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.