Precursory signatures of protein folding/unfolding: From time series correlation analysis to atomistic mechanisms

Abstract

Folded conformations of proteins in thermodynamically stable states have long lifetimes. Before it folds into a stable conformation, or after unfolding from a stable conformation, the protein will generally stray from one random conformation to another leading thus to rapid fluctuations. Brief structural changes therefore occur before folding and unfolding events. These short-lived movements are easily overlooked in studies of folding/unfolding for they represent momentary excursions of the protein to explore conformations in the neighborhood of the stable conformation. The present study looks for precursory signatures of protein folding/unfolding within these rapid fluctuations through a combination of three techniques: (1) ultrafast shape recognition, (2) time series segmentation, and (3) time series correlation analysis. The first procedure measures the differences between statistical distance distributions of atoms in different conformations by calculating shape similarity indices from molecular dynamics simulation trajectories. The second procedure is used to discover the times at which the protein makes transitions from one conformation to another. Finally, we employ the third technique to exploit spatial fingerprints of the stable conformations; this procedure is to map out the sequences of changes preceding the actual folding and unfolding events, since strongly correlated atoms in different conformations are different due to bond and steric constraints. The aforementioned high-frequency fluctuations are therefore characterized by distinct correlational and structural changes that are associated with rate-limiting precursors that translate into brief segments. Guided by these technical procedures, we choose a model system, a fragment of the protein transthyretin, for identifying in this system not only the precursory signatures of transitions associated with α helix and β hairpin, but also the important role played by weaker correlations in such protein folding dynamics.

A new perspective of shape recognition to discover the phase transition of finite‐size clusters

“…Regarding the numbers of reference configurations, it is suggested that the similarity functions be statistically analyzed. The shape similarity technique has also been applied to a large system, namely, the folding of a transthyretin peptide . Twelve similarity functions were generated for substructures, which were characterized based on residues, and a cross‐correlation analysis was performed to evaluate folding dynamics.…”

“…Ultimately, shape similarity is applicable not only for finite‐size clusters but also for any type of molecule that presents shape. The dynamical analysis of the folding and unfolding of the peptide molecule was conducted using the same technique . The proposed method should become a powerful tool for studying nanostructures and biological systems.…”