Distribution of reciprocal of interatomic distances: A fast structural metric

We present a structural metric based on the Distribution of Reciprocal of Interatomic Distances (DRID) for evaluating geometrical similarity between two conformations of a molecule. A molecular conformation is described by a vector of 3N orientation-independent DRID descriptors where N is the number of molecular centroids, for example, the non-hydrogen atoms in all nonsymmetric groups of a peptide. For two real-world applications (pairwise comparison of snapshots from an explicit solvent simulation of a protease/peptide substrate complex and implicit solvent simulations of reversible folding of a 20-residue β-sheet peptide), the DRID-based metric is shown to be about 5 and 15 times faster than coordinate root-mean-square deviation (cRMSD) and distance root-mean-square deviation (dRMSD), respectively. A single core of a mainstream processor can perform about 108 DRID comparisons in one-half a minute. Importantly, the DRID metric has closer similarity to kinetic distance than does either cRMSD or dRMSD. Therefore, DRID is suitable for clustering molecular dynamics trajectories for kinetic analysis, for example, by Markov state models. Moreover, conformational space networks and free energy profiles derived by DRID-based clustering preserve the kinetic information.