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Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding.

Radford IH, Fersht AR, Settanni G - J Phys Chem B (2011)

Bottom Line: The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach.The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis.The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

View Article: PubMed Central - PubMed

Affiliation: MRC-Centre for Protein Engineering, Cambridge, UK.

ABSTRACT
Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

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Autocorrelation functions for the first three eigenvectors (continuous lines) of the rate matrix R at 330 K and the corresponding exponential decay associated with the eigenvector (dashed lines). Only data for times larger than lag time are shown.
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fig9: Autocorrelation functions for the first three eigenvectors (continuous lines) of the rate matrix R at 330 K and the corresponding exponential decay associated with the eigenvector (dashed lines). Only data for times larger than lag time are shown.

Mentions: The method was therefore extended to use both HB and rmsd (see Methods), and in this case, the slowest eigenvalues at the three simulation temperatures studied were found to converge for lag times larger than 2.5 ns (Figure 2b). As a further and more stringent test of the Markovian assumption, the decay times of the autocorrelation functions of the first three eigenvectors of R projected along the simulations were examined. Figure 9 shows that these decay times are in good agreement with the decay times expected from the corresponding eigenvalues (Table 1), confirming that this representation is Markovian. The Markovianity of the representation provides a validation, a posteriori, for both the choice of observables (HB and rmsd) and the fine graining of the binning procedure. Indeed, if either of the two was not good enough, then the representation would not be Markovian. We note also that other choices of observables should provide similar slow eigenmodes, as long as the observables report the same amount of information about the slow dynamics of the system.(17)


Combination of Markov state models and kinetic networks for the analysis of molecular dynamics simulations of peptide folding.

Radford IH, Fersht AR, Settanni G - J Phys Chem B (2011)

Autocorrelation functions for the first three eigenvectors (continuous lines) of the rate matrix R at 330 K and the corresponding exponential decay associated with the eigenvector (dashed lines). Only data for times larger than lag time are shown.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC3106446&req=5

fig9: Autocorrelation functions for the first three eigenvectors (continuous lines) of the rate matrix R at 330 K and the corresponding exponential decay associated with the eigenvector (dashed lines). Only data for times larger than lag time are shown.
Mentions: The method was therefore extended to use both HB and rmsd (see Methods), and in this case, the slowest eigenvalues at the three simulation temperatures studied were found to converge for lag times larger than 2.5 ns (Figure 2b). As a further and more stringent test of the Markovian assumption, the decay times of the autocorrelation functions of the first three eigenvectors of R projected along the simulations were examined. Figure 9 shows that these decay times are in good agreement with the decay times expected from the corresponding eigenvalues (Table 1), confirming that this representation is Markovian. The Markovianity of the representation provides a validation, a posteriori, for both the choice of observables (HB and rmsd) and the fine graining of the binning procedure. Indeed, if either of the two was not good enough, then the representation would not be Markovian. We note also that other choices of observables should provide similar slow eigenmodes, as long as the observables report the same amount of information about the slow dynamics of the system.(17)

Bottom Line: The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach.The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis.The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

View Article: PubMed Central - PubMed

Affiliation: MRC-Centre for Protein Engineering, Cambridge, UK.

ABSTRACT
Atomistic molecular dynamics simulations of the TZ1 beta-hairpin peptide have been carried out using an implicit model for the solvent. The trajectories have been analyzed using a Markov state model defined on the projections along two significant observables and a kinetic network approach. The Markov state model allowed for an unbiased identification of the metastable states of the system, and provided the basis for commitment probability calculations performed on the kinetic network. The kinetic network analysis served to extract the main transition state for folding of the peptide and to validate the results from the Markov state analysis. The combination of the two techniques allowed for a consistent and concise characterization of the dynamics of the peptide. The slowest relaxation process identified is the exchange between variably folded and denatured species, and the second slowest process is the exchange between two different subsets of the denatured state which could not be otherwise identified by simple inspection of the projected trajectory. The third slowest process is the exchange between a fully native and a partially folded intermediate state characterized by a native turn with a proximal backbone H-bond, and frayed side-chain packing and termini. The transition state for the main folding reaction is similar to the intermediate state, although a more native like side-chain packing is observed.

Show MeSH
Related in: MedlinePlus