Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations
Open accessAbstract
Characterizing the equilibrium ensemble of folding pathways, including their relative probability, is one of the major challenges in protein folding theory today. Although this information is in principle accessible via all-atom molecular dynamics simulations, it is difficult to compute in practice because protein folding is a rare event and the affordable simulation length is typically not sufficient to observe an appreciable number of folding events, unless very simplified protein models are used. Here we present an approach that allows for the reconstruction of the full ensemble of folding pathways from simulations that are much shorter than the folding time. This approach can be applied to all-atom protein simulations in explicit solvent. It does not use a predefined reaction coordinate but is based on partitioning the state space into small conformational states and constructing a Markov model between them. A theory is presented that allows for the extraction of the full ensemble of transition pathways from the unfolded to the folded configurations. The approach is applied to the folding of a PinWW domain in explicit solvent where the folding time is two orders of magnitude larger than the length of individual simulations. The results are in good agreement with kinetic experimental data and give detailed insights about the nature of the folding process which is shown to be surprisingly complex and parallel. The analysis reveals the existence of misfolded trap states outside the network of efficient folding intermediates that significantly reduce the folding speed.
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The MSM approach has led to the construction of extremely detailed statistical models of folding mechanism and unfolded state dynamics for some small peptides and proteins.
“By contrast, the MSM approach has led to the construction of extremely detailed statistical models of folding mechanism and unfolded state dynamics for some small peptides and proteins (e.g. [44, 45]).”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [45]
The paper’s application to PinWW constructs a detailed Markov model and reports complex, parallel folding pathways and misfolded trap states (Application to the Folding of PinWW; Conclusions, page unavailable). This supports the folding-mechanism part of the claim, but our copy does not separately characterize unfolded-state dynamics. (LLM, conf=0.82)
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- Authors
- Noé, F., Schütte, C., Vanden-Eijnden, E., Reich, L., & Weikl, T. R.
- Affiliations
- Freie Universität Berlin (DE)
- Courant Institute, New York University, 251 Mercer Street, New York, NY 10012; and
- Max Planck Institute of Colloids and Interfaces (DE)
- Max Planck Society (DE)
- Venue
- Proceedings of the National Academy of Sciences
- Publisher
- National Academy of Sciences
- Published
- 2009-11-10
- Volume
- 106
- Issue
- 45
- Pages
- 19011-19016
- ISSN
- 0027-8424 (ISSN-L)
- 1091-6490
- PMC
- PMC2772816
- OpenAlex
- W1979070806
- Cited by
- 820
- References
- 40
- Citations by year
- 2026: 27 · 2025: 36 · 2024: 54 · 2023: 46 · 2022: 49 · 2021: 65 · 2020: 50 · 2019: 42 · 2018: 55 · 2017: 50 · 2016: 51 · 2015: 49 · 2014: 59 · 2013: 58 · 2012: 51
- FWCI
- 17.30
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- Proceedings of the National Academy of Sciences (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Max Planck Institute for Plasma Physics (submittedVersion)
- Max Planck Digital Library (submittedVersion)
- MPG.PuRe (Max Planck Society) (submittedVersion)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein Structure and Dynamics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › RNA and protein synthesis mechanisms
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Protein purification and stability
- Keywords
- protein folding, folding pathways, equilibrium ensembles, Markov state models, rare events, folding intermediates, folding kinetics
- MeSH terms
- Computer Simulation, Models, Chemical, Protein Conformation, Proteins, Protein Folding, Computational Biology
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