Transition States in Protein Folding Kinetics: Modeling Φ-Values of Small β-Sheet Proteins

Weikl, Thomas R.

doi:10.1529/biophysj.107.109868

Cited by 18 publications

(25 citation statements)

References 74 publications

(122 reference statements)

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“…4: In 30% of the folding trajectories, hairpin 1 forms before hairpin 2 (confidence interval 18%-34%) and in 70% it is the other way around. Thus, there is no unique mechanism in terms of the order of secondary structure formation, which is in qualitative agreement with a structural interpretation of mutational Φ values for the PinWW domain (34).…”

Section: Application To the Folding Of Pinwwsupporting

confidence: 84%

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Noé

Schütte

Vanden‐Eijnden

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

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797

717

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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. D iscovering the mechanism by which proteins fold into their native 3D structure remains an intriguing problem (1, 2). Essential questions are: How does an ensemble of denatured molecules find the same native structure, starting from different conformations? Are there particular sequences in which the structural elements of a protein are formed (3-5)? Are there multiple parallel routes by which protein structure formation can proceed (6, 7)?Full answers to these questions require one to characterize the ensemble of folding pathways, including their relative probabilities. In principle, this detailed information is accessible via molecular dynamics (MD) simulations which, when used in concert with experimental evidence, are becoming an increasingly accepted tool to understanding structural details that are not easily accessible via the experimental observables (8). MD simulations with atomistic models of proteins have been used to study the dynamics of small proteins with folding times in the microsecond range (9-13). However, even though MD simulations make the full spatiotemporal detail accessible to observation, the characterization of the pathway ensemble is computationally difficult: A brute-force approach would start simulations from an equilibrium of unfolded structures, say A, and simulate until they relax into a set of folded state B. The analysis would then only be comprised of those trajectory segments that leave A and relax to B without...

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Section: Application To the Folding Of Pinwwsupporting

confidence: 84%

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Noé

Schütte

Vanden‐Eijnden

et al. 2009

Proc. Natl. Acad. Sci. U.S.A.

Self Cite

797

717

View full text Add to dashboard Cite

show abstract

“…predict that the formation of the secondary structures predominantly occurs in a definite sequence and that in the most likely mechanism the terminal hairpin folds before the terminal [1], [6], in agreement with the -values analysis of Ref. [16].…”

Section: Validation In All-atom Protein Folding Simulationssupporting

confidence: 87%

Computing Reaction Pathways of Rare Biomolecular Transitions using Atomistic Force-Fields

Faccioli

Beccara

2016

Biophysical Chemistry

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“…The mutational ΔΔ G f † /ΔΔ G f ) quantifies changes in the free energy of activation (ΔΔ G f † ) relative to the ground state free energy of folding (ΔΔ G f ) between wild type and mutant proteins [17, 18] Computational modeling of Φ M values is now possible for WW domains [14, 19], making direct comparisons with experiments achievable.…”

Section: Resultsmentioning

confidence: 99%

High-Resolution Mapping of the Folding Transition State of a WW Domain

Dave

Jäger

Nguyen

et al. 2016

Journal of Molecular Biology

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Fast-folding WW domains are among the best-characterized systems for comparing experiments and simulations of protein folding. Recent microsecond-resolution experiments and long (totaling milliseconds) single-trajectory modeling have shown that even mechanistic changes due to mutation in folding kinetics can now be analyzed. Thus, a comprehensive set of experimental data would be helpful to benchmark the predictions made by simulations. Here, we use T-jump relaxation in conjunction with protein engineering and report Φ values as indicators for folding transition state structure for 65 side chain, 7 backbone hydrogen bond and 6 loop 1 deletion and/or insertion mutants of the 34-residue hPin1 WW domain. 45 cross-validated consensus mutants could be identified that provide structural constraints for transition state structure within all substructures of the WW domain fold (hydrophobic core, loop 1, loop 2, β sheet). We probe the robustness of the two hydrophobic clusters in the folding transition state, discuss how local backbone disorder in the native state can lead to non-classical ΦM values (ΦM > 1) in the rate-determining loop 1 substructure, and conclusively identify mutations and positions along the sequence that perturb the folding mechanism from loop 1-limited towards loop 2-limited folding.

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Transition States in Protein Folding Kinetics: Modeling Φ-Values of Small β-Sheet Proteins

Cited by 18 publications

References 74 publications

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Constructing the equilibrium ensemble of folding pathways from short off-equilibrium simulations

Computing Reaction Pathways of Rare Biomolecular Transitions using Atomistic Force-Fields

High-Resolution Mapping of the Folding Transition State of a WW Domain

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