On Quality Thresholds for the Clustering of Molecular Structures

It has been recently
suggested that diametral (so-called quality)
similarity thresholds are superior to radial ones for the clustering
of molecular three-dimensional structures (González-Alemán
et al., 2020). The argument has been made for two clustering algorithms
available in various software packages for the analysis of molecular
structures from ensembles generated by computer simulations, attributed
to Daura et al. (1999) (radial threshold) and Heyer et al. (1999)
(diametral threshold). Here, we compare these two algorithms using
the root-mean-squared difference (rmsd) between the Cartesian coordinates
of selected atoms as pairwise similarity metric. We discuss formally
the relation between these two methods and illustrate their behavior
with two examples, a set of points in two dimensions and the coordinates
of the tau polypeptide along a trajectory extracted from a replica-exchange
molecular-dynamics simulation (Shea and Levine, 2016). We show that
the two methods produce equally sized clusters as long as adequate
choices are made for the respective thresholds. The real issue is
not whether the threshold is radial or diametral but how to choose
in either case a threshold value that is physically meaningful. We
will argue that, when clustering molecular structures with the rmsd
as a metric, the simplest best guess for a threshold is actually radial
in nature.