Dynamic Invariants in Protein Folding Pathways Revealed by Tensor Analysis

Recent advances in molecular dynamics simulation technologies (e.g., Folding@Home, NAMD, Desmond/Anton) have, for the first time, enabled scientists to perform all-atom simulations over timescales relevant to protein folding. Unfortunately, the concomitant increase in the size of the resulting data sets presents a barrier to understanding the molecular basis of folding. In particular, long simulations make it harder to identify and characterize important microstates, and the collective conformational dynamics that influence and enable the transitions between them. We address these problems by introducing a novel tensor-based method for performing a spatio-temporal analysis of protein folding pathways. We applied our method to folding simulations of the villin head-piece generated by the Pande group using Folding@Home. Using our method, we were able to identify three regions in this protein that exhibit similar collective behaviors across multiple simulations. We were also able to identify cross-over points in these simulations leading to different conformational subspaces. Our results indicate that these three regions may act as folding units, and that the observed collective motions may represent important dynamic invariants in the folding process. Thus, our spatio-temporal analysis method shows promise as a means for obtaining novel insights into protein folding pathways.