Markov state models based on milestoning
Open accessAbstract
Markov state models (MSMs) have become the tool of choice to analyze large amounts of molecular dynamics data by approximating them as a Markov jump process between suitably predefined states. Here we investigate “Core Set MSMs,” a new type of MSMs that build on metastable core sets acting as milestones for tracing the rare event kinetics. We present a thorough analysis of Core Set MSMs based on the existing milestoning framework, Bayesian estimation methods and Transition Path Theory (TPT). We show that Core Set MSMs can be used to extract phenomenological rate constants between the metastable sets of the system and to approximate the evolution of certain key observables. The performance of Core Set MSMs in comparison to standard MSMs is analyzed and illustrated on a toy example and in the context of the torsion angle dynamics of alanine dipeptide.
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In the MSM framework, the core projection method effectively uses core committor functions as basis functions, which often provides a superior approximation to the eigenfunctions of the transfer operator when the number of cores is small.
“In the MSM framework, this core projection method effectively uses the core committor functions as basis functions, which often provides a superior approximation to the eigenfunctions of the transfer operator when the number of cores is small [23].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [23]
Section III.C (page not available) explicitly defines the projection space as spanned by core committor functions. In the model example, the first nontrivial eigenfunction of the generator is nearly identical to its projection for one choice of two cores, but the paper does not establish that a small number of cores often gives a superior approximation to transfer-operator eigenfunctions. It emphasizes that approximation quality depends on the choice of core sets. (LLM, conf=0.84)
Experimental — accuracy not yet measuredThe core discretization scheme is equivalent to milestoning, with the cores being milestones.
“This core discretization scheme was subsequently shown to be equivalent to milestoning, with the cores being milestones [23].”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [23]
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Margazoglou, G., Grafke, T., Laio, A., & Lucarini, V. (2021) · Proceedings of the Royal Society A Mathematical Physical and Engineering Sciences · doi:10.1098/rspa.2021.0019 · Cited by 58 · see citing works
Markov State Models and tICA Reveal a Nonnative Folding Nucleus in Simulations of NuG2.
Schwantes, C. R., Shukla, D., & Pande, V. (2016) · Biophysical Journal · doi:10.1016/j.bpj.2016.03.026 · Cited by 40 · see citing works
Optimal Data-Driven Estimation of Generalized Markov State Models for Non-Equilibrium Dynamics
Koltai, P., Wu, H., Noé, F., & Schütte, C. (2018) · De Computis · doi:10.3390/computation6010022 · Cited by 39 · see citing works
Self-citationMarkov State Models for Rare Events in Molecular Dynamics
Sarich, M., Banisch, R., Hartmann, C., & Schütte, C. (2013) · Entropy · doi:10.3390/e16010258 · Cited by 35 · see citing works
Self-citationSharma, A. K., Bukau, B., & O’Brien, E. P. (2015) · Journal of the American Chemical Society · doi:10.1021/jacs.5b08145 · Cited by 35 · see citing works
Folding kinetics and unfolded state dynamics of the GB1 hairpin from molecular simulation
De Sancho, D., Mittal, J., & Best, R. B. (2013) · Journal of Chemical Theory and Computation · doi:10.1021/ct301033r · Cited by 35 · see citing works
Rapid Calculation of Molecular Kinetics Using Compressed Sensing
Litzinger, F., Boninsegna, L., Wu, H., Nüske, F., Patel, R., Baraniuk, R. G., Noé, F., & Clementi, C. (2018) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.8b00089 · Cited by 35 · see citing works
Self-citationLi, M., Liu, X., Zhang, S., Liang, S., Zhang, Q., & Chen, J. (2022) · Physical Chemistry Chemical Physics · doi:10.1039/d2cp03446h · Cited by 35 · see citing works
A critical appraisal of Markov state models
Schütte, C., & Sarich, M. (2015) · The European Physical Journal Special Topics · doi:10.1140/epjst/e2015-02421-0 · Cited by 35 · see citing works
Self-citationSchütte, C., Klus, S., & Hartmann, C. (2023) · Acta Numerica · doi:10.1017/s0962492923000016 · Cited by 34 · see citing works
Self-citationPinamonti, G., Paul, F., Noé, F., Rodríguez, Á., & Bussi, G. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5083227 · Cited by 33 · see citing works
Self-citationA kernel-based approach to molecular conformation analysis
Klus, S., Bittracher, A., Schuster, I., & Schütte, C. (2018) · Journal of Chemical Physics · doi:10.1063/1.5063533 · Cited by 33 · see citing works
Self-citationCombining molecular dynamics with mesoscopic Green’s function reaction dynamics simulations
Vijaykumar, A., Bolhuis, P. G., & ten Wolde, P. R. (2015) · The Journal of Chemical Physics · doi:10.1063/1.4936254 · Cited by 33 · see citing works
Theoretical and computational validation of the Kuhn barrier friction mechanism in unfolded proteins
Avdoshenko, S. M., Das, A., Satija, R., Papoian, G. A., & Makarov, D. E. (2017) · Scientific Reports · doi:10.1038/s41598-017-00287-5 · Cited by 33 · see citing works
Identification of kinetic order parameters for non-equilibrium dynamics
Paul, F., Wu, H., Vossel, M., de Groot, B. L., & Noé, F. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5083627 · Cited by 32 · see citing works
Self-citationExtending Transition Path Theory: Periodically Driven and Finite-Time Dynamics
Helfmann, L., Borrell, E. R., Schütte, C., & Koltai, P. (2020) · Journal of Nonlinear Science · doi:10.1007/s00332-020-09652-7 · Cited by 33 · see citing works
Self-citationDynamical coring of Markov state models
Nagel, D., Weber, A., Lickert, B., & Stock, G. (2019) · The Journal of Chemical Physics · doi:10.1063/1.5081767 · Cited by 31 · see citing works
Violation of local detailed balance upon lumping despite a clear timescale separation
Hartich, D., & Godec, A. (2021) · Physical Review Research · doi:10.1103/physrevresearch.5.l032017 · Cited by 30 · see citing works
MSM/RD: Coupling Markov state models of molecular kinetics with reaction-diffusion simulations
Dibak, M., del Razo, M. J., Sancho, D. D., Schütte, C., & Noé, F. (2018) · The Journal of Chemical Physics · doi:10.1063/1.5020294 · Cited by 29 · see citing works
Self-citationDiffusion maps, clustering and fuzzy Markov modeling in peptide folding transitions
Nedialkova, L. V., Amat, M. A., Kevrekidis, I. G., & Hummer, G. (2014) · The Journal of Chemical Physics · doi:10.1063/1.4893963 · Cited by 29 · see citing works
An Overview and Practical Guide to Building Markov State Models
Bowman, G. R. (2013) · Advances in experimental medicine and biology · doi:10.1007/978-94-007-7606-7_2 · Cited by 29 · see citing works
Common Nearest Neighbor Clustering—A Benchmark
Lemke, O., & Keller, B. G. (2018) · Algorithms · doi:10.3390/a11020019 · Cited by 25 · see citing works
Analyzing milestoning networks for molecular kinetics: Definitions, algorithms, and examples
Viswanath, S., Kreuzer, S. M., Cárdenas, A. E., & Elber, R. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4827495 · Cited by 28 · see citing works
Optimal control of molecular dynamics using Markov state models
Schütte, C., Winkelmann, S., & Hartmann, C. (2012) · Mathematical Programming · doi:10.1007/s10107-012-0547-6 · Cited by 27 · see citing works
Self-citationA Basis Set for Peptides for the Variational Approach to Conformational Kinetics
Vitalini, F., Noé, F., & Keller, B. G. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/acs.jctc.5b00498 · Cited by 27 · see citing works
Self-citationTwo Mathematical Tools to Analyze Metastable Stochastic Processes
Tony Lelièvre, A. (2012) · Springer eBooks · doi:10.1007/978-3-642-33134-3_83 · Cited by 26 · see citing works
Data-driven computation of molecular reaction coordinates.
Bittracher, A., Banisch, R., & Schütte, C. (2017) · Journal of Chemical Physics · doi:10.1063/1.5035183 · Cited by 29 · see citing works
Self-citationMathematical modeling of spatio-temporal population dynamics and application to epidemic spreading
Winkelmann, S., Zonker, J., Schütte, C., & Conrad, N. D. (2021) · Mathematical Biosciences · doi:10.1016/j.mbs.2021.108619 · Cited by 29 · see citing works
Self-citationSultan, M. M., Kiss, G., Shukla, D., & Pande, V. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct500353m · Cited by 23 · see citing works
Catch bond-like kinetics of helix cracking: Network analysis by molecular dynamics and Milestoning
Kreuzer, S. M., Moon, T. J., & Elber, R. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4811366 · Cited by 24 · see citing works
Wang, H., Schütte, C., Ciccotti, G., & Site, L. D. (2014) · Journal of Chemical Theory and Computation · doi:10.1021/ct400993e · Cited by 25 · see citing works
Self-citationTrajectory Stratification of Stochastic Dynamics
Dinner, A. R., Mattingly, J. C., Tempkin, J. O. B., Koten, B. V., & Weare, J. (2018) · SIAM Review · doi:10.1137/16m1104329 · Cited by 24 · see citing works
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 · see citing works
Winkelmann, S., & Schütte, C. (2016) · Journal of Chemical Physics · doi:10.1063/1.4971163 · Cited by 29 · see citing works
Self-citationDynamic neutron scattering from conformational dynamics. I. Theory and Markov models
Lindner, B., Yi, Z., Prinz, J.-H., Smith, J. C., & Noé, F. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4824070 · Cited by 23 · see citing works
Self-citationEarly Events in Helix Unfolding Under External Forces: A Milestoning Analysis
Kreuzer, S., Elber, R., & Moon, T. (2012) · Journal of Physical Chemistry B · doi:10.1021/jp300788e · Cited by 21 · see citing works
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 23 · see citing works
Building Markov State Models for Periodically Driven Non-Equilibrium Systems
Wang, H., & Schütte, C. (2015) · Journal of Chemical Theory and Computation · doi:10.1021/ct500997y · Cited by 20 · see citing works
Self-citationFujisaki, H., Moritsugu, K., Mitsutake, A., & Suetani, H. (2018) · Journal of Chemical Physics · doi:10.1063/1.5049420 · Cited by 16 · see citing works
Pseudogenerators of Spatial Transfer Operators
Bittracher, A., Koltai, P., & Junge, O. (2014) · SIAM Journal on Applied Dynamical Systems · doi:10.1137/14099872x · Cited by 25 · see citing works
The construction and application of Markov state models for colloidal self-assembly process control
Tang, X., Bevan, M. A., & Grover, M. A. (2016) · Molecular Systems Design & Engineering · doi:10.1039/c6me00092d · Cited by 22 · see citing works
Experiments and Comprehensive Simulations of the Formation of a Helical Turn
Jas, G. S., Hegefeld, W. A., Májek, P., Kuczera, K., & Elber, R. (2012) · The Journal of Physical Chemistry B · doi:10.1021/jp211645s · Cited by 21 · see citing works
Spectral rate theory for two-state kinetics
Prinz, J.-H., Chodera, J. D., & Noé, F. (2014) · Physical Review X · doi:10.1103/physrevx.4.011020 · Cited by 21 · see citing works
Self-citationOn metastability and Markov state models for non-stationary molecular dynamics.
Koltai, P., Ciccotti, G., & Schütte, C. (2016) · Journal of Chemical Physics · doi:10.1063/1.4966157 · Cited by 22 · see citing works
Self-citationDeep Representation Learning for Complex Free-Energy Landscapes
Zhang, J., Lei, Y.-K., Che, X., Zhang, Z., Yang, Y., & Gao, Y. Q. (2019) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.9b02012 · Cited by 21 · see citing works
Computation of transit times using the milestoning method with applications to polymer translocation
Hawk, A. T., Konda, S. S. M., & Makarov, D. E. (2013) · The Journal of Chemical Physics · doi:10.1063/1.4817200 · Cited by 21 · see citing works
- Authors
- Schütte, C., Noé, F., Lu, J., Sarich, M., & Vanden-Eijnden, E.
- Affiliations
- Freie Universität Berlin (DE)
- Courant Institute of Mathematical Sciences (US)
- New York University 2 Courant Institute of Mathematical Sciences, , New York, New York 10012, USA
- Venue
- The Journal of Chemical Physics
- Publisher
- AIP Publishing
- Published
- 2011-05-24
- Volume
- 134
- Issue
- 20
- Pages
- 204105-204105
- ISSN
- 0021-9606 (ISSN-L)
- 1089-7690
- OpenAlex
- W1977875643
- Cited by
- 228
- References
- 51
- Citations by year
- 2026: 10 · 2025: 7 · 2024: 6 · 2023: 13 · 2022: 10 · 2021: 23 · 2020: 17 · 2019: 15 · 2018: 18 · 2017: 24 · 2016: 16 · 2015: 21 · 2014: 11 · 2013: 18 · 2012: 18
- FWCI
- 6.21
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Locations
- The Journal of Chemical Physics (publishedVersion)
- PubMed (publishedVersion)
- Refubium (Universitätsbibliothek der Freien Universität Berlin) (submittedVersion)
- Universitätsbibliothek der FU Berlin Hochschulschriftenstelle u. Dokumentenserver
- Funders
- Office of Naval Research (N00014-04-1-6046)
- National Science Foundation (DMS-0708140, DMS-0718172)
- 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 state models, milestoning, metastable states, transition path theory, Bayesian estimation, alanine dipeptide
- MeSH terms
- Kinetics, Models, Chemical, Quantum Theory, Molecular Dynamics Simulation
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