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In this work we continue the studyof the first-passage foldingof an antiparallel β-sheet miniprotein (beta3s) that was initiatedin the previous work [Kalgin etal. J. Phys. Chem. B,2014, 118, 4287]. We consider a largerensemble of folding trajectories, which allows us to gain a closerinsight into the folding dynamics. In particular, we calculate thepotential for the driving force of folding in a reduced space of collectivevariables. The potential has two components. One component (Φ)is responsible for the source and sink of the folding flow, whichare formed, respectively, in the regions of the unfolded and nativestates of the protein, and the other (Ψ) accounts for the flowvorticity inherently generated at the sides of the reaction channeland provides the canalization of the folding flow between the sourceand sink. We show that both components obey Poisson’s equationswith the corresponding source/sink terms. The resulting componentshave a very simple form: the Φ-surface consists of two well-definedpeaks of different signs, which correspond, respectively, to the sourceand sink of the folding flow, and the Ψ-surface consists oftwo ridges of different signs that connect the source and sink ofthe flow. [ABSTRACT FROM AUTHOR]

Simulations of first-passage foldingof the antiparallel β-sheetminiprotein beta3s, which has been intensively studied under equilibriumconditions by A. Caflisch and co-workers, show that the kinetics anddynamics are significantly different from those for equilibrium folding.Because the folding of a protein in a living system generally correspondsto the former (i.e., the folded protein is stable and unfolding isa rare event), the difference is of interest. In contrast to equilibriumfolding, the Ch-curl conformations become very rare because they containunfavorable parallel β-strand arrangements, which are difficultto form dynamically due to the distant N- and C-terminal strands.At the same time, the formation of helical conformations becomes mucheasier (particularly in the early stage of folding) due to short-rangecontacts. The hydrodynamic descriptions of the folding reaction havealso revealed that while the equilibrium flow field presented a collectionof local vortices with closed ”streamlines”, the first-passagefolding is characterized by a pronounced overall flow from the unfoldedstates to the native state. The flows through the locally stable structuresCs-or and Ns-or, which are conformationally close to the native state,are negligible due to detailed balance established between these structuresand the native state. Although there are significant differences inthe general picture of the folding process from the equilibrium andfirst-passage folding simulations, some aspects of the two are inagreement. The rate of transitions between the clusters of characteristicprotein conformations in both cases decreases approximately exponentiallywith the distance between the clusters in the hydrogen bond distancespace of collective variables, and the folding time distribution inthe first-passage segments of the equilibrium trajectory is in goodagreement with that for the first-passage folding simulations. [ABSTRACT FROM AUTHOR]

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]