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One-dimensional barrier-preserving free-energy projections of a beta-sheet miniprotein: new insights into the folding process.

ABSTRACT: The conformational space of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 micros. The resulting one-dimensional free-energy profiles (FEPs) provide a detailed description of the free-energy basins and barriers for the folding reaction. The similarity of the FEPs obtained using the probability of folding before unfolding (pfold) or the mean first passage time supports the robustness of the procedure. The folded state and the most populated free-energy basins in the denatured state are described by the one-dimensional FEPs, which avoid the overlap of states present in the usual one- or two-dimensional projections. Within the denatured state, a basin with fluctuating helical conformations and a heterogeneous entropic state are populated near the melting temperature at about 11% and 33%, respectively. Folding pathways from the helical basin or enthalpic traps (with only one of the two hairpins formed) reach the native state through the entropic state, which is on-pathway and is separated by a low barrier from the folded state. A simplified equilibrium kinetic network based on the FEPs shows the complexity of the folding reaction and indicates, as augmented by additional analyses, that the basins in the denatured state are connected primarily by the native state. The overall folding kinetics shows single-exponential behavior because barriers between the non-native basins and the folded state have similar heights.

SUBMITTER: Krivov SV

PROVIDER: S-EPMC2736680 | biostudies-literature | 2008 Jul

REPOSITORIES: biostudies-literature

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One-dimensional barrier-preserving free-energy projections of a beta-sheet miniprotein: new insights into the folding process.

Krivov Sergei V SV Muff Stefanie S Caflisch Amedeo A Karplus Martin M

The journal of physical chemistry. B 20080701 29

The conformational space of a 20-residue three-stranded antiparallel beta-sheet peptide (double hairpin) was sampled by equilibrium folding/unfolding molecular dynamics simulations for a total of 20 micros. The resulting one-dimensional free-energy profiles (FEPs) provide a detailed description of the free-energy basins and barriers for the folding reaction. The similarity of the FEPs obtained using the probability of folding before unfolding (pfold) or the mean first passage time supports the r ...[more]

PMID: 18590307

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Project description:A new analysis of the 20 ?s equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel ?-sheet miniprotein (beta3s) in implicit solvent is presented. The conformation space is reduced in dimensionality by introduction of linear combinations of hydrogen bond distances as the collective variables making use of a specially adapted principal component analysis (PCA); i.e., to make structured conformations more pronounced, only the formed bonds are included in determining the principal components. It is shown that a three-dimensional (3D) subspace gives a meaningful representation of the folding behavior. The first component, to which eight native hydrogen bonds make the major contribution (four in each beta hairpin), is found to play the role of the reaction coordinate for the overall folding process, while the second and third components distinguish the structured conformations. The representative points of the trajectory in the 3D space are grouped into conformational clusters that correspond to locally stable conformations of beta3s identified in earlier work. A simplified kinetic network based on the three components is constructed, and it is complemented by a hydrodynamic analysis. The latter, making use of "passive tracers" in 3D space, indicates that the folding flow is much more complex than suggested by the kinetic network. A 2D representation of streamlines shows there are vortices which correspond to repeated local rearrangement, not only around minima of the free energy surface but also in flat regions between minima. The vortices revealed by the hydrodynamic analysis are apparently not evident in folding pathways generated by transition-path sampling. Making use of the fact that the values of the collective hydrogen bond variables are linearly related to the Cartesian coordinate space, the RMSD between clusters is determined. Interestingly, the transition rates show an approximate exponential correlation with distance in the hydrogen bond subspace. Comparison with the many published studies shows good agreement with the present analysis for the parts that can be compared, supporting the robust character of our understanding of this "hydrogen atom" of protein folding.

Dataset Information

One-dimensional barrier-preserving free-energy projections of a beta-sheet miniprotein: new insights into the folding process.

Publications

One-dimensional barrier-preserving free-energy projections of a beta-sheet miniprotein: new insights into the folding process.

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