Hydrogen bonding heterogeneity correlates with protein folding transition state passage time as revealed by data sonification.

Protein-protein and protein-water hydrogen bonding interactions play essential roles in the way a protein passes through the transition state during folding or unfolding, but the large number of these interactions in molecular dynamics (MD) simulations makes them difficult to analyze. Here, we introduce a state space representation and associated "rarity" measure to identify and quantify transition state passage (transit) events. Applying this representation to a long MD simulation trajectory that captured multiple folding and unfolding events of the GTT WW domain, a small protein often used as a model for the folding process, we identified three transition categories: Highway (faster), Meander (slower), and Ambiguous (intermediate). We developed data sonification and visualization tools to analyze hydrogen bond dynamics before, during, and after these transition events. By means of these tools, we were able to identify characteristic hydrogen bonding patterns associated with "Highway" versus "Meander" versus "Ambiguous" transitions and to design algorithms that can identify these same folding pathways and critical protein-water interactions directly from the data. Highly cooperative hydrogen bonding can either slow down or speed up transit. Furthermore, an analysis of protein-water hydrogen bond dynamics at the surface of WW domain shows an increase in hydrogen bond lifetime from folded to unfolded conformations with Ambiguous transitions as an outlier. In summary, hydrogen bond dynamics provide a direct window into the heterogeneity of transits, which can vary widely in duration (by a factor of 10) due to a complex energy landscape.