Delineation of Folding Pathways of a β-sheet Miniprotein

Several methods have been developed in the past few years for the analysis of molecular dynamics simulations of biological (macro)molecules whose complexity is difficult to capture by simple projections of the free-energy surface onto one or two geometric variables. The locally scaled diffusion map (LSDMap) method is a nonlinear dimensionality reduction technique for describing the dynamics of complex systems in terms of a few collective coordinates. Here, we compare LSDMap to two previously developed approaches for the characterization of the configurational landscape associated with the folding dynamics of a three-stranded antiparallel β-sheet peptide, termed Beta3s. The analysis is aided by an improved procedure for extracting pathways from the equilibrium transition network, which enables calculation of pathway-specific cut-based free energy profiles. We find that the results from LSDMap are consistent with analysis based on transition networks and allow a coherent interpretation of metastable states and folding pathways in terms of different time scales of transitions between minima on the free energy projections.