Improvements in Markov State Model Construction Reveal Many Non-Native Interactions in the Folding of NTL9
Open accessAbstract
Markov State Models (MSMs) provide an automated framework to investigate the dynamical properties of high-dimensional molecular simulations. These models can provide a human-comprehensible picture of the underlying process and have been successfully used to study protein folding, protein aggregation, protein ligand binding, and other biophysical systems. The MSM requires the construction of a discrete state-space such that two points are in the same state if they can interconvert rapidly. In the following, we suggest an improved method, which utilizes second order Independent Component Analysis (also known as time-structure based Independent Component Analysis, or tICA), to construct the state-space. We apply this method to simulations of NTL9 (provided by Lindorff-Larsen et al. Science 2011, 334, 517–520) and show that the MSM is an improvement over previously built models using conventional distance metrics. Additionally, the resulting model provides insight into the role of non-native contacts by revealing many slow time scales associated with compact, non-native states.
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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 [20]
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 [20]
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“The reaction coordinates are obtained from TICA 57,58 (see Appen-dices D and E).”
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“These are attributes of meaningful CVs (182), which explains the consensus regarding tICA as a suitable strategy for building MSMs (119, 124, 188, 189).”
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BackgroundMachine learning for protein folding and dynamics
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“69,70 The resulting low-dimensional projected space is then discretized using a clustering algorithm for the MSM construction.”
MethodVariational encoding of complex dynamics
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Self-citationTwo 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
Residual dynamic mode decomposition: robust and verified Koopmanism
Colbrook, M. J., Ayton, L. J., & Szőke, M. (2022) · Journal of Fluid Mechanics · doi:10.1017/jfm.2022.1052 · Cited by 139
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
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
Ryckbosch, S., Wender, P., & Pande, V. (2017) · Nature Communications · doi:10.1038/s41467-016-0015-8 · Cited by 125 · see citing works
Self-citationNonlinear 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
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
Trozzi, F., Wang, X., & Tao, P. (2021) · Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.1c02081 · Cited by 114 · 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
“To address this scaling issue, we demonstrate that transforming the original feature input space to projections in tICA 12,13,15,33 space prior to encoding in the VDE alleviates this scaling problem (tICA-VDE). tICA seeks to embed protein configurations along their set of slowest de-correlating…”
BackgroundMethodSelf-citationMarkov 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
Naritomi, Y., & Fuchigami, S. (2013) · Journal of Chemical Physics · doi:10.1063/1.4834695 · Cited by 109 · see citing works
Application of Molecular-Dynamics Based Markov State Models to Functional Proteins
Malmstrom, R. D., Lee, C. T., VanWart, A., & Amaro, R. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct5002363 · Cited by 105 · 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
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 independentcomponents(TICs)(11,45).”
BackgroundMultiensemble 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
“To detect rare events in the unbiased coordinates, time-lagged independent component analysis (TICA) (29, 30) was used with the Cartesian coordinates of residues around the binding site.”
MethodTime-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
Distant 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
Self-citationGating 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
Self-citationGalerkin 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
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
Free energy landscape of activation in a signaling protein at atomic resolution
Pontiggia, F., Pachov, D. V., Clarkson, M. W., Villali, J., Hagan, M. F., Pande, V. S., & Kern, D. (2015) · Nature Communications · doi:10.1038/ncomms8284 · Cited by 82 · see citing works
Self-citationAccurate 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
How to learn from inconsistencies: Integrating molecular simulations with experimental data
Orioli, S., Larsen, A. H., Bottaro, S., & Lindorff‐Larsen, K. (2020) · Progress in molecular biology and translational science · doi:10.1016/bs.pmbts.2019.12.006 · Cited by 89 · see citing works
“This task can become easier with the help of automatic selection tools [170, 171]; (ii) the features are used to generate a lower-dimensional representation of the system dynamics [172, 173]; (iii) the lower dimensionality [174] allows one to cluster similar configurations in the dimensionally reduced space.”
MethodBridging Microscopic and Macroscopic Mechanisms of p53-MDM2 Binding with Kinetic Network Models
Zhou, G., Pantelopulos, G. A., Mukherjee, S., & Voelz, V. A. (2017) · Biophysical Journal · doi:10.1016/j.bpj.2017.07.009 · Cited by 89 · see citing works
Rudzinski, J. F. (2019) · De Computis · doi:10.3390/computation7030042 · Cited by 73 · see citing works
A Markov State-based Quantitative Kinetic Model of Sodium Release from the Dopamine Transporter
Razavi, A. M., Khelashvili, G., & Weinstein, H. (2017) · Scientific Reports · doi:10.1038/srep40076 · Cited by 70 · see citing works
Pérez‐Hernández, G., & Noé, F. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00738 · Cited by 76 · see citing works
Towards simple kinetic models of functional dynamics for a kinase subfamily
Sultan, M. M., Kiss, G., & Pande, V. S. (2018) · Nature Chemistry · doi:10.1038/s41557-018-0077-9 · Cited by 68 · see citing works
Self-citationCollective variable-based enhanced sampling and machine learning
Chen, M. (2021) · The European Physical Journal B · doi:10.1140/epjb/s10051-021-00220-w · Cited by 72 · see citing works
Gill, S. C., Lim, N. M., Grinaway, P., Rustenburg, A. S., Fass, J., Ross, G. A., Chodera, J. D., & Mobley, D. L. (2018) · The Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.7b11820 · Cited by 79 · see citing works
Sidky, H., Chen, W., & Ferguson, A. L. (2019) · Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.9b05578 · Cited by 67 · see citing works
Quantitative comparison of adaptive sampling methods for protein dynamics.
Hruska, E., Abella, J. R., Nüske, F., Kavraki, L., & Clementi, C. (2018) · Journal of Chemical Physics · doi:10.1063/1.5053582 · Cited by 66 · see citing works
Girsanov reweighting for metadynamics simulations.
Donati, L., & Keller, B. (2018) · Journal of Chemical Physics · doi:10.1063/1.5027728 · Cited by 66 · see citing works
Variational tensor approach for approximating the rare-event kinetics of macromolecular systems
Nüske, F., Schneider, R., Vitalini, F., & Noé, F. (2016) · The Journal of Chemical Physics · doi:10.1063/1.4940774 · Cited by 67 · see citing works
Suárez, E., Wiewiora, R. P., Wehmeyer, C., Noé, F., Chodera, J. D., & Zuckerman, D. M. (2021) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.0c01154 · Cited by 65 · see citing works
Discovering Reaction Pathways, Slow Variables, and Committor Probabilities with Machine Learning
Chen, H., Roux, B., & Chipot, C. J. (2023) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.3c00028 · Cited by 65 · see citing works
Enspara: Modeling molecular ensembles with scalable data structures and parallel computing
Porter, J., Zimmerman, M. I., & Bowman, G. R. (2018) · bioRxiv · doi:10.1101/431072 · Cited by 65
Suárez, E., Wiewiora, R. P., Wehmeyer, C., Noé, F., Chodera, J. D., & Zuckerman, D. M. (2020) · doi:10.1101/2020.11.09.374496 · Cited by 65 · see citing works
Nguyen, H., Jiang, Y., Mohapatra, S., Wang, W., Barnes, J. C., Oldenhuis, N. J., Chen, K. K., Axelrod, S., Huang, Z., Chen, Q., et al. (2021) · Nature Chemistry · doi:10.1038/s41557-021-00826-8 · Cited by 64 · see citing works
Computational estimation of ms-sec atomistic folding times
Adhikari, U., Mostofian, B., Copperman, J., Subramanian, S., Petersen, A. A., & Zuckerman, D. (2019) · Journal of the American Chemical Society · doi:10.1021/jacs.8b10735 · Cited by 63 · see citing works
On the advantages of exploiting memory in Markov state models for biomolecular dynamics.
Cao, S.-Q., Montoya-Castillo, A., Wang, W., Markland, T., & Huang, X.-H. (2020) · Journal of Chemical Physics · doi:10.1063/5.0010787 · Cited by 62 · see citing works
Mechanisms of lipid scrambling by the G protein-coupled receptor opsin
Morra, G., Razavi, A. M., Pandey, K., Weinstein, H., Menon, A., & Khelashvili, G. (2017) · Structure · doi:10.1016/j.str.2017.11.020 · Cited by 61 · see citing works
“…of the system described by all the frames of the combined trajectory [stages 1–4]), was carried out with the tICA (time-structure based independent component analysis) approach (Molgedey and Schuster, 1994; Naritomi and Fuchigami, 2011; Perez-Hernandez et al., 2013; Schwantes and Pande, 2013).”
The mpEDMD Algorithm for Data-Driven Computations of Measure-Preserving Dynamical Systems
Colbrook, M. J. (2022) · SIAM Journal on Numerical Analysis · doi:10.48550/arxiv.2209.02244 · Cited by 60
“Popular applications include epidemiology [64], finance [52], fluid dynamics [67, 66, 56], neuroscience [11], molecular dynamics [41, 70], and robotics [7, 10].”
BackgroundSpangler, J. B., Trotta, E., Tomala, J., Peck, A., Young, T. A., Savvides, C. S., Silveria, S. L., Votavová, P., Salafsky, J., Pande, V., et al. (2018) · Journal of Immunology · doi:10.4049/jimmunol.1800578 · Cited by 60 · see citing works
“Adaptive sampling was performed by reseeding simulations from poorly sampled regions of the mIL-2 conformational landscape; conformations in these regions were identified by time-structure independent component analysis (34), an unbiased method to determine the slowest degrees of conformational freedom.”
MethodSelf-citationMapping the Substrate Recognition Pathway in Cytochrome P450
Ahalawat, N., & Mondal, J. (2018) · doi:10.1101/416305 · Cited by 60 · see citing works
Optimized parameter selection reveals trends in Markov state models for protein folding.
Husic, B., McGibbon, R., Sultan, M. M., & Pande, V. (2016) · Journal of Chemical Physics · doi:10.1063/1.4967809 · Cited by 59 · see citing works
Self-citationConformational heterogeneity of the calmodulin binding interface
Shukla, D., Peck, A., & Pande, V. (2016) · Nature Communications · doi:10.1038/ncomms10910 · Cited by 59 · see citing works
Self-citationUsing Markov state models to study self-assembly.
Perkett, M. R., & Hagan, M. (2014) · Journal of Chemical Physics · doi:10.1063/1.4878494 · Cited by 59 · see citing works
Time-Lagged t-Distributed Stochastic Neighbor Embedding (t-SNE) of Molecular Simulation Trajectories
Spiwok, V., & Kříž, P. (2020) · Frontiers in Molecular Biosciences · doi:10.3389/fmolb.2020.00132 · Cited by 58 · see citing works
“This can be done by Time-lagged Independent Component Analysis (TICA) (Molgedey and Schuster, 1994; Perez-Hernandez et al., 2013; Schwantes and Pande, 2013).”
MethodRationalization of the Membrane Permeability Differences in a Series of Analogue Cyclic Decapeptides
Witek, J., Wang, S., Schroeder, B. R., Lingwood, R., Dounas, A., Roth, H., Fouché, M., Blatter, M., Lemke, O., Keller, B., et al. (2018) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.8b00485 · Cited by 58 · see citing works
Commute Maps: Separating Slowly Mixing Molecular Configurations for Kinetic Modeling.
Noé, F., Banisch, R., & Clementi, C. (2016) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.6b00762 · Cited by 58 · see citing works
Multi-body effects in a coarse-grained protein force field
Wang, J., Charron, N. E., Husic, B. E., Olsson, S., Noé, F., & Clementi, C. (2021) · The Journal of Chemical Physics · doi:10.1063/5.0041022 · Cited by 61 · see citing works
- Authors
- Schwantes, C. R., & Pande, V. S.
- Affiliations
- Stanford University (US)
- Corresponding author
- Pande, Vijay S.
- ORCID
- Pande, Vijay S.
- Venue
- Journal of Chemical Theory and Computation
- Publisher
- American Chemical Society (ACS)
- Published
- 2013-03-18
- Volume
- 9
- Issue
- 4
- Pages
- 2000-2009
- ISSN
- 1549-9618 (ISSN-L)
- 1549-9626
- PMC
- PMC3673732
- OpenAlex
- W2315297180
- Cited by
- 597
- References
- 54
- Citations by year
- 2026: 31 · 2025: 42 · 2024: 52 · 2023: 65 · 2022: 49 · 2021: 80 · 2020: 47 · 2019: 45 · 2018: 69 · 2017: 41 · 2016: 29 · 2015: 26 · 2014: 16 · 2013: 5
- FWCI
- 11.36
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Journal of Chemical Theory and Computation (publishedVersion)
- PubMed (publishedVersion)
- Europe PMC (PubMed Central) (acceptedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Science Foundation
- National Institutes of Health
- National Institute of General Medical Sciences (R01GM101935, R01GM062868)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
- Keywords
- Markov state models, protein folding, state space construction, time-lagged independent component analysis, independent component analysis, non-native interactions, slow time scale, distance measures, protein folding kinetics
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