The DOI matches its Crossref record; 94 of the 98 references it cites were found in a registry or an index.
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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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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“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]
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
Comparison of simple potential functions for simulating liquid water
Jorgensen, W. L., Chandrasekhar, J., Madura, J., Impey, R., & Klein, M. (1983) · The Journal of Chemical Physics · doi:10.1063/1.445869 · Cited by 38,397 · cited 1×
“MKClconcentration(matchingtheexperimentalionicstrength). ThesystemwasthenparametrizedwiththeAMBERff99SB-ILDNforcefield [49];waterandionsweremodeledrespectivelywiththeTIP3PandJoung-Cheathamparametersets [38,37]. Thesystemthuspreparedwasfirstequilibratedfor24nsintheconstant-pressureensemble, during which it stabilized at a…”
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
Lloyd, S. (1982) · IEEE Transactions on Information Theory · doi:10.1109/tit.1982.1056489 · Cited by 15,836 · cited 1×
“thetrajectory isexploredandnrepresentativepointsofthecoordinatespaceareselectedas 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…”
MethodIndependent Component Analysis
Hyvärinen, A., Karhunen, J., & Oja, E. (2001) · Encyclopedia of Biometrics · doi:10.1007/978-0-387-73003-5_305 · Cited by 10,459 · cited 1×
“We assume that the molecular dynamics implementation is 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…”
BackgroundImproved side-chain torsion potentials for the Amber ff99SB protein force field
Lindorff-Larsen, K., Piana, S., Palmo, K., Maragakis, P., Klepeis, J., Dror, R., & Shaw, D. (2010) · Proteins: Structure, Function, and Bioinformatics · doi:10.1002/prot.22711 · Cited by 6,056 · cited 1×
“The system was then parametrized with the AMBER ff99SB-ILDN forcefield [49]; water and ions were modeled respectively with the TIP3P and Joung-Cheatham parameter sets [38, 37].”
MethodIndependent Component Analysis
Hyvärinen, A., Karhunen, J., & Erkki Oja, A. (2001) · Wiley eBooks · doi:10.1002/0471221317 · Cited by 5,003
Joung, I. S., & Cheatham, T. E. (2008) · The Journal of Physical Chemistry B · doi:10.1021/jp8001614 · Cited by 3,504
Essential dynamics of proteins
Amadei, A., Linssen, A. B. M., & Berendsen, H. J. C. (1993) · Proteins Structure Function and Bioinformatics · doi:10.1002/prot.340170408 · Cited by 3,487 · cited 2×
“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
Kabsch, W. (1976) · Acta Crystallographica Section A · doi:10.1107/s0567739476001873 · Cited by 3,462 · cited 2×
“A metric often used in (2) is the normalized Euclidean metric after rigid-body translation and rotation has been removed, in short the minimal RMSD (or least RMSD) metric [39].”
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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Flagged first, then by citations
4 of the 98 references couldn’t be matched to a known paper.
Research works printed but not linked: 5
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Items 1,001–1,004 of 1,004
Lyu, L., & Lei, H. (2024) · arXiv.org · doi:10.48550/arxiv.2409.11519
“We note that this is somewhat similar to the time-lagged independent component analysis (TICA) [55, 56, 57] and dynamic mode decomposition (DMD) [58, 59, 60] to identify the dominant dynamics from the simulation data.”
ResultWang, J., Li, Z., & Zhang, W. (2024) · Physical Chemistry, Chemical Physics - PCCP · doi:10.1039/d4cp02271h
The effect of the loop on the thermodynamic and kinetic of single base pair in pseudoknot.
Zhang, S., Wang, Z., Qiao, J., Yu, T., & Zhang, W. (2024) · Journal of Chemical Physics · doi:10.1063/5.0216593
Temporal Subspace Clustering for Molecular Dynamics Data
Beer, A., Heinrigs, M., Plant, C., & Assent, I. (2024) · arXiv.org · doi:10.48550/arxiv.2408.00056
“The ICs are computed by maximizing the autocovariance for a fixed lagtime 𝜏 , and are frequently used for MD data ([24], [17]).”
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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