How kinetics within the unfolded state affects protein folding: an analysis based on Markov state models and an ultra-long MD trajectory
Open accessAbstract
Understanding how kinetics in the unfolded state affects protein folding is a fundamentally important yet less well-understood issue. Here we employ three different models to analyze the unfolded landscape and folding kinetics of the miniprotein Trp-cage. The first is a 208 μs explicit solvent molecular dynamics (MD) simulation from D. E. Shaw Research containing tens of folding events. The second is a Markov state model (MSM-MD) constructed from the same ultralong MD simulation; MSM-MD can be used to generate thousands of folding events. The third is a Markov state model built from temperature replica exchange MD simulations in implicit solvent (MSM-REMD). All the models exhibit multiple folding pathways, and there is a good correspondence between the folding pathways from direct MD and those computed from the MSMs. The unfolded populations interconvert rapidly between extended and collapsed conformations on time scales ≤40 ns, compared with the folding time of ∼5 μs. The folding rates are independent of where the folding is initiated from within the unfolded ensemble. About 90% of the unfolded states are sampled within the first 40 μs of the ultralong MD trajectory, which on average explores ∼27% of the unfolded state ensemble between consecutive folding events. We clustered the folding pathways according to structural similarity into "tubes", and kinetically partitioned the unfolded state into populations that fold along different tubes. From our analysis of the simulations and a simple kinetic model, we find that, when the mixing within the unfolded state is comparable to or faster than folding, the folding waiting times for all the folding tubes are similar and the folding kinetics is essentially single exponential despite the presence of heterogeneous folding paths with nonuniform barriers. When the mixing is much slower than folding, different unfolded populations fold independently, leading to nonexponential kinetics. A kinetic partition of the Trp-cage unfolded state is constructed which reveals that different unfolded populations have almost the same probability to fold along any of the multiple folding paths. We are investigating whether the results for the kinetics in the unfolded state of the 20-residue Trp-cage is representative of larger single domain proteins.
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Heterogeneous structure acquisition within the unfolded state was also observed in a fast-folding protein.
“a phenomenon also observed in a fast-folding protein [48]”
From Markov state models of biomolecular conformational dynamics (2014) · cites this paper as [48]
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“In this respect, the hydrodynamic approach is essentially different from the previously employed transition path and pfold methods (Juraszek and Bolhuis 2006; Zheng et al. 2011; Deng et al. 2013; Han and Schulten 2013; Juraszek et al. 2013; Du and Bolhuis 2014), which consider only the progress to the native state; in…”
BackgroundMethodResultInfluentialPineda-Alemán, R., Amador, A. A., Galindo‐Murillo, R., Pérez-González, H., Rodríguez-Cavallo, E., & Méndez-Cuadro, D. (2023) · Journal of Molecular Graphics and Modelling · doi:10.1016/j.jmgm.2023.108533 · Cited by 9 · see citing works
Transition paths of Met-enkephalin from Markov state modeling of a molecular dynamics trajectory.
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Imaging Metastable States and Transitions in Proteins by Trajectory Map.
Zhang, C.-B., Yu, J., & Zhou, X. (2017) · Journal of Physical Chemistry B · doi:10.1021/acs.jpcb.7b00664 · Cited by 5 · see citing works
Andryushchenko, V. A., & Chekmarev, S. F. (2017) · Journal of Biological Physics · doi:10.1007/s10867-017-9470-7 · Cited by 5 · see citing works
“[21, 29], where the Trp-cage folding was studied at elevated temperatures.”
BackgroundMethodResultInfluentialAnalysis of Two-State Folding Using Parabolic Approximation I: HypothesisPreprint
Sade, R. S. (2016) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/036491 · Cited by 3 · see citing works
“and systematically varying the separation between their vertices along the abscissa and ordinate, and calculating the position of the curve-crossing along the abscissa for each case according to Eqs. (9) and (10). Despite the model being very simplistic (because the curvature of the parabolas can change with structura…”
BackgroundResultInfluentialThe “Beacon” Structural Model of Protein Folding: Application for Trp-Cage in Water
Sun, Q., He, X., & Yan-fang, F. (2023) · Molecules · doi:10.3390/molecules28135164 · Cited by 3 · see citing works
Improved Estimates of Folding Stabilities and Kinetics with Multiensemble Markov Models.
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Find slow dynamic modes via analyzing molecular dynamics simulation trajectories
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Ensemble descriptions of IDPs and IDRs: Integrating simulation and experiment
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Approximating dynamic proximity with a hybrid geometry energy-based kernel for diffusion maps
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“The above could be due to cannabidiol having a lower affinity or specificity for the RPL7A receptor, resulting in weak or transient interactions with the receptor [37].”
BackgroundMolecular crowding and amyloidogenic self-assembly: Emergent perspectives from modern computations
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Structural Heterogeneity and Dynamics of the Unfolded Ensemble
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“According to the previous paper (Deng et al., 2013), we could determine three macroscopic states on the basis of the RMSD distribution: protein folded (RMSD 2.2 Å), intermediate (2.2 Å < RMSD 5Å) and unfolded (RMSD > 5Å) (Jana et al., 2012).”
MethodInfluentialPrediction of SHP2-E76K binding sites based on molecular dynamics simulation and Markov algorithm
Zhang, S., Chen, L., Shi, Z., Li, X., & Ma, Y. (2024) · Journal of Biomolecular Structure and Dynamics · doi:10.1080/07391102.2024.2431193 · Cited by 1 · see citing works
“MSMs converted numerous MD trajectories into microscopic state models, analyzing intermediate states of conformational changes, and giving details about the dynamic process of ligand binding into the protein (Del Razo et al., 2021; Deng et al., 2013; Mitxelena et al., 2021; Narayan et al., 2020).”
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Variational embedding of protein folding simulations using gaussian mixture variational autoencoders
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Palyanov, A. Y., & Chekmarev, S. F. (2016) · Journal of Biomolecular Structure and Dynamics · doi:10.1080/07391102.2016.1248490
Actions of the A.M.A. House of Delegates.
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EspcTM: Kinetic Transition Network Based on Trajectory Mapping in Effective Energy Rescaling Space
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- Authors
- Deng, N.-J., Dai, W., & Levy, R. M.
- Affiliations
- BioMaPS Institute for Quantitative Biology and Department of Chemistry and Chemical Biology, Rutgers, the State University of New Jersey, Piscataway, New Jersey 08854, United States
- Rutgers, The State University of New Jersey (US)
- Corresponding author
- Levy, Ronald M.
- Venue
- The Journal of Physical Chemistry B
- Publisher
- American Chemical Society (ACS)
- Published
- 2013-06-13
- Volume
- 117
- Issue
- 42
- Pages
- 12787-12799
- ISSN
- 1520-5207 (ISSN-L)
- 1520-6106
- PMC
- PMC3808496
- OpenAlex
- W2005768448
- Cited by
- 64
- References
- 63
- Citations by year
- 2026: 2 · 2025: 3 · 2024: 4 · 2023: 8 · 2022: 2 · 2021: 4 · 2020: 5 · 2019: 6 · 2018: 3 · 2017: 3 · 2016: 6 · 2015: 10 · 2014: 6 · 2013: 1
- FWCI
- 3.43
- Type
- journal article
- Language
- en
- Open access
- green
- www.ncbi.nlm.nih.gov
- Locations
- The Journal of Physical Chemistry B (publishedVersion)
- PubMed (publishedVersion)
- PubMed Central (acceptedVersion)
- Funders
- National Institute of General Medical Sciences (R01GM030580, GM30580)
- 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
- Physical Sciences › Chemistry › Physical and Theoretical Chemistry › Advanced Physical and Chemical Molecular Interactions
- Keywords
- protein folding kinetics, unfolded state, Trp-cage, Markov state models, folding pathways, kinetic partitioning, non-exponential kinetics, kinetic heterogeneity, replica exchange molecular dynamics, implicit solvent
- MeSH terms
- Kinetics, Markov Chains, Peptides, Solvents, Temperature, Time Factors, Protein Folding, Molecular Dynamics Simulation
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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