# 4.2.6. Calculating path similarity — `MDAnalysis.analysis.psa`

- Author:
Sean Seyler

- Year:
2015

- Copyright:
GNU Public License v3

New in version 0.10.0.

The module contains code to calculate the geometric similarity of trajectories using path metrics such as the Hausdorff or Fréchet distances [Seyler2015]. The path metrics are functions of two paths and return a nonnegative number, i.e., a distance. Two paths are identical if their distance is zero, and large distances indicate dissimilarity. Each path metric is a function of the individual points (e.g., coordinate snapshots) that comprise each path and, loosely speaking, identify the two points, one per path of a pair of paths, where the paths deviate the most. The distance between these points of maximal deviation is measured by the root mean square deviation (RMSD), i.e., to compute structural similarity.

One typically computes the pairwise similarity for an ensemble of paths to produce a symmetric distance matrix, which can be clustered to, at a glance, identify patterns in the trajectory data. To properly analyze a path ensemble, one must select a suitable reference structure to which all paths (each conformer in each path) will be universally aligned using the rotations determined by the best-fit rmsds. Distances between paths and their structures are then computed directly with no further alignment. This pre-processing step is necessary to preserve the metric properties of the Hausdorff and Fréchet metrics; using the best-fit rmsd on a pairwise basis does not generally preserve the triangle inequality.

Note

The PSAnalysisTutorial outlines a typical application of PSA to a set of trajectories, including doing proper alignment, performing distance comparisons, and generating heat map-dendrogram plots from hierarchical clustering.

References

Sean L. Seyler, Avishek Kumar, M. F. Thorpe, and Oliver Beckstein. Path similarity analysis: a method for quantifying macromolecular pathways. *PLOS Computational Biology*, 11(10):1–37, 10 2015. doi:10.1371/journal.pcbi.1004568.