journal of Chemical Theory and Computation · doi:10.48550/arxiv.2312.13868 · Cited by 22
Activation mechanism of the human Smoothened receptor
Bansal, P. D., Dutta, S., & Shukla, D. (2023) · bioRxiv · doi:10.1101/2022.06.07.493647 · Cited by 22
Morishita, T. (2021) · Journal of Chemical Physics · doi:10.1063/5.0061874 · Cited by 22
A deep autoencoder framework for discovery of metastable ensembles in biomacromolecules
Bandyopadhyay, S., & Mondal, J. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0059965 · Cited by 29
Confronting pitfalls of AI-augmented molecular dynamics using statistical physics
Pant, S., Smith, Z., Wang, Y., Tajkhorshid, E., & Tiwary, P. (2020) · bioRxiv · doi:10.1101/2020.06.11.146985 · Cited by 22
Dimensionality reduction to maximize prediction generalization capability
Isomura, T., & Toyoizumi, T. (2021) · Nature Machine Intelligence · doi:10.1038/s42256-021-00306-1 · Cited by 22
Free Energy Landscape and Conformational Kinetics of Hoogsteen Base-Pairing in DNA vs RNA
Ray, D., & Andricioaei, I. (2020) · bioRxiv · doi:10.1101/2020.01.09.868018 · Cited by 22
“Figure 4: Absolute value of the correlation coefficient of the independent components (IC) obtained from TICA analysis with the input features i.e dihedral angles and possible hydrogen bond donor-acceptor distances for DNA and RNA.”
MethodInfluentialShehu, A., & Plaku, E. (2016) · Journal of Artificial Intelligence Research · doi:10.1613/jair.5040 · Cited by 25
Wu, Y., Yang, Y., Lu, G., Xiang, W., Sun, T.-Y., Chen, K.-W., Lv, X., Gui, Y., Zeng, R., Du, Y., et al. (2024) · Journal of Agricultural and Food Chemistry · doi:10.1021/acs.jafc.4c03245 · Cited by 21
Wu, Y., Cao, S., Qiu, Y., & Huang, X. (2024) · The Journal of Chemical Physics · doi:10.1063/5.0189429 · Cited by 22
Folding-upon-binding pathways of an intrinsically disordered protein from a deep Markov state model
Sisk, T. R., & Robustelli, P. (2024) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2313360121 · Cited by 27
“Here, we construct a hidden Markov state model (HMSM) (95) using time - lagged independent component analysis (tICA) (79, 80, 96, 97), a linear dimensionality reduction technique, and a deep MSM by applying the VAMPnet approach with physical constraints (85).”
InfluentialRescuing off-equilibrium simulation data through dynamic experimental data with dynAMMo
Kolloff, C., & Olsson, S. (2023) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ad10ce · Cited by 16
“In line with previous analyses [88, 103], we used time-lagged independent component analysis [104] to define a low dimensional space which we discretized into 384 states and aggregated into four metastable structural states.”
MethodToward a Benchmark for Markov State Models: The Folding of HP35
Nagel, D., Sartore, S., & Stock, G. (2023) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.3c01561 · Cited by 21
Slicing and Dicing: Optimal Coarse-Grained Representation to Preserve Molecular Kinetics
Yang, W., Templeton, C., Rosenberger, D., Bittracher, A., Nüske, F., Noé, F., & Clementi, C. (2023) · ACS Central Science · doi:10.1021/acscentsci.2c01200 · Cited by 26
Self-citationMahmoud, A. H., Masters, M. R., Lee, S. J., & Lill, M. A. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.1c01438 · Cited by 16
Preservation of HIV-1 Gag Helical Bundle Symmetry by Bevirimat Is Central to Maturation Inhibition
Pak, A. J., Purdy, M. D., Yeager, M. J., & Voth, G. A. (2021) · Journal of the American Chemical Society · doi:10.1021/jacs.1c08922 · Cited by 22
Paul, F., Meng, Y., & Roux, B. (2020) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.9b01158 · Cited by 26
Self-citationRelaxation mode analysis for molecular dynamics simulations of proteins
Mitsutake, A., & Takano, H. (2018) · Biophysical Reviews · doi:10.1007/s12551-018-0406-7 · Cited by 24
Dynamics of the excised base release in thymine DNA glycosylase during DNA repair process
Da, L., Shi, Y., Ning, G., & Yu, J. H. (2017) · Nucleic Acids Research · doi:10.1093/nar/gkx1261 · Cited by 22
Dimensionality reduction methods for molecular simulationsPreprint
Doerr, S., Ariz-Extreme, I., Harvey, M. J., & Fabritiis, G. D. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1710.10629 · Cited by 30
“12,24 The reason for its great success in such problems is that the tICA projections are the linear transform of the input data which maximizes the auto-correlations of the output data.”
BackgroundNote: MSM lag time cannot be used for variational model selection.
Husic, B., & Pande, V. (2017) · Journal of Chemical Physics · doi:10.1063/1.5002086 · Cited by 21
Toward a direct and scalable identification of reduced models for categorical processes
Gerber, S., & Horenko, I. (2017) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1612619114 · Cited by 22
“…Gaussian distance kernel matrices (5, 6), Laplacian matrices [as in the case of spectral clustering methods for graphs (7, 8)], adjacency matrices [in community identification methods for networks (9)], or Markov transition matrices [as in spectral reduction methods for Markov processes (10, 11)].”
BackgroundDimensional reduction of Markov state models from renormalization group theory
Orioli, S., & Faccioli, P. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4963196 · Cited by 21
Mukherjee, S., Pantelopulos, G. A., & Voelz, V. A. (2016) · doi:10.1101/053603 · Cited by 20
“To identify these metastable states, we first used tICA 22,23 to find a low-dimensional subspace reflecting the slowest conformational motions of the N-terminal region (residues 1–25) and residues in the binding site.”
Transferable generative models bridge femtosecond to nanosecond time-step molecular dynamics
Diez, J. V., Schreiner, M., & Olsson, S. (2026) · Science Advances · doi:10.1126/sciadv.aed2333 · Cited by 22
Markov state modeling reveals alternative unbinding pathways for peptide–MHC complexes
Abella, J. R., Antunes, D. A., Jackson, K. R., Lizee, G. A., Clementi, C., & Kavraki, L. E. (2020) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2007246117 · Cited by 28
“We extract 2 independent components using TICA using 606 a lag time of 10 ns based on the convergence of timescales (SI 607 Appendix, Fig.”
MethodInfluentialExchange of water for sterol underlies sterol egress from a StARkin domain
Khelashvili, G., Pandey, K., Chauhan, N., Eliezer, D., & Menon, A. K. (2019) · eLife · doi:10.7554/elife.53444 · Cited by 23
Guo, Y., Duan, M., & Yang, M. (2019) · International Journal of Molecular Sciences · doi:10.3390/ijms20143476 · Cited by 19
“time-lagged independent component analysis (tICA) [38], the conformational space was projected to a four-dimensional space.”
Method
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
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