New Insights into the Folding of a β-SheetMiniprotein in a Reduced Space of Collective Hydrogen Bond Variables:Application to a Hydrodynamic Analysis of the Folding Flow.

A newanalysis of the 20 μs equilibrium folding/unfoldingmolecular dynamics simulations of the three-stranded antiparallelβ-sheet miniprotein (beta3s) in implicit solvent is presented.The conformation space is reduced in dimensionality by introductionof linear combinations of hydrogen bond distances as the collectivevariables making use of a specially adapted principal component analysis(PCA); i.e., to make structured conformations more pronounced, onlythe formed bonds are included in determining the principal components.It is shown that a three-dimensional (3D) subspace gives a meaningfulrepresentation of the folding behavior. The first component, to whicheight native hydrogen bonds make the major contribution (four in eachbeta hairpin), is found to play the role of the reaction coordinatefor the overall folding process, while the second and third componentsdistinguish the structured conformations. The representative pointsof the trajectory in the 3D space are grouped into conformationalclusters that correspond to locally stable conformations of beta3sidentified in earlier work. A simplified kinetic network based onthe three components is constructed, and it is complemented by a hydrodynamicanalysis. The latter, making use of “passive tracers”in 3D space, indicates that the folding flow is much more complexthan suggested by the kinetic network. A 2D representation of streamlinesshows there are vortices which correspond to repeated local rearrangement,not only around minima of the free energy surface but also in flatregions between minima. The vortices revealed by the hydrodynamicanalysis are apparently not evident in folding pathways generatedby transition-path sampling. Making use of the fact that the valuesof the collective hydrogen bond variables are linearly related tothe Cartesian coordinate space, the RMSD between clusters is determined.Interestingly, the transition rates show an approximate exponentialcorrelation with distance in the hydrogen bond subspace. Comparisonwith the many published studies shows good agreement with the presentanalysis for the parts that can be compared, supporting the robustcharacter of our understanding of this “hydrogen atom”of protein folding. [ABSTRACT FROM AUTHOR]