New insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: Application to a hydrodynamic analysis of the folding flow

TitleNew insights into the folding of a β-sheet miniprotein in a reduced space of collective hydrogen bond variables: Application to a hydrodynamic analysis of the folding flow
Publication TypeJournal Article
Year of Publication2013
AuthorsKalgin I.V, Caflisch A., Chekmarev S.F, Karplus M.
JournalThe Journal of Physical Chemistry B
Volume117
Issue20
Pagination6092-6105
Date Published2013 May 23
Type of ArticleResearch Article
ISSN1520-5207
KeywordsCluster Analysis, Hydrodynamics, Hydrogen Bonding, Molecular Dynamics Simulation, Protein Conformation, Protein Folding, Protein Structure, Secondary, Proteins, Thermodynamics
Abstract

A new analysis of the 20 μs equilibrium folding/unfolding molecular dynamics simulations of the three-stranded antiparallel β-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 β 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.

DOI10.1021/jp401742y
pubindex

0172

Alternate JournalJ. Phys. Chem. B
PubMed ID23621790
PubMed Central IDPMC3740565
Grant ListR01 GM030804 / GM / NIGMS NIH HHS / United States