Proteins such as molecular motors or active membrane transporters function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. Because such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. We developed the Path Similarity Analysis (PSA) approach [1] to alleviate these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space without having to rely on low-dimensional projections on collective variables. PSA employs the Hausdorff or Fréchet path (distance) metrics adopted from computational geometry to quantify path (dis)similarity. These metrics induce a map ("Hausdorff/Fréchet pairs") between conformations of different pathways that enable the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of hundreds of paths, including collections of transition ensembles. We applied PSA to compare conformational transitions of the substrate-free form of the enzyme adenylate kinase (AdK), generated by twelve fast computational path sampling methods, which included elastic network based approaches, dynamic importance sampling molecular dynamics (DIMS-MD), targeted MD (TMD), and a purely geometrical targeting algorithm (FRODA). Multiple observations indicate that in general paths generated by the methods studied here occupy different, non-overlapping regions of path space. Nevertheless, some notable exceptions occur, for instance, when the geometry-based FRODA method infrequently samples regions covered by force-field-based DIMS-MD or when tuning the pulling speed of the restraint in TMD can create paths that are either similar to naive linear interpolation or close to DIMS-MD. A Hausdorff pairs analysis of these ensembles revealed that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. PSA also enabled the quantitative comparison of transitions sampled with brute-force MD to those generated with path sampling algorithms, paving the way for assessing the quality of these methods.<br/><br/>[1] Seyler, Kumar, Thorpe, Beckstein. PLoS Comput Biol (2015), doi:10.1371/journal.pcbi.1004568

Quantitative comparison of macromolecular pathways

251st National Meeting (2016)

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